On the Connexion of the Physical Sciences (part 3 of 4)

On the Connexion of the Physical Sciences (part 3 of 4)

By far the greater number of the known species of plants are indigenous in equinoctial America; Europe contains about half the number; Asia, with its islands, somewhat less than Europe; Australia, with the islands in the Pacific, still less; and in Africa there are fewer known vegetable productions than in any part of the globe of equal extent, for that rich and luxuriant region discovered by Dr. Livingstone has yet to be explored botanically. Very few social plants, such as grasses and heaths that cover large tracts of land, are to be found between the tropics, except on the sea-coasts and elevated plains. Some exceptions to this, however, are to be met with in the jungles of the Deccan, &c. In the equatorial regions, where the heat is always great, the distribution of plants depends upon the mean annual temperature; whereas in temperate zones the distribution is regulated in some degree by the summer heat. Some plants require a gentle heat of long continuance, others flourish most where the extremes of heat and cold are greater. The range of wheat is very great; it may be cultivated as far north as the 60th degree of latitude; but in the torrid zone it will seldom form an ear below an elevation of 4500 feet above the level of the sea from exuberance of vegetation; nor will it ripen generally above the height of 12,000 feet; in Tibet it ripens at a still greater elevation. Colonel Sykes states that in the Deccan wheat thrives as low as 1800 feet above the sea. The best wines are produced between the 30th and 45th degrees of north latitude. With regard to the vegetable kingdom, elevation is equivalent to latitude as far as temperature is concerned. In ascending the mountains of the torrid zone, the richness of the tropical vegetation diminishes with the height; a succession of plants similar to, though not identical with, those found in latitudes of corresponding mean temperature takes place; the lofty forests by degrees lose their splendour; stunted shrubs succeed; till at last the progress of the lichen is checked by perpetual snow. On the volcano of Teneriffe there are five successive zones, each producing distinct families of plants. The first is the region of vines, the next that of laurels; these are followed by the region of pines, of Ericas or heaths, of grass; the whole covering the declivity of the peak through an extent of 11,200 feet of perpendicular height.

Near the equator oaks flourish at the height of 9200 feet above the sea; and, on the lofty range of the Himalaya, the primula, the convallaria, and the veronica flower, but not the primrose, the lily of the valley, or the veronica, which adorn our meadows; for, although the herbarium collected by Moorcroft, on his route from Neetee to Daba and Gartope in Chinese Tartary, at elevations as high or even higher than Mont Blanc, abound in Alpine and European genera, the species are universally different, with the single exception of the Rhodiola rosea, which is identical with the species that blooms in Scotland. It is not in this instance alone that similarity of climate obtains without identity of productions; throughout the whole globe a certain analogy both of structure and appearance is frequently discovered between plants under corresponding circumstances which are yet specifically different. It is even said that a difference of 25° of latitude occasions a total change, not only of vegetable productions, but of organised beings. Certain it is that each separate region both of land and water, from the frozen shores of the polar circles to the burning regions of the torrid zone, possesses a flora peculiarly its own. The whole globe has been divided by physical geographers into various botanical districts, differing almost entirely in their specific vegetable productions, the limits of which are most decided when they are separated by a wide expanse of ocean, mountain chains, sandy deserts, salt plains, or internal seas. A considerable number of plants are common to the northern regions of Asia, Europe, and America, where the continents almost unite; but, in approaching the south, the floras of these three great divisions of the globe differ more and more even in the same parallels of latitude, which shows that temperature alone is not the cause of the almost complete diversity of species that everywhere prevails. The floras of China, Siberia, Tartary, of the European district including central Europe and the coast of the Mediterranean, and the Oriental region comprising the countries round the Black and Caspian Seas, all differ in specific character. Only twenty-four species were found by MM. Humboldt and Bonpland in Equinoctial America identical with those of the Old World; and Dr. Robert Brown not only found that a peculiar vegetation exists in Australia between the 33rd and 35th parallels of south latitude, but that at the eastern and western extremities of these parallels not one species is common to both, and that certain genera also are almost entirely confined to these spots. The number of species common to Australia and Europe are only 166 out of 4100, and probably some of these have been conveyed thither by the colonists; but the greater part of that continent is still unexplored. However, this proportion exceeds what has hitherto been observed in southern Africa, and, from what has been already stated, the proportion of European species in Equinoctial America is still less.

Islands partake of the vegetation of the nearest continents; but, when very remote from land, their floras are altogether peculiar. The Aleutian Islands, extending between Asia and America, partake of the vegetation of the northern parts of both continents, and may have served as a chain of communication. In Madeira and Teneriffe, the plants of Portugal, Spain, the Azores, and of the northern coast of Africa, are found; and the Canaries contain a great number of plants belonging to the African coast. But each of these islands possesses a flora that exists nowhere else; and St. Helena, standing alone in the midst of the Atlantic Ocean, produces only two or three species of plants recognised as belonging to any other part of the world.

It appears from the investigations of M. de Humboldt that between the tropics the plants, such as grasses and palms, which have only one seed-lobe, are to the tribe which have two seed-lobes, like most of the European species, in the proportion of one to four; in the temperate zones they are as one to six; and in the Arctic regions, where mosses and lichens, which form the lowest order of the vegetable creation, abound, the proportion is as one to two. Annuals with one and two seed-lobes, in the temperate zones, amount to one-sixth of the whole, omitting the cryptogamia (N. 218); in the torrid zone they scarcely form one-twentieth, and in Lapland one-thirtieth part. In approaching the equator the ligneous exceed the number of herbaceous plants; in America there are 120 different species of forest trees, whereas in the same latitudes in Europe only 34 are to be found.

Similar laws regulate the distribution of marine plants. Groups of algæ, or marine plants, affect particular temperatures or zones of latitude and different depths, though some few genera prevail throughout the ocean. The polar Atlantic basin to the 40th degree of north latitude presents a well-defined vegetation. The West India seas, including the Gulf of Mexico, the eastern coast of South America, the Indian Ocean and its gulfs, the shores of New Holland, and the neighbouring islands, have each their distinct species. The Mediterranean possesses a vegetation peculiar to itself, extending to the Black Sea; and the species of marine plants on the coast of Syria and in the port of Alexandria differ almost entirely from those of Suez and the Red Sea. It is observed that shallow seas have a different set of plants from such as are deeper and colder; and, unlike terrestrial vegetation, the algæ are more numerous in the mean latitudes than either towards the equator or the poles. They vary also with the depth: completely different kinds affect different depths, their seeds being of such specific gravity as to remain and germinate where the parent plant grew. The quantity of algæ in that accumulation known as the sargassa or grassy sea is so great, that the early navigators, Columbus and Lerius, compared it to extensively inundated meadows: it impeded their ships, and alarmed their sailors. It is in the North Atlantic, a little to the west of the meridian of Fayal, one of the Azores, between the 25th and 36th parallels of latitude. A smaller bank lies between the 22nd and 26th degrees of north latitude, about 80 leagues west of the meridian of the Bahama Islands. These masses chiefly consist of one or two species of sargassa, the most extensive genus of the order Fucoideæ.

Some of the seaweeds grow to enormous lengths, and all are highly coloured, though many of them must grow in deep water. Light, however, may not be the only principle on which the colour of vegetables depends, since Baron Humboldt met with green plants growing in complete darkness in one of the mines at Freyberg.

In the dark and tranquil caves of the ocean, on the shores alternately covered and deserted by the restless waves, on the lofty mountain and extended plain, in the chilly regions of the north, and in the genial warmth of the south, specific diversity is a general law of the vegetable kingdom, which cannot be accounted for by diversity of climate; and yet the similarity, though not identity, of species is such, under the same isothermal lines, that if the number of species belonging to one of the great families of plants be known in any part of the globe, the whole number of the flowering or more perfect plants, and also the number of species composing the other vegetable families, may be estimated with considerable accuracy.

Various opinions have been formed on the original or primitive distribution of plants over the face of the globe; but, since botanical geography has become a science, the phenomena observed have led to the conclusion that vegetable creation must have taken place in a number of distinctly different centres, as the islands and continents rose above the ocean, each of which was the original seat of a certain number of peculiar species which at first grew there and nowhere else. Heaths are exclusively confined to the Old World; and no indigenous rose-tree has ever been seen in the New, the whole southern hemisphere being destitute of that beautiful and fragrant plant. But this is still more confirmed by multitudes of particular plants, having an entirely local and insulated existence, growing spontaneously in some particular spot, and in no other place: for example, the cedar of Lebanon, which grows indigenously on that mountain, and in no other part of the world. On the other hand, as there can be no doubt that many races of plants have been extinguished, Sir John Herschel thinks it possible that these solitary instances may be the last surviving remnants of the same group universally disseminated, but in course of extinction, or that perhaps two processes may be going on at the same time:—“Some groups may be spreading from their foci, others retreating to their last holds.”

The same laws obtain in the distribution of the animal creation. Even the microscopic existences, which seem to be the most widely spread, have their specific localities; and the zoophyte (N. 219), occupying the next lowest place in animated nature, is widely scattered through the seas of the torrid zone, each species being confined to the district and depth best suited to its wants. Mollusks, or the animals of shells, decrease in size and beauty with their distance from the equator; and not only each sea and every basin of the ocean, but each depth, is inhabited by its peculiar tribe of fish. Indeed, MM. Peron and Le Sueur assert that, among the many thousands of marine animals which they had examined, there is not a single animal of the southern regions which is not distinguishable by essential characters from the analogous species in the northern seas.

Reptiles are not exempt from the general law. The saurian (N. 220) tribes of the four quarters of the globe differ in species; and, although warm countries abound in venomous snakes, they are specifically different in different localities, and decrease both in numbers and in the virulence of their poison with decrease of temperature. The dispersion of insects necessarily follows that of the vegetables which supply their food; and in general it is observed that each kind of plant is peopled by its peculiar inhabitants. Each species of bird has its peculiar haunt, notwithstanding the locomotive powers of the winged tribes. The emu is confined to Australia, the condor to the Andes and their declivities, and the bearded vulture or lemmergeyer to the Alps. Some birds, like the common sparrow, have a wide range; but those met with in every country are few in number. Quadrupeds are distributed in the same manner wherever man has not interfered. Such as are indigenous in one country are not the same with their congeners in another; and, with the exception of some kind of bats, no mammiferous animal is indigenous in the Polynesian Archipelago, nor in any of the islands on the borders of the central part of the Pacific.

In reviewing the infinite variety of organised beings that people the surface of the globe, nothing is more remarkable than the distinctions which characterise the different tribes of mankind, from the ebony skin of the torrid zone to the fair and ruddy complexion of the Scandinavian—a difference which existed in the earliest recorded times, since the African is represented in the sacred writings to have been as black as he is at the present day, and the most ancient Egyptian paintings confirm that truth; yet it appears, from a comparison of the principal circumstances relating to the animal economy or physical character of the various tribes of mankind, that the different races are identical in species. Many attempts have been made to trace the various tribes back to a common origin, by collating the numerous languages which are or have been spoken. Some classes of these have few or no words in common, yet exhibit a remarkable analogy in the laws of their grammatical construction. The languages spoken by the native American nations afford examples of these; indeed, the refinement in the grammatical construction of the tongues of the American savages leads to the belief that they must originally have been spoken by a much more civilised class of mankind. Some tongues have little or no resemblance in structure, though they correspond extensively in their vocabularies, as the Syrian dialects. In all these cases it may be inferred that the nations speaking the languages in question descended from the same stock; but the probability of a common origin is much greater in the Indo-European nations, whose languages, such as the Sanscrit, Greek, Latin, German, &c., have an affinity both in structure and correspondence of vocables. In many tongues not the smallest resemblance can be traced; length of time, however, may have obliterated original identity; but so many ages have passed before the subject became a study, and so many languages have worn out of use, that it may be doubted whether any satisfactory result will ever be arrived at with regard to the original speech of mankind.

SECTION XXVII.

Terrestrial Heat—Radiation—Transmission—Melloni’s experiments—Heat in Solar Spectrum—Polarization of Heat—Nature of Heat—Absorptions—Dew—Rain—Combustion—Expansion—Compensation Pendulum—Transmission through Crystals—Propagation—Dynamic Theory of Heat—Mechanical equivalent of Heat—Latent Heat is the Force of Expansion—Steam—Work performed by Heat—Conservation of Force—Mechanical Power in the Tides—Dynamical Power of Light—Analogy between Light, Heat, and Sound.

THAT heat producing rays exist independently of those of light is a matter of constant experience in the abundant emission of them from boiling water. They dart in divergent straight lines from flame and from each point in the surfaces of hot bodies, in the same manner as diverging rays of light proceed from every point of those that are luminous. According to the experiments of Sir John Leslie, radiation proceeds not only from the surface of substances, but also from the particles at a minute depth below it. He found that the emission is most abundant in a direction perpendicular to the radiating surface, and that it is more rapid from a rough than from a polished surface: radiation, however, can only take place in air and in vacuo; it is altogether imperceptible when the hot body is enclosed in a solid or liquid. Heated substances, when exposed to the open air, continue to radiate heat till they become nearly of the temperature of the surrounding medium. The radiation is very rapid at first, but diminishes according to a known law with the temperature of the heated body. It appears, also, that the radiating power of a surface is inversely as its reflecting power; and bodies that are most impermeable to heat radiate least. Substances, however, have an elective power, only reflecting heat of a certain refrangibility. Mr. Grove gives paper, snow, and lime as instances, which, although all white, radiate heat of different refrangibilities, while metals, whatever their colour may be, radiate all kinds alike.

Rays of heat, whether they proceed from the sun, from flame, or other terrestrial sources, luminous or non-luminous, are instantaneously transmitted through solid and liquid substances, there being no appreciable difference in the time they take to pass through layers of any nature or thickness whatever. They pass also with the same facility whether the media be agitated or at rest; and in these respects the analogy between light and heat is perfect. Radiant heat passes through the gases with the same facility as light; but a remarkable difference obtains in the transmission of light and heat through most solid and liquid substances, the same body being often perfectly permeable to the luminous, and altogether impermeable to the calorific rays. For example, thin and perfectly transparent plates of alum and citric acid sensibly transmit all the rays of light from an argand lamp, but stop eight or nine tenths of the concomitant heat; whilst a large piece of brown rock-crystal gives a free passage to the radiant heat, but intercepts almost all the light. Alum united to green glass is also capable of transmitting the brightest light, but it gives not the slightest indication of heat; while rock-salt covered thickly over with soot, so as to be perfectly opaque to light, transmits a considerable quantity of heat. M. Melloni has established the general law in uncrystallized substances such as glass and liquids, that the property of instantaneously transmitting heat is in proportion to their refractive powers. The law, however, is entirely at fault in bodies of a crystalline texture. Carbonate of lead, for instance, which is colourless, and possesses a very high refractive power with regard to light, transmits less radiant heat than Iceland spar or rock-crystal, which are very inferior to it in the order of refrangibility; whilst rock-salt, which has the same transparency and refractive power with alum and citric acid, transmits six or eight times as much heat. This remarkable difference in the transmissive power of substances having the same appearance is attributed by M. Melloni to their crystalline form, and not to the chemical composition of their molecules, as the following experiments prove. A block of common salt cut into plates entirely excludes calorific radiation; yet, when dissolved in water, it increases the transmissive power of that liquid: moreover, the transmissive power of water is increased in nearly the same degree, whether salt or alum be dissolved in it; yet these two substances transmit very different quantities of heat in their solid state. Notwithstanding the influence of crystallization on the transmissive power of bodies, no relation has been traced between that power and the crystalline form.

The transmission of radiant heat is analogous to that of light through coloured media. When common white light passes through a red liquid, almost all the more refrangible rays, and a few of the red, are intercepted by the first layer of the fluid; fewer are intercepted by the second, still less by the third, and so on: till at last the losses become very small and invariable, and those rays alone are transmitted which give the red colour to the liquid. In a similar manner, when plates of the same thickness of any substance, such as glass, are exposed to an argand lamp, a considerable portion of the radiant heat is arrested by the first plate, a less portion by the second, still less by the third, and so on, the quantity of lost heat decreasing till at last the loss becomes a constant quantity. The transmission of radiant heat through a solid mass follows the same law. The losses are very considerable on first entering it, but they rapidly diminish in proportion as the heat penetrates deeper, and become constant at a certain depth. Indeed, the only difference between the transmission of radiant heat through a solid mass, or through the same mass when cut into plates of equal thickness, arises from the small quantity of heat that is reflected at the surface of the plates. It is evident, therefore, that the heat gradually lost is not intercepted at the surface, but absorbed in the interior of the substance, and that heat which has passed through one stratum of air experiences a less absorption in each of the succeeding strata, and may therefore be propagated to a greater distance before it is extinguished. The experiments of M. de Laroche show that glass, however thin, totally intercepts the obscure rays of heat when they flow from a body whose temperature is lower than that of boiling water; that, as the temperature increases, the calorific rays are transmitted more and more abundantly; and, when the body becomes highly luminous, that they penetrate the glass with perfect ease. The extreme brilliancy of the sun is probably the reason why his heat, when brought to a focus by a lens, is more intense than any that has been produced artificially. It is owing to the same cause that glass screens, which entirely exclude the heat of a common fire, are permeable by the solar heat.

The results obtained by M. de Laroche have been confirmed by the experiments of M. Melloni on heat radiated from sources of different temperatures, whence it appears that the calorific rays pass less abundantly not only through glass, but through rock-crystal, Iceland spar, and other diaphanous bodies, both solid and liquid, according as the temperature of their origin is diminished, and that they are altogether intercepted when the temperature is about that of boiling water.

In fact, he has proved that the heat emanating from the sun or from a bright flame consists of rays which differ from each other as much as the coloured rays do which constitute white light. This explains the reason of the loss of heat as it penetrates deeper and deeper into a solid mass, or in passing through a series of plates; for, of the different kinds of rays which dart from a vivid flame, all are successively extinguished by the absorbing nature of the substance through which they pass, till those homogeneous rays alone remain which have the greatest facility in passing through that particular substance; exactly as in a red liquid the violet, blue, green, orange, and yellow rays are extinguished, and the red are transmitted.

M. Melloni employed four sources of heat, two of which were luminous and two obscure; namely, an oil-lamp without a glass, incandescent platina, copper heated to 696°, and a copper vessel filled with water at the temperature of 178-1/2° of Fahrenheit. Rock-salt transmitted heat in the proportion of 92 rays out of 100 from each of these sources; but all other substances pervious to radiant heat, whether solid or liquid, transmitted more heat from sources of high temperature than from such as are low. For instance, limpid and colourless fluate of lime transmitted in the proportion of 78 rays out of 100 from the lamp, 69 from the platina, 42 from the copper, and 33 from the hot water; while transparent rock-crystal transmitted 38 rays in 100 from the lamp, 28 from the platina, 6 from the copper, and 9 from the hot water. Pure ice transmitted only in the proportion of 6 rays in the 100 from the lamp, and entirely excluded those from the other three sources. Out of 39 different substances, 34 were pervious to the calorific rays from hot water, 14 excluded those from the hot copper, and 4 did not transmit those from the platinum.

Thus it appears that heat proceeding from these four sources is of different kinds: this difference in the nature of the calorific rays is also proved by another experiment, which will be more easily understood from the analogy of light. Red light, emanating from red glass, will pass in abundance through another piece of red glass, but it will be absorbed by green glass; green rays will more readily pass through a green medium than through one of any other colour. This holds with regard to all colours; so in heat. Rays of heat of the same intensity, which have passed through different substances, are transmitted in different quantities by the same piece of alum, and are sometimes stopped altogether; showing that rays which emanate from different substances possess different qualities. It appears that a bright flame furnishes rays of heat of all kinds, in the same manner as it gives light of all colours; and, as coloured media transmit some coloured rays and absorb the rest, so bodies transmit some rays of heat and exclude the others. Rock-salt alone resembles colourless transparent media in transmitting all kinds of heat, even that of the hand, just as they transmit white light, consisting of rays of all colours. Radiant heat is unequally refracted by a prism of rock-salt like light, and the rays of heat thus dispersed are found to possess properties analogous to the rays of the coloured spectrum.

The property of transmitting the calorific rays diminishes to a certain degree with the thickness of the body they have to traverse, but not so much as might be expected. A piece of very transparent alum transmitted three or four times less radiant heat from the flame of a lamp than a piece of nearly opaque quartz about a hundred times as thick. However, the influence of thickness upon the phenomena of transmission increases with the decrease of temperature in the origin of the rays, and becomes very great when that temperature is low. This is a circumstance intimately connected with the law established by M. de Laroche; for M. Melloni observed that the difference between the quantities of heat transmitted by the same plate of glass, exposed successively to several sources of heat, diminished with the thinness of the plate, and vanished altogether at a certain limit; and that a film of mica transmitted the same quantity of heat, whether it was exposed to incandescent platinum or to a mass of iron heated to 360°.

Coloured glasses transmit rays of light of certain degrees of refrangibility, and absorb those of other degrees. For example, red glass absorbs the more refrangible rays, and transmits the red, which are the least refrangible. On the contrary, violet glass absorbs the least refrangible, and transmits the violet, which are the most refrangible. Now M. Melloni has found, that, although the colouring matter of glass diminishes its power of transmitting heat, yet red, orange, yellow, blue, violet, and white glass transmit calorific rays of all degrees of refrangibility; whereas green glass possesses the peculiar property of transmitting the least refrangible calorific rays, and stopping those that are most refrangible. It has therefore the same elective action for heat that coloured glass has for light, and its action on heat is analogous to that of red glass on light. Alum and sulphate of lime are exactly opposed to green glass in their action on heat, by transmitting the most refrangible rays with the greatest facility.

The heat which has already passed through green or opaque black glass will not pass through alum, whilst that which has been transmitted through glasses of other colours traverses it readily.

By reversing the experiment, and exposing different substances to heat that had already passed through alum, M. Melloni found that the heat emerging from alum is almost totally intercepted by opaque substances, and is abundantly transmitted by all such as are transparent and colourless, and that it suffers no appreciable loss when the thickness of the plate is varied within certain limits. The properties of the heat therefore which issues from alum nearly approach to those of light and solar heat.

Radiant heat in traversing various media is not only rendered more or less capable of being transmitted a second time, but, according to the experiments of Professor Powell, it becomes more or less susceptible of being absorbed in different quantities by black or white surfaces.

M. Melloni has proved that solar heat contains rays which are affected by different substances in the same way as if the heat proceeded from a terrestrial source; whence he concludes that the difference observed between the transmission of terrestrial and solar heat arises from the circumstance of solar heat containing all kinds of heat, whilst in other sources some of the kinds are wanting.

Radiant heat, from sources of any temperature whatever, is subject to the same laws of reflection and refraction as rays of light. The index of refraction from a prism of rock-salt, determined experimentally, is nearly the same for light and heat.

Liquids, the various kinds of glass, and probably all substances, whether solid or liquid, that do not crystallize regularly, are more pervious to the calorific rays according as they possess a greater refractive power. For example, the chloride of sulphur, which has a high refractive power, transmits more of the calorific rays than the oils, which have a less refractive power: oils transmit more radiant heat than the acids; the acids more than aqueous solutions; and the latter more than pure water, which of all the series has the least refractive power, and is the least pervious to heat. M. Melloni observed also that each ray of the solar spectrum follows the same law of action with that of terrestrial rays having their origin in sources of different temperatures; so that the very refrangible rays may be compared to the heat emanating from a focus of high temperature, and the least refrangible to the heat which comes from a source of low temperature. Thus, if the calorific rays emerging from a prism be made to pass through a layer of water contained between two plates of glass, it will be found that these rays suffer a loss in passing through the liquid as much greater as their refrangibility is less. The rays of heat that are mixed with the blue or violet light pass in great abundance, while those in the obscure part which follows the red light are almost totally intercepted. The first, therefore, act like the heat of a lamp, and the last like that of boiling water.

These circumstances explain the phenomena observed by several philosophers with regard to the point of greatest heat in the solar spectrum, which varies with the substance of the prism. Sir William Herschel, who employed a prism of flint glass, found that point to be a little beyond the red extremity of the spectrum; but, according to M. Seebeck, it is found to be upon the yellow, upon the orange, on the red, or at the dark limit of the red, according as the prism consists of water, sulphuric acid, crown or flint glass. If it be recollected that, in the spectrum from crown glass, the maximum heat is in the red part, and that the solar rays, in traversing a mass of water, suffer losses inversely as their refrangibility, it will be easy to understand the reason of the phenomenon in question. The solar heat which comes to the anterior face of the prism of water consists of rays of all degrees of refrangibility. Now, the rays possessing the same index of refraction with the red light suffer a greater loss in passing through the prism than the rays possessing the refrangibility of the orange light, and the latter lose less in their passage than the heat of the yellow. Thus the losses, being inversely proportional to the degree of refrangibility of each ray, cause the point of maximum heat to tend from the red towards the violet, and therefore it rests upon the yellow part. The prism of sulphuric acid, acting similarly, but with less energy than that of water, throws the point of greatest heat on the orange; for the same reason, the crown and flint glass prisms transfer that point respectively to the red and to its limit. M. Melloni, observing that the maximum point of heat is transferred farther and farther towards the red end of the spectrum, according as the substance of the prism is more and more permeable to heat, inferred that a prism of rock-salt, which possesses a greater power of transmitting the calorific rays than any known body, ought to throw the point of greatest heat to a considerable distance beyond the visible part of the spectrum,—an anticipation which experiment fully confirmed, by placing it as much beyond the dark limits of the red rays as the red part is distant from the blueish green band of the spectrum.

In all these experiments M. Melloni employed a thermomultiplier,—an instrument that measures the intensity of the transmitted heat with an accuracy far beyond what any thermometer ever attained. It is a very elegant application of M. Seebeck’s discovery of thermo-electricity; but the description of this instrument is reserved for a future occasion, because the principle on which it is constructed has not yet been explained.

In the beginning of the present century, not long after M. Malus had discovered the polarization of light, he and M. Berard proved that the heat which accompanies the sun’s light is capable of being polarized; but their attempts totally failed with heat derived from terrestrial, and especially from non-luminous sources. M. Berard, indeed, imagined that he had succeeded; but, when his experiments were repeated by Mr. Lloyd and Professor Powell, no satisfactory result could be obtained. M. Melloni resumed the subject, and endeavoured to effect the polarization of heat by tourmaline, as in the case of light. It was already shown that two slices of tourmaline, cut parallel to the axis of the crystal, transmit a great portion of the incident light when looked through with their axes parallel, and almost entirely exclude it when they are perpendicular to one another. Should radiant heat be capable of polarization, the quantity transmitted by the slices of tourmaline in their former position ought greatly to exceed that which passes through them in the latter, yet M. Melloni found that the quantity of heat was the same in both cases: whence he inferred that heat from a terrestrial source is incapable of being polarized. Professor Forbes of Edinburgh, who prosecuted this subject with great acuteness and success, came to the same conclusion in the first instance; but it occurred to him, that, as the pieces of tourmaline became heated by being very near the lamp, the secondary radiation from them rendered the very small difference in the heat that was transmitted in the two positions of the pieces of tourmaline imperceptible. Nevertheless he succeeded in proving, by numerous observations, that heat from various sources is polarized by the tourmaline; but that the effect with non-luminous heat is very minute and difficult to perceive, on account of the secondary radiation. Though light is almost entirely excluded in one position of the pieces of tourmaline, and transmitted in the other, a vast quantity of radiant heat passes through them in all positions. Eighty-four per cent. of the heat from an argand lamp passed through them in the case where light was altogether stopped. It is only the difference in the quantity of transmitted heat that gives evidence of its polarization. The second slice of tourmaline, when perpendicular to the first, stops all the light, but transmits a great proportion of heat; alum, on the contrary, stops almost all the heat, and transmits the light; whence it may be concluded that heat, though intimately partaking the nature of light, and accompanying it under certain circumstances, as in reflection and refraction, is capable of almost complete separation from it under others. The separation has since been perfectly effected by M. Melloni, by passing a beam of light through a combination of water and green glass, coloured by the oxide of copper. Even when the transmitted light was concentrated by lenses, so as to render it almost as brilliant as the direct light of the sun, it showed no sensible heat.

Professor Forbes next employed two bundles of laminæ of mica, placed at the polarizing angle, and so cut that the plane of incidence of the heat corresponded with one of the optic axes of this mineral. The heat transmitted through this apparatus was polarized from a source whose temperature was even as low as 200°; heat was also polarized by reflection; but the experiments, though perfectly successful, are more difficult to conduct.

It appears, from the various experiments of M. Melloni and Professor Forbes, that all the calorific rays emanating from the sun and terrestrial sources are equally capable of being polarized by reflection and by refraction, whether double or single, and that they are also capable of circular polarization by all the methods employed in the circular polarization of light. Plates of quartz cut at right angles to the axis of the prism possess the property of turning the calorific rays in one direction, while other plates of the same substance from a differently modified prism cause the rays to rotate in the contrary direction; and two plates combined, when of different affection, and of equal thickness, counteract each other’s effects as in the case of light. Tourmaline separates the heat into two parts, one of which it absorbs, while it transmits the other; in short, the transmission of radiant heat is precisely similar to that of light.

Since heat is polarized in the same manner as light, it may be expected that polarized heat transmitted through doubly refracting substances should be separated into two pencils, polarized in planes at right angles to each other; and that when received on an analyzing plate they should interfere and produce invisible phenomena, perfectly analogous to those described in Section XXII. with regard to light (N. 221).

It was shown, in the same section, that if light polarized by reflection from a pane of glass be viewed through a plate of tourmaline, with its longitudinal section vertical, an obscure cloud, with its centre wholly dark, is seen on the glass. When, however, a plate of mica uniformly about the thirteenth of an inch in thickness is interposed between the tourmaline and the glass, the dark spot vanishes, and a succession of very splendid colours are seen; and, as the mica is turned round in a plane perpendicular to the polarized ray, the light is stopped when the plane containing the optic axis of the mica is parallel or perpendicular to the plane of polarization. Now, instead of light, if heat from a non-luminous source be polarized in the manner described, it ought to be transmitted and stopped by the interposed mica under the same circumstances under which polarized light would be transmitted or stopped. Professor Forbes found that this is really the case, whether he employed heat from luminous or non-luminous sources: and he had evidence, also, of circular and elliptical polarization of heat. It therefore follows, that if heat were visible, under similar circumstances we should see figures perfectly similar to those given in Note 213, and those following; and, as these figures are formed by the interference of undulations of light, it may be inferred that heat, like light, is propagated by undulations of the ethereal medium, which interfere under certain conditions, and produce figures analogous to those of light. It appears also, from Mr. Forbes’s experiments, that the undulations of heat are longer than the undulations of light; and it has already been mentioned that Professor Draper considers them to be normal, like those of sound.

That light and heat are both vibrations of the ethereal medium is not the less true on account of the rays of heat being unseen, for the condition of visibility or invisibility may only depend upon the construction of our eyes, and not upon the nature of the motion which produces these sensations in us. The sense of seeing may be confined within certain limits. The chemical rays beyond the violet end of the spectrum may be too rapid, or not sufficiently excursive, in their vibrations, to be visible to the human eye; and the calorific rays beyond the other end of the spectrum may not be sufficiently rapid, or too extensive, in their undulations, to affect our optic nerves, though both may be visible to certain animals or insects. We are altogether ignorant of the perceptions which direct the carrier-pigeon to his home, or of those in the antennæ of insects which warn them of the approach of danger; nor can we understand the telescopic vision which directs the vulture to his prey before he himself is visible even as a speck in the heavens. So, likewise, beings may exist on earth, in the air, or in the waters, which hear sounds our ears are incapable of hearing, and which see rays of light and heat of which we are unconscious. Our perceptions and faculties are limited to a very small portion of that immense chain of existence which extends from the Creator to evanescence.

The identity of action under similar circumstances is one of the strongest arguments in favour of the common nature of the chemical, visible, and calorific rays. They are all capable of reflection from polished surfaces, of refraction through diaphanous substances, of polarization by reflection and by doubly refracting crystals; their velocity is prodigious; they may be concentrated and dispersed by convex and concave mirrors; they pass with equal facility through rock-salt and are capable of radiation; and they are subject to the same law of interference with those of light: hence there can be no doubt that the whole assemblage of rays visible and invisible which constitute a solar beam are propagated by the undulations of the ethereal medium, and consequently as motions they come under the same laws of analysis.

When radiant heat falls upon a surface, part of it is reflected and part of it is absorbed; consequently, the best reflectors possess the least absorbing powers. The temperature of very transparent fluids is not raised by the passage of the sun’s rays, because they do not absorb any of them; and, as his heat is very intense, transparent solids arrest a very small portion of it. The absorption of the sun’s rays is the cause both of the colour and temperature of solid bodies. A black substance absorbs all the rays of light, and reflects none; and since it absorbs, at the same time, all the calorific rays, it becomes sooner warm, and rises to a higher temperature, than bodies of any other colour. Blue bodies come next to black in their power of absorption. And, since substances of a blue tint absorb all the other colours of the spectrum, they absorb by far the greatest part of the calorific rays, and reflect the blue where they are least abundant. Next in order come the green, yellow, red, and, last of all, white bodies, which reflect nearly all the rays both of light and heat. However, there are certain limpid and colourless media, which in some cases intercept calorific radiations and become heated, while in other cases they transmit them and undergo no change of temperature.

All substances may be considered to radiate heat, whatever their temperature may be, though with different intensities, according to their nature, the state of their surfaces, and the temperature of the medium into which they are brought. But every surface absorbs as well as radiates heat; and the power of absorption is always equal to that of radiation; for, under the same circumstances, matter which becomes soon warm also cools rapidly. There is a constant tendency to an equal diffusion of heat, since every body in nature is giving and receiving it at the same instant; each will be of uniform temperature when the quantities of heat given and received during the same time are equal—that is, when a perfect compensation takes place between each and all the rest. Our sensations only measure comparative degrees of heat: when a body, such as ice, appears to be cold, it imparts fewer calorific rays than it receives; and when a substance seems to be warm—for example, a fire—it gives more heat than it takes. The phenomena of dew and hoar-frost are owing to this inequality of exchange; the heat radiated during the night by substances on the surface of the earth, into a clear expanse of sky, is lost to us, and no return is made from the blue vault, so that their temperature sinks below that of the air, whence they abstract a part of that heat which holds the atmospheric humidity in solution, and a deposition of dew takes place. If the radiation be great, the dew is frozen and becomes hoar-frost, which is the ice of dew. Cloudy weather is unfavourable to the formation of dew, by preventing the free radiation of heat; and actual contact is requisite for its deposition, since it is never suspended in the air like fog. Plants derive a great part of their nourishment from this source; and, as each possesses a power of radiation peculiar to itself, they are capable of procuring a sufficient supply for their wants. The action of the chemical rays imparts to all substances more or less the power of condensing vapour on those parts on which they fall, and must therefore have a considerable influence on the deposition of dew. There may be a low degree of humidity in the air which may yet contain a great quantity of aqueous vapour, for vapour while it exists as gas is dry. The temperature at which the atmosphere can contain no more vapour without precipitation is called the dew point, and is measured by the hygrometer. In foretelling the changes of weather it is scarcely inferior to the barometer.

Steam is formed throughout the whole mass of a boiling liquid, whereas evaporation takes place only at the free surface of liquids, and that under the ordinary temperature and pressure of the atmosphere. There is a constant evaporation from the land and water all over the earth. The rapidity of the formation does not depend altogether on the dryness of the air; according to Dr. Dalton’s experiments, it depends also on the difference between the tension of the vapour which is forming, and that which is already in the atmosphere. In calm weather vapour accumulates in the stratum of air immediately above the evaporating surface, and retards the formation of more; whereas a strong wind accelerates the process by carrying off the vapour as soon as it rises, and making way for a succeeding portion of dry air.

Rain is formed by the mixing of two masses of air of different temperatures; the colder part, by abstracting from the other the heat which holds it in solution, occasions the particles to approach each other and form drops of water, which, becoming too heavy to be sustained by the atmosphere, sink to the earth by gravitation in the form of rain. The contact of two strata of air of different temperatures, moving rapidly in opposite directions, occasions an abundant precipitation of rain. When the masses of air differ very much in temperature, and meet suddenly, hail is formed. This happens frequently in hot plains near a ridge of mountains, as in the south of France, from the sudden descent of an intensely cold current of wind into a mass of air nearly saturated with vapour. Such also is the cause of the severe hail-storms which occasionally take place on extensive plains within the tropics.

An accumulation of heat invariably produces light: with the exception of the gases, all bodies which can endure the requisite degree of heat without decomposition begin to emit light at the same temperature; but, when the quantity of heat is so great as to render the affinity of their component particles less than their affinity for the oxygen of the atmosphere, a chemical combination takes place with the oxygen, light and heat are evolved, and fire is produced. Combustion—so essential for our comfort, and even existence—takes place very easily from the small affinity between the component parts of atmospheric air, the oxygen being nearly in a free state; but, as the cohesive force of the particles of different substances is very variable, different degrees of heat are requisite to produce their combustion. The tendency of heat to a state of equal diffusion or equilibrium, either by radiation or contact, makes it necessary that the chemical combination which occasions combustion should take place instantaneously; for, if the heat were developed progressively, it would be dissipated by degrees, and would never accumulate sufficiently to produce a temperature high enough for the evolution of flame.

It is a general law that all bodies expand by heat and contract by cold. The expansive force of heat has a constant tendency to overcome the attraction of cohesion, and to separate the constituent particles of solids and fluids; by this separation the attraction of aggregation is more and more weakened, till at last it is entirely overcome, or even changed into repulsion. By the continual addition of heat, solids may be made to pass into liquids, and from liquids to the aëriform state, the dilatation increasing with the temperature; and every substance expands according to a law of its own. Gases expand more than liquids, and liquids more than solids. The expansion of air is more than eight times that of water, and the increase in the bulk of water is at least forty-five times greater than that of iron. Metals dilate uniformly from the freezing to the boiling points of the thermometer; the uniform expansion of the gases extends between still wider limits; but, as liquidity is a state of transition from the solid to the aëriform condition, the equable dilatation of liquids has not so extensive a range. This change of bulk, corresponding to the variation of heat, is one of the most important of its effects, since it furnishes the means of measuring relative temperature by the thermometer and pyrometer. The rate of expansion of solids varies at their transition to liquidity, and that of liquidity is no longer equable near their change to an aëriform state. There are exceptions, however, to the general laws of expansion; some liquids have a maximum density corresponding to a certain temperature, and dilate whether that temperature be increased or diminished. For example—water expands whether it be heated above or cooled below 40°. The solidification of some liquids, and especially their crystallization, is always accompanied by an increase of bulk. Water dilates rapidly when converted into ice, and with a force sufficient to split the hardest substances. The formation of ice is therefore a powerful agent in the disintegration and decomposition of rocks, operating as one of the most efficient causes of local changes in the structure of the crust of the earth; of which we have experience in the tremendous éboulemens of mountains in Switzerland. But Professor W. Thomson has proved experimentally that it requires a lower temperature to freeze water under pressure than when free.

The dilatation of substances by heat, and their contraction by cold, occasion such irregularities in the rate of clocks and watches as would render them unfit for astronomical or nautical purposes, were it not for a very beautiful application of the laws of unequal expansion. The oscillations of a pendulum are the same as if its whole mass were united in one dense particle, in a certain point of its length, called the centre of oscillation. If the distance of this point from the point by which the pendulum is suspended were invariable, the rate of the clock would be invariable also. The difficulty is to neutralize the effects of temperature, which is perpetually increasing or diminishing its length. Among many contrivances, Graham’s compensation pendulum is the most simple. He employed a glass tube containing mercury. When the tube expands from the effects of heat, the mercury expands much more; so that its surface rises a little more than the end of the pendulum is depressed, and the centre of oscillation remains stationary. Harrison invented a pendulum which consists of seven bars of steel and of brass, joined in the shape of a gridiron, in such a manner that, if by change of temperature the bars of brass raise the weight at the end of the pendulum, the bars of steel depress it as much. In general, only five bars are used; three being of steel, and two a mixture of silver and zinc. The effects of temperature are neutralized in chronometers upon the same principle; and to such perfection are they brought, that the loss or gain of one second in twenty-four hours for two days running would render one unfit for use. Accuracy in surveying depends upon the compensation rods employed in measuring bases. Thus, the laws of the unequal expansion of matter judiciously applied have an immediate influence upon our estimation of time; of the motions of bodies in the heavens, and of their fall upon the earth; on our determination of the figure of the globe, and on our system of weights and measures; on our commerce abroad, and the mensuration of our lands at home.

The expansion of the crystalline substances takes place under very different circumstances from the dilatation of such as are not crystallized. The latter become both longer and thicker by an accession of heat, whereas M. Mitscherlich has found that the former expand differently in different directions; and, in a particular instance, extension in one direction is accompanied by contraction in another: for example, Iceland spar is dilated in the direction of its axis of double refraction (N. 205), but at right angles to that axis it is contracted, which brings the crystal nearer to the form of the cube and diminishes its double refractive power. When heat is applied to crystals of sulphate of lime, the two optical axes (N. 207) gradually approach, and at last coincide; when the heat is increased, the axes open again, but in a direction at right angles to their former position. By experiment M. Senarmont has concluded, that in media constituted like crystals of the rhomboidal (N. 169) system the conducting power varies in such a manner, that, supposing a centre of heat to exist within them, and the medium to be indefinitely extended in all directions, the isothermal surfaces are concentric ellipsoids of revolution round the axes of symmetry, or at least surfaces differing but little from them. The internal structure of crystallized matter must be very peculiar thus to modify the expansive power of heat.

Heat applied to the surface of a fluid is propagated downwards very slowly, the warmer, and consequently lighter strata, always remaining at the top. This is the reason why the water at the bottom of lakes fed from Alpine chains is so cold; for the heat of the sun is transfused but a little way below the surface. When the heat is applied below a liquid, the particles continually rise as they become specifically lighter, and diffuse the heat through the mass, their place being perpetually supplied by those that are more dense. The power of conducting heat varies materially in different liquids. Mercury conducts twice as fast as an equal bulk of water, and therefore it appears to be very cold. A hot body diffuses its heat in the air by a double process: the air in contact with it becoming lighter ascends and scatters its heat by transmission, while at the same time another portion is discharged in straight lines by the radiating power of the surface. Hence a substance cools more rapidly in air than in vacuo, because in the latter case the process is carried on by radiation alone. It is probable that the earth having been originally of very high temperature has become cooler by radiation alone, the ethereal medium being too rare to carry off much heat by contact.

Heat is propagated with more or less rapidity through all bodies; air is the worst conductor, and consequently mitigates the severity of cold climates by preserving the heat imparted to the earth by the sun. On the contrary, dense bodies, especially metals, possess the power of conduction in the greatest degree, but the transmission requires time. If a bar of iron twenty inches long be heated at one extremity, the heat takes four minutes in passing to the other. The particle of the metal that is first heated communicates the heat to the second, and the second to the third: so that the temperature of the intermediate molecule at any instant is increased by the excess of the temperature of the first above its own, and diminished by the excess of its own temperature above that of the third. That however will not be the temperature indicated by the thermometer, because as soon as the particle is more heated than the surrounding atmosphere it loses its heat by radiation, in proportion to the excess of its actual temperature above that of the air. The velocity of the discharge is directly proportional to the temperature, and inversely as the length of the bar. As there are perpetual variations in the temperature of all terrestrial substances, and of the atmosphere, from the rotation of the earth, and its revolution round the sun, from combustion, friction, fermentation, electricity, and an infinity of other causes, the tendency to restore the equability of temperature by the transmission of heat must maintain all the particles of matter in a state of perpetual oscillation, which will be more or less rapid according to the conducting powers of the substances. From the motion of the heavenly bodies about their axes, and also round the sun, exposing them to perpetual changes of temperature, it may be inferred that similar causes will produce like effects in them too. The revolutions of the double stars show that they are not at rest; and although we are totally ignorant of the changes that may be going on in the nebulæ and millions of other remote bodies, it is hardly possible that they should be in absolute repose; so that, as far as our knowledge extends, motion is a law of the universe and the immediate cause of heat, as in the sunbeam so also in all terrestrial phenomena.

This is by no means hypothetical, but founded upon fact and experiment. Heat is produced by motion and is equivalent to it, for we measure heat by motion in the thermometer. The heat evolved by percussion is proportional to the force of the blow; by repeated blows iron becomes red hot; and the quantity of heat produced by friction, whether the matter be solid or fluid, is always in proportion to the force employed: in cold weather we rub our hands to make them warm, and the harder we rub the warmer they become. The warmth of the sea after a storm is in proportion to the force of the wind; and in Sir Humphry Davy’s experiment of melting ice by friction in the receiver of an air-pump kept at the freezing point, the heat which melted the ice was exactly proportional to the force of friction. This experiment proves the immateriality of heat, since the capacity of ice for heat is less than that of water. Thus mechanical action and heat are equivalent to one another. Mr. Joule of Manchester[13] has proved that the quantity of heat requisite to raise the temperature of a pound of water one degree of Fahrenheit’s thermometer, is equivalent to the mechanical force developed by the fall of a body weighing 772·69 pounds through the perpendicular height of one foot. This quantity is the mechanical equivalent of heat. Thus heat is motion, and it is measured by force. In fact, for every unit of force expended in friction or percussion, a definite quantity of heat is generated; and conversely, when work is performed by the consumption of heat, for each unit of force gained, a unit of heat disappears. For since heat is a dynamical force of mechanical effect, there must be an equivalent between mechanical work and heat as between cause and effect. (N. 222.)

Besides the temperature indicated by the thermometer, bodies absorb heat, and their capacity for heat is so various that very different quantities of heat are required to raise different substances to the same sensible temperature. It is evident, therefore, that much of the heat is absorbed and becomes insensible to the thermometer. That portion of heat requisite to raise a body to a given temperature is its specific heat, but the latent or absorbed heat is an expansive force or energy, which, acting upon the ether surrounding the ultimate particles of bodies, changes them from solid to liquid, and from liquid to vapour or gas. According to the law of absorption, the transfer of heat from a warm body to one that is cold is a mere transfer of force, in which the force of compression is exactly proportional to the force of expansion. Ice remains at the temperature of 32° Fahrenheit till it has absorbed 140° of heat, and then it melts, but without raising the temperature of the water above 32°. On the contrary, when a liquid is converted into a solid, a quantity of heat leaves it without any diminution of temperature. Thus water at 32° must part with 140° of heat before it freezes. The slowness with which water freezes or ice thaws, is a consequence of the time required for the ethereal atmospheres round the particles of the water to contract or expand with a force equivalent to 140° of heat. A considerable degree of cold is felt during a thaw, because the ice in its transition from a solid to a liquid state absorbs sensible heat from the atmosphere and surrounding objects. The heat absorbed and evolved by the rarefaction and condensation of air is exactly proportional to the force evolved and absorbed in these operations. In fact, the changes of temperature produced by these rarefactions and condensations of air show that the heat of elastic fluids is the mechanical force possessed by them; and since the temperature of a gas determines its elastic force, it follows that the elastic force or pressure must be the effect of the motion of the constituent particles in any gas. Sir Humphry Davy, who first demonstrated the immateriality of heat, assumed the hypothesis that the motion we call heat is a rotation or vibration among the particles of the fluid, which, according to Mr. Joule, agrees perfectly with the observed phenomena, but he prefers the more simple view of Mr. Herapath, that the elastic force or pressure is due to the impact of the particles against any surface presented to them. Absorbed or latent heat may be regarded as a quiescent energy ready to be restored to the form of sensible heat when called forth: its vibrations as heat are extinguished for the time by being transferred to the internal expansive force, and are restored by compression. The absorbed heat of air and all elastic fluids may be forced out by sudden compression like squeezing water out of a sponge. The quantity of heat brought into action in this way is well illustrated by the experiment of igniting tinder by the sudden compression of air by a piston thrust into a cylinder closed at one end. The development of heat on a stupendous scale is exhibited in lightning: it is proportional to the square of the quantity of electricity discharged, and is due to its excessive velocity and the violent compression of the air in its transit through the atmosphere. Prodigious quantities of heat are constantly absorbed or disengaged by the changes to which substances are liable in passing from the solid to the liquid and from the liquid to the gaseous form and the contrary, causing endless vicissitudes of temperature over the globe, and endless expansions and contractions, which are correlative terms for heat and cold, while radiation of heat is merely a transfer of motion from the particles on the surface of bodies to the adjacent particles of the atmosphere.

By the continual application of heat, that is of the expansive force, liquids are converted into steam or vapour, which is invisible and highly elastic. Under the mean pressure of the atmosphere, that is when the barometer stands at 30 inches, water in a boiler absorbs heat continually till it attains the temperature of the boiling point, which is 212° Fahrenheit. After that it ceases to show any increase of sensible heat; but when it has absorbed an additional 1000° of heat or expansive energy, that energy converts it into steam, and a condensing force equivalent to 1000° of heat reduces it again to water. Water boils at different temperatures under different degrees of pressure. It boils at a lower temperature on the top of a mountain than on the plain below, because the weight of the atmosphere is less at the higher station. There is no limit to the temperature to which water might be raised: it might even be made red hot, could a vessel be found strong enough to resist the pressure, for the intensity of the expansive force prevented from having effect by the extreme pressure of the boiler would be converted into sensible heat which might eventually render the water red hot. Thus, since the force of steam is in proportion to the temperature at which the water boils, or to the pressure, it is under control, and, perhaps with the exception of electricity, it is the greatest power that has been made subservient to the wants of man.

It is found that the absolute quantity of heat consumed in the process of converting water into steam is the same at whatever temperature water may boil, but that the absolute heat of the steam is greater exactly in proportion as its sensible heat is less. Thus, steam raised at 212° Fahrenheit under the mean pressure of the atmosphere, and steam raised at 180° under half the pressure, contain the same quantity of heat, with this difference, that the one has more absorbed heat and less sensible heat than the other. It is evident that, as the same quantity of heat is requisite for converting a given weight of water into steam, at whatever temperature or under whatever pressure the water may be boiled, therefore, in the steam engine, equal weights of steam at a high pressure and a low pressure are produced by the same quantity of fuel; and whatever the pressure of the steam may be, the consumption of fuel is proportional to the quantity of water converted into vapour. Steam of whatever tension expands on being set free, but the expansion of high pressure steam at the expense of its sensible heat is so great, that the hand may be plunged into it without injury the instant it issues from the orifice of a boiler. The steam becomes hotter by friction in issuing through the orifice which maintains it in its dry form, for there is no doubt that high-pressure steam is dry.

The elasticity or tension of steam, like that of common air, varies inversely as its volume—that is, when the space it occupies is doubled, its elastic force is reduced to one half. The expansion of steam is indefinite; the smallest quantity of water expanded into vapour will occupy many millions of cubic feet; a wonderful illustration of the minuteness of the ultimate particles of matter.

The force of steam, tremendous as the lightning itself when uncontrolled, is merely the result of chemical affinity: it is the chemical attraction between the particles of carbon, of coal or wood, and the oxygen of the atmosphere. Mr. Joule has ascertained that a pound of the best coal when burnt gives sufficient heat to raise the temperature of 8086 pounds of water one degree of the Centigrade thermometer, whence it has been computed by M. Helmholtz that the chemical force arising from the combustion of that pound of coal is capable of lifting a body of one hundred pounds weight to the height of twenty miles. That is the work performed by the heat arising from the combustion of a pound of coal. In all cases where work is produced by heat, a quantity of heat proportional to the work done is expended; and conversely, by the expenditure of a like quantity of work, the same amount of heat may be produced. The equivalence of heat and work is a law of nature. The mechanical force exerted by the steam engine for example is exactly proportional to the consumption of heat, nor more nor less; if we could produce a greater quantity than its equivalent we should have perpetual motion, which is impossible. Mechanical engines generate no force. We cannot create force; we can only avail ourselves of the inexhaustible stores of nature, the lightning, fire, water, wind, chemical action, &c. The quantity of mechanical power in nature is ever the same; it is never increased, it is never diminished, throughout the whole circuit of natural powers. The conservation of force is as permanent and unchangeable as matter. It may be dormant for a time, but it ever exists. We are unconscious of the enormous dynamic power that is either active or latent throughout the globe, because we do not attend to it. By the ebb and flow of the tide alone a power is exerted by which 25,000 cubic miles of water is moved over a quarter of the globe every twelve hours; and Professor W. Thomson has computed, by means of Pouillet’s data of solar radiation and Mr. Joule’s mechanical equivalent of heat, that the mechanical value of the whole energy active and potential of the disturbances kept up in the ethereal medium by the vibrations of the solar light within a cubic mile of our atmosphere is equal to 12,050 times the unit of mechanical force, that is to say, 12,050 times the force that would raise a pound of matter to the height of one foot, whence some idea may be formed of the vast amount of force exerted by the sun’s light within the limits of the whole terrestrial atmosphere. (N. 223.)

The dynamic energy of the undulations of the solar light gives the leaves of plants the power of decomposing carbonic acid, and of separating the particles of carbon and hydrogen from the oxygen for which they have so strong an affinity. In this operation the undulations of the sunbeam are extinguished as light and heat, and Professor W. Thomson has proved that the quantity of these undulations thus extinguished is precisely equal to the potential or quiescent energy thus created, and that precisely that very quantity of light and heat is restored when the plants are burned, whatever state they may be in; and that thus, as Mr. George Stephenson[14] has truly and beautifully observed, our coal fires and gas lamps restore to our use the light and heat of the sun of the early geological epochs which have rested as dormant powers under the seas and mountains for unnumbered ages. The sun is therefore the source of the mechanical energy of all the heat and motion of inanimate things, of all the motions of the heat and light of fires and artificial flames, and of the heat of all living creatures. For animal heat, and weights raised or resistance overcome, are mechanical effects of the chemical combination of food with oxygen; and food is either directly or indirectly vegetable, consequently dependent upon the sun.

Professor Helmholtz of Bonn has put in a strong point of view the enormous store of force possessed by our system by comparing it with its equivalent of heat. The force with which the earth moves in its orbit is such, that if brought to rest by a sudden shock, a quantity of heat would be generated by the blow equal to that produced by the combustion of fourteen such earths of solid coal; and supposing the capacity of the earth for heat as low as that of water, the globe would be heated to 11,200° Cent. It would be quite fused and for the most part reduced to vapour. If it should fall to the sun, which it would certainly do, the quantity of heat developed by the shock would be four hundred times as great.

The application of heat to the various branches of the mechanical and chemical arts has within the present century effected a greater change in the condition of man than had been accomplished in any equal period of his existence. Armed by the expansion and condensation of fluids with a power equal to that of the lightning itself, conquering time and space, he flies over plains, and travels on paths cut by human industry even through mountains with a velocity and smoothness more like planetary than terrestrial motion; he crosses the deep in opposition to wind and tide; by releasing the strain on the cable, he rides at anchor fearless of the storm; he makes the lightning his messenger; and like a magician he raises from the gloomy abyss of the mine the sunbeam of former ages to dispel the midnight darkness.

The principal phenomena of heat may be illustrated by a comparison with those of sound. Their excitation is not only similar but identical, as in friction and percussion; they are both communicated by contact and radiation; and Dr. Young observes that the effect of radiant heat in raising the temperature of a body upon which it falls, resembles the sympathetic agitation of a string when the sound of another string which is in unison with it is transmitted through the air. Light, heat, sound, and the waves of fluids are all subject to the same laws; their undulatory theories are perfectly similar: hence the interference of two hot rays must produce cold, that is, they must extinguish one another: darkness results from the interference of two undulations of light, silence ensues from the interference of two undulations of sound, and still water or no tide is the consequence of the interference of two tides. The propagation of sound, however, requires a much denser medium than that of light and heat; its intensity diminishes as the rarity of the air increases: so that, at a very small height above the surface of the earth, the noise of the tempest ceases, and the thunder is heard no more in those boundless regions where the heavenly bodies accomplish their periods in eternal and sublime silence.

A consciousness of the fallacy of our senses is one of the most important consequences of the study of nature. This study teaches us that no object is seen by us in its true place, owing to aberration; that the colours of substances are solely the effects of the action of matter upon light; and that light itself as well as heat and sound are not real beings, but mere motions communicated to our perceptions by the nerves. The human frame may therefore be regarded as an elastic system, the different parts of which are capable of receiving the tremors of elastic media, and of vibrating in unison with any number of superimposed undulations, all of which have their perfect and independent effect. Here our knowledge ends: the mysterious influence of matter on mind will in all probability be for ever hid from man.

SECTION XXVIII.

Common or Static Electricity, or Electricity of Tension—A Dual Power—Methods of exciting it—Attraction and Repulsion—Conduction—Electrics and Non-electrics—Induction—Dielectrics—Tension—Law of the Electric Force—Distribution—Laws of Distribution—Heat of Electricity—Electrical Light and its Spectrum—Velocity—Atmospheric Electricity—Its cause—Electric Clouds—Violent effects of Lightning—Back Stroke—Electric Glow—Phosphorescence.

ELECTRICITY is a dual power which gives no visible sign of its existence when in equilibrio, but when elicited forces are developed capable of producing the most sudden, violent, and destructive effects in some cases, while in others their action, though generally less energetic, is of indefinite and uninterrupted continuance. These modifications of the electric forces, incidentally depending upon the manner in which they are excited, present phenomena of great diversity, but yet so connected as to justify the conclusion that they originate in a common principle. The hypothesis of electricity being a fluid is untenable in the present advanced state of the science; we only know that it is a force whose action is twofold; that bodies in one electric state attract, and in another repel each other; in the former the electricity is said to be positive, in the latter negative; and thus regarding it as a force, its modes of action come under the laws of mechanics and mathematical analysis.

Electricity may be called into activity by the friction of heterogeneous substances, as in the common electrifying machine, by mechanical power, heat, chemical action, and the influence of magnetism. We are totally ignorant why it is roused from its neutral state by these means, or of the manner of its existence in bodies; but when excited it seems to produce a molecular polarity or chemical change in the ultimate particles of matter.

The science is divided into various branches, of which static or common electricity comes first under consideration, including that of the atmosphere. Substances in a neutral state neither attract nor repel. There is a numerous class called electrics in which the electric equilibrium is destroyed by friction; then the positive and negative electricities are called into action or separated; the positive is impelled in one direction, and the negative in another. Electricities of the same kind repel, whereas those of different kinds attract each other. The attractive power is exactly equal to the repulsive power at equal distances, and when not opposed they coalesce with great rapidity and violence, producing the electric flash, explosion, and shock; then the equilibrium is restored. One kind of electricity cannot be evolved without the evolution of an equal quantity of the opposite kind. Thus when a glass rod is rubbed with a piece of silk, as much positive electricity is elicited in the glass as there is negative in the silk. The kind of electricity depends more upon the mechanical condition than on the nature of the surface; for when two plates of glass, one polished and the other rough, are rubbed against each other, the polished surface acquires positive and the rough negative electricity. The manner in which friction is performed also alters the kind of electricity. Equal lengths of black and white ribbon applied longitudinally to one another, and drawn between the finger and thumb so as to rub their surfaces together, become electric. When separated the white ribbon is found to have acquired positive electricity, and the black negative; but if the whole length of the black ribbon be drawn across the breadth of the white, the black will be positively and the white negatively electric when separated. The friction of the rubber on the glass plate of the electrifying machine produces abundance of static electricity. The friction of the steam on the valve of an insulated locomotive steam-engine produces seven times the quantity of electricity that an electrifying machine would do with a plate three feet in diameter, worked at the rate of 70 revolutions in a minute. Pressure is a source of electricity which M. Becquerel has found to be common to all bodies; but it is necessary to separate them to prevent the reunion of the electricities. When two substances of any kind whatever are insulated and pressed together they assume different electric states, but they only show contrary electricities when one of them is a good conductor. When both are good conductors they must be separated with extreme rapidity to prevent a return to equilibrium. When the separation is very sudden the tension of the two electricities may be great enough to produce light. M. Becquerel attributes the light produced by the collision of icebergs to this cause. Iceland spar is made electric by the smallest pressure between the finger and the thumb, and retains it for a long time. All these circumstances are modified by the temperature of the substances, the state of their surfaces and that of the atmosphere. Several crystalline bodies become electric when heated, especially tourmaline, one end of which acquires positive, and the other negative electricity, while the intermediate part is neutral. If the tourmaline be broken through the middle, each fragment is found to possess positive electricity at one end and negative at the other. Electricity is evolved by substances passing from a liquid to a solid state, and by chemical action during the production and condensation of vapour, which is a great source of atmospheric electricity. In short, it may be generally stated, that when any cause whatever tends to destroy molecular attraction there is a development of electricity; if, however, the substances be not immediately separated, there will be an instantaneous restoration of equilibrium.

Electricity may be transferred from one body to another in the same manner as heat is communicated, and like it too the body loses by the transmission.

Although no substance is altogether impervious to electricity, nor is there any that does not offer some resistance to its passage, yet it moves with more facility through a certain class of substances called conductors, such as metals, water, the human body, &c., than through atmospheric air, glass, silk, &c., which are therefore called non-conductors. The conducting power is affected both by temperature and moisture. The terrestrial globe is a conductor on account of its moisture, though dry earth is not. Though metals are the best conductors of electricity, it affects their molecular structure, for the heat which accompanies its passage acts as a transverse expansive force, which increases their breadth by diminishing their length, as may be seen by passing electricity through a platinum wire sufficiently thick to resist fusion. Through air the force is disruptive on account of its non-conducting quality, and it seems to act chemically on the oxygen, producing the substance known as ozone during its passage through the atmosphere. If a conductor be good and of sufficient size the electricity passes imperceptibly but it is shivered to pieces in an instant if it be a bad conductor or too small to carry off the charge. In that case the physical change is generally a separation of the particles, or expansion from the heat, as in trees, where it turns the moisture into steam, but all these effects are in proportion to the obstacles opposed to the freedom of its course.

Bodies surrounded by non-conductors are said to be insulated, because when charged the electricity cannot escape. When that is not the case, the electricity is conveyed to the earth: consequently it is impossible to accumulate electricity in a conducting substance that is not insulated. There are a great many substances called non-electrics in which electricity is not sensibly developed by friction unless they be insulated, because it is carried off by their conducting power as soon as elicited. Metals, for example, which are said to be non-electrics can be excited, but being conductors they cannot retain this state if in communication with the earth. It is probable that no bodies exist which are either perfect non-electrics or perfect non-conductors. But it is evident that electrics must be non-conductors to a certain degree, otherwise they could not retain their electric state.

A body charged with electricity, although perfectly insulated, so that all escape of electricity is prevented, tends to produce an electric state of the opposite kind in all bodies in its vicinity. Positive electricity tends to produce negative electricity in a body near to it, and vice versâ, the effect being greater as the distance diminishes. This power which electricity possesses of causing an opposite electrical state in its vicinity is called induction. A Leyden jar, for example, or glass jar coated half way up both outside and in with tin foil, when charged with positive electricity, immediately induces negative electricity on the tin foil outside. Notwithstanding their strong mutual attraction they are prevented from coalescing by the glass, which is a non-conductor; but if the tin inside and out be connected by a conducting wire they instantly unite. When a body in either electric state is presented to a neutral one, its tendency in consequence of the law of induction is to disturb the condition of the neutral body by inducing electricity contrary to its own in the adjacent side, and therefore an electrical state similar to its own in the remote part. Hence the neutrality of the second body is destroyed by the action of the first, and the adjacent parts of the two, having now opposite electricities, will attract each other. The attraction between electrified and unelectrified substances is a consequence of the altered state of their molecules. Induction depends upon the facility with which the equilibrium of the neutral body can be overcome, a facility which is proportional to its conducting power. Consequently the attraction exerted by an electrified substance upon another substance previously neutral will be much more energetic if the latter be a conductor than if it be a non-conductor.

It is clear that one body cannot act upon another at a distance without some means of communication. Dr. Faraday has proved that the intervening non-conducting substance or dielectric has a great influence upon induction. Thus the inductive force is greater when sulphur is interposed between the two bodies than when shellac is the dielectric, and greater when shellac is the dielectric than glass, &c. Professor Matteucci has proved by the following experiment that the intervening substance is itself polarized by induction. A number of plates of mica in contact were placed between two plates of metal, one of which was electrified, so that the whole was charged like a Leyden jar. On separating the plates with insulating handles, each plate of mica was electrified; one side of it was positive and the other negative, showing decidedly a polarization by induction throughout the whole intervening non-conducting substance; and thus, although the interposed substance or dielectric is incapable of conducting the electrical force from one body to the other, it becomes by induction capable of transmitting it. In the atmosphere induction is transmitted by that of the intervening strata of air. It is true that induction takes place through the most perfect vacuum we can make, but there always remains some highly elastic air; and even if air could be altogether excluded, the ethereal medium cannot, and it must be capable of induction, since, however attenuated, it must consist of material atoms, otherwise it would be a nonentity.

The law of electrical attraction and repulsion has been determined by suspending a needle of gum-lac horizontally by a silk fibre, the needle carrying at one end a piece of electrified gold leaf. A globe in the same or opposite electrical state when presented to the gold leaf will repel or attract it, and will therefore cause the needle to vibrate more or less rapidly according to the distance of the globe. A comparison of the number of oscillations performed in a given time at different distances will determine the law of the variation of the electrical intensity, in the same manner that the force of gravitation is measured by the oscillations of the pendulum. Coulomb invented an instrument which balances the forces in question by the force of the torsion of a thread, which consequently measures the intensity; and Sir William Snow Harris has constructed an instrument with which he has measured the intensity of the electrical force in terms of the weight requisite to balance it. By these methods it has been found that the intensity of electrical attraction and repulsion varies inversely as the square of the distance. However, the law of repulsive force is liable to great disturbances from inductive action, which Sir William Snow Harris has found to exist not only between a charged and neutral body, but also between bodies similarly charged; and that, in the latter case, the inductive process may be indefinitely modified by the various circumstances of the quantity and intensity of the electricity and the distance between the charged bodies.

The quantity of electricity bodies are capable of receiving does not follow the proportion of their bulk, but depends principally upon the form and extent of their surface. It appears from the experiments of Sir W. S. Harris that a given quantity of electricity, divided between two perfectly equal and similar bodies, exerts upon external bodies only one fourth of the attractive force apparent when disposed upon one of them; and if it be distributed among three equal and similar bodies, the force is one ninth of that apparent when it is disposed on one of them. Hence, if the quantity of electricity be the same, the force varies inversely as the square of the surface on which it is disposed; and if the surface be the same, the force varies directly as the square of the quantity of electricity. These laws however do not hold when the form of the surface is changed. A given quantity of electricity disposed on a given surface has the greatest intensity when the surface has a circular form, and the least intensity when the surface is expanded into an indefinite straight line. The decrease of intensity seems to arise from some peculiar arrangement of the electricity depending on the extension of the surface. It is quite independent of the extent of the edge, the area being the same; for Sir W. S. Harris found that the electrical intensity of a charged sphere is the same with that of a plane circular area of the same superficial extent, and that of a charged cylinder the same as if it were cut open and expanded into a plane surface.

The same able electrician has shown that the attractive force between an electrified and a neutral uninsulated body is the same whatever be the forms of their unopposed parts. Thus two hemispheres attract each other with precisely the same force as if they were spheres; and as the force is as the number of attracting points in operation directly, and as the squares of the respective distances inversely, it follows that the attraction between a mere ring and a circular area is no greater than that between two similar rings, and the force between a sphere and an opposed spherical segment of the same curvature is no greater than that of two similar segments, each equal to the given segment.

Electricity may be accumulated to a great extent in insulated bodies, and so long as it is quiescent it occasions no sensible change in their properties. When restrained by the non-conducting power of the atmosphere, its tension or the pressure it exerts is proportional to the coercive force of the air. If the pressure be less than the coercive force, the electricity is retained; but the instant it exceeds that force in any one point it escapes, and that more readily when the air is attenuated or saturated with moisture, for the resistance of the air is proportional to the square of its density, but the inductive action of electricity on distant bodies is independent of atmospheric pressure. The power of retaining electricity depends also on the shape of the charged body. It is most easily retained by a sphere, next to that by a spheroid, but it readily escapes from a point, and a pointed object receives it with most facility.

The heat produced by the electric shock is proportional to the square of the quantity of electricity discharged, and is so intense that it fuses metals and volatilizes substances, but its intensity is not felt to its full extent on account of the shortness of its duration. It is only accompanied by light when the electricity is obstructed in its passage through substance.

Electrical light when analysed by a prism differs very much from solar light. Fraunhofer found that, instead of the fixed dark lines, the spectrum of an electric spark is crossed by numerous bright lines; and Professor Wheatstone has observed that the number and position of the lines differ with the metal from which the spark is taken, and believes the spark itself results from the ignition and volatilization of the matter of the conductor.

According to the experiments of Sir Humphry Davy, the density of the air has an influence on the colour. He passed the electric spark through a vacuum over mercury, which from green became successively sea-green, blue, and purple, on admitting different quantities of air. When the vacuum was made over a fusible alloy of tin and bismuth, the spark was yellowish and extremely pale. Sir Humphry thence concluded that electrical light principally depends upon some properties belonging to the ponderable matter through which it passes, and that space is capable of exhibiting luminous appearances, though it does not contain an appreciable quantity of matter. He thought that the superficial particles of bodies which form vapour, when detached by the repulsive power of heat, might be equally separated by the electric forces, and produce luminous appearances in vacuo by the destruction of their opposite electric states.

The velocity of electricity is so great that the most rapid motion which can be produced by art appears to be actual rest when compared with it. A wheel revolving with celerity sufficient to render its spokes invisible, when illuminated by a flash of lightning, is seen for an instant with all its spokes distinct, as if it were in a state of absolute repose; because, however rapid the rotation may be, the light has come and already ceased before the wheel has had time to turn through a sensible space. This beautiful experiment is due to Professor Wheatstone, as well as the following variation of it, which is not less striking: If a circular piece of pasteboard be divided into three sectors, one of which is painted blue, another yellow, and a third red, it will appear to be white when revolving quickly, because of the rapidity with which the impressions of the colours succeed each other on the retina. But, the instant it is illuminated by an electric spark, it seems to stand still, and each colour is as distinct as if it were at rest. This transcendent speed of electricity has been ingeniously measured, as follows, by Professor Wheatstone, who has ascertained that it much surpasses the velocity of light.

In the horizontal diameter of a small disc, fixed on the wall of a darkened room, are disposed six small brass balls, well insulated from each other. An insulated copper wire, half a mile long, is disjointed in its middle, and also near its two extremities; the six ends thus obtained are connected with the six-balls on the disc. When an electric discharge is sent through the wire by connecting its two extremities, one with the positive, and the other with the negative coating of a Leyden jar, three sparks are seen on the disc, apparently at the same instant. At the distance of about ten feet a small revolving mirror is placed so as to reflect these three sparks during its revolution. From the extreme velocity of the electricity, it is clear that, if the three sparks be simultaneous, they will be reflected, and will vanish before the mirror has sensibly changed its position, however rapid its rotation may be, and they will be seen in a straight line. But if the three sparks be not simultaneously transmitted to the disc—if one, for example, be later than the other two—the mirror will have time to revolve through an indefinitely small arc in the interval between the reflection of the two sparks and that of the single one. However, the only indication of this small motion of the mirror will be, that the single spark will not be reflected in the same straight line with the other two, but a little above or below it, for the reflection of all three will still be apparently simultaneous, the time intervening being much too short to be appreciated.

Since the number of revolutions which the revolving mirror makes in a second is known, and the angular deviation of the reflection of the single spark from the reflection of the other two can be measured, the time elapsed between their consecutive reflections can be ascertained. And, as the length of that part of the wire through which the electricity has passed is given, its velocity may be found.

The number of pulses in a second, requisite to produce a musical note of any pitch, are known; hence the number of revolutions accomplished by the mirror in a given time may be determined from the musical note produced by a tooth or peg, in its axis of rotation, striking against a card, or from the notes of a siren attached to the axis. It was thus that Professor Wheatstone found the mirror which he employed in his experiments made 800 revolutions in a second; and, as the angular velocity of the reflected image in a revolving mirror is double that of the mirror itself, an angular deviation of one degree in the appearance of the two sparks would indicate an interval of the 576,000th of a second; the deviation of half a degree would, therefore, indicate more than the millionth of a second. The use of sound as a measure of velocity is a happy illustration of the connexion of the physical sciences.

The earth possesses a powerful electrical tension, and the atmosphere when clear is almost always positively electric. Its electricity is stronger in winter than in summer, during the day than in the night. The intensity increases for two or three hours from the time of sunrise, comes to a maximum between seven and eight, then decreases towards the middle of the day, arrives at its minimum between one and two, and again augments as the sun declines till about the time of sunset, after which it diminishes and continues feeble during the night. The mere condensation of vapour is a source of atmospheric electricity; but although it is also produced by the vapour that rises from the surface of the earth, it is not under all circumstances. M. Pouillet found that electricity is only developed when accompanied by chemical action: for example, when the water whence the vapour proceeds contains lime, chalk, or any solid alkali, negative electricity is produced; and when it holds in solution either gas, acid, or some of the salts, the vapour is positively electric. Besides, the contact of earth with salt and fresh water generates positive electricity, and the contact of fresh and salt currents of water negative, so that the ocean must afford a great supply to the atmosphere; hence thunderstorms are most frequent near the coasts: but as electricity of one kind or another is developed whenever the molecules of matter are deranged from their natural state of equilibrium, there must be many partial variations in the electric state of the air. When the invisible vapour rises charged with electricity into the cold regions of the atmosphere, it is condensed into cloud, in which the tension is increased because the electricity is confined to a smaller space; and if the condensation be sufficient to produce drops of rain, they carry the electricity to the ground, so that in general a shower is a conductor between the clouds and the earth. When two clouds charged with opposite kinds, but of equal tension, approach within a certain distance, the intensity increases on the sides of the clouds that are nearest to one another; and when the tension is great enough to overcome the coercive pressure of the atmosphere, a discharge takes place which causes a flash of lightning, the stroke being given either by the cloud or the rain. The actual quantity of electricity in any part of a cloud is extremely small. The intensity of the flash arises from the great extent of surface over which it is spread, so that clouds may be compared to enormous Leyden jars thinly coated with electricity, which only acquires its intensity by its instantaneous condensation. The rapid and irregular motions of thunder clouds are probably more owing to strong electrical attractions and repulsions among themselves than to currents of air, though both are no doubt concerned in these hostile movements. The atmosphere becomes intensely electric on the approach of rain, hail, snow, sleet, and wind; but it varies afterwards, and the transitions are very rapid on the approach of a thunderstorm.

Since air is a non-conductor, it does not convey the electricity from the clouds to the earth, but it acquires from them an opposite kind, and when the tension is very great the force of the electricity becomes irresistible, and an interchange takes place between the clouds and the earth; but so rapid is the motion of lightning, that it is difficult to ascertain whether it goes from the clouds to the earth or shoots upwards from the earth to the clouds, though there can be no doubt that it does both. In a storm that occurred at Manchester in June 1835, the lightning was observed to issue from various points of a road, attended by explosions as if pistols had been fired out of the ground, and a man seems to have been killed by one of these explosions taking place under his foot. M. Gay Lussac ascertained that a flash of lightning sometimes darts more than three miles in a straight line. A person may be killed by lightning, although the explosion takes place at a distance of twenty miles, by what is called the back stroke. Suppose that the two extremities of a highly charged cloud hang down towards the earth, they will repel the electricity from the earth’s surface if it be of the same kind with their own, and will attract the other kind; and if a discharge should suddenly take place at one end of the cloud, the equilibrium will be instantly restored by a flash at that point of the earth which is under the other. Though the back stroke is often sufficiently powerful to destroy life, it is never so terrible in its effects as the direct stroke, which is often of inconceivable intensity. Instances have occurred when large masses of iron and stone, and even many feet of a stone wall, have been carried to a considerable distance by a stroke of lightning. Rocks and the tops of mountains often bear the marks of fusion from its intense heat; and occasionally vitreous tubes descending many feet into banks of sand mark its path. Dr. Fiedler exhibited several of these fulgorites in London of considerable length, which had been dug out of the sandy plains of Silesia and Eastern Prussia. One found at Paderborn was forty feet long. Their ramifications generally terminate in pools or springs of water below the sand, which are supposed to determine the course of the lightning. No doubt the soil and substrata must influence its direction, since it is found by experience that places which have been once struck by lightning are often struck again. An insulated conductor on the approach of a storm gives out such quantities of sparks that it is dangerous to approach it, as was fatally experienced by Professor Richman at Petersburg, who was struck dead by a globe of fire from the extremity of a conductor, while making experiments on atmospheric electricity. Copper conductors afford the best protection, especially if they expose a broad surface, since electricity is conveyed along the surface of bodies. There is no instance of an electric cloud of high tension being dispelled by a conductor, yet those invented by Sir William Snow Harris, and universally employed in the navy, afford a complete protection in the most imminent danger. The Shannon, a 50-gun frigate, commanded by the brave and lamented Sir William Peel, was enveloped in a thunder-storm when about 90 miles to the north-west of Java. It began at fifty minutes past four in the afternoon; the ship was driven before the storm, in a high sea, amid streams of vivid lightning, deafening thunder, hail, and rain. At five o’clock an immense ball of fire covered the maintopgallant mast, ran up the royal pole, and exploded in the air with a terrific concussion, covering all the surrounding space with sparks of electric light, which were driven rapidly to leeward by the wind. Fifteen minutes later an immense mass of lightning struck the mainmast, attended by a violent gust of wind; and another heavy discharge fell on it a quarter of an hour afterwards. From that time till six o’clock the ship was continually encompassed by sharp forked lightning, accompanied by incessant peals of thunder. Though actually enveloped in electricity, and struck three times, neither the hull nor the rigging sustained the slightest injury.

When the air is rarefied by heat, its coercive power is diminished, so that the electricity escapes from the clouds in those lambent diffuse flashes without thunder so frequent in warm summer evenings; and when the atmosphere is highly charged with electricity, it not unfrequently happens that electric light, in the form of a star, is seen on the topmasts and yard-arms of ships. In 1831 the French officers at Algiers were surprised to see brushes of light on the heads of their comrades, and at the points of their fingers when they held up their hands. This phenomenon was well known to the ancients, who reckoned it a lucky omen.

Many substances, in decaying, emit light, which is attributed to electricity, such as fish and rotten wood. Oyster-shells, and a variety of minerals, become phosphorescent at certain temperatures when exposed to electric shocks or friction: indeed, most of the causes which disturb molecular equilibrium give rise to phosphoric phenomena. The minerals possessing this property are generally coloured or imperfectly transparent; and, though the colour of this light varies in different substances, it has no fixed relation to the colour of the mineral. An intense heat entirely destroys this property, and the phosphorescent light developed by heat has no connexion with light produced by friction; for Sir David Brewster observed that bodies deprived of the faculty of emitting the one are still capable of giving out the other. Among the bodies which generally become phosphorescent when exposed to heat, there are some specimens which do not possess this property; wherefore phosphorescence cannot be regarded as an essential character of the minerals possessing it. Sulphuret of calcium, known as Canton’s phosphorus, and the sulphuret of barium, or Bologna stone, possess the phosphorescent property in an eminent degree.

Multitudes of fish are endowed with the power of emitting light at pleasure, no doubt to enable them to pursue their prey at depths where the sunbeams cannot penetrate. Flashes of light are frequently seen to dart along a shoal of herrings or pilchards; and the Medusa tribes are noted for their phosphorescent brilliancy, many of which are extremely small, and so numerous as to make the wake of a vessel look like a stream of silver. Nevertheless, the luminous appearance which is frequently observed in the sea during the summer months cannot always be attributed to marine animalculæ, as the following narrative will show:—

Captain Bonnycastle, coming up the Gulf of St. Lawrence on the 7th of September, 1826, was roused by the mate of the vessel in great alarm from an unusual appearance. It was a starlight night, when suddenly the sky became overcast in the direction of the high land, and an instantaneous and intensely vivid light, resembling the aurora, shot out of the hitherto gloomy and dark sea on the lee bow, which was so brilliant that it lighted everything distinctly even to the mast-head. The light spread over the whole sea between the two shores, and the waves, which before had been tranquil, now began to be agitated. Captain Bonnycastle describes the scene as that of a blazing sheet of awful and most brilliant light. A long and vivid line of light, superior in brightness to the parts of the sea not immediately near the vessel, showed the base of the high, frowning, and dark land abreast; the sky became lowering and more intensely obscure. Long tortuous lines of light showed immense numbers of very large fish darting about as if in consternation. The sprit-sail yard and mizen-boom were lighted by the glare, as if gaslights had been burning directly below them; and until just before daybreak, at four o’clock, the most minute objects were distinctly visible. Day broke very slowly, and the sun rose of a fiery and threatening aspect. Rain followed. Captain Bonnycastle caused a bucket of this fiery water to be drawn up; it was one mass of light when stirred by the hand, and not in sparks as usual, but in actual coruscations. A portion of the water preserved its luminosity for seven nights. On the third night, the scintillations of the sea reappeared; the sun went down very singularly, exhibiting in its descent a double sun; and, when only a few degrees high, its spherical figure changed into that of a long cylinder, which reached the horizon. In the night the sea became nearly as luminous as before, but on the fifth night the appearance entirely ceased. Captain Bonnycastle did not think it proceeded from animalculæ, but imagined it might be some compound of phosphorus, suddenly evolved and disposed over the surface of the sea. It had probably been that peculiar form of electricity known as the glow discharge, of which the author once saw a very remarkable instance.

M. E. Becquerel assures us that almost all substances are phosphorescent after being exposed to the sun if instantly withdrawn into darkness, and that it depends upon the arrangement of the particles and not upon chemical action. The salts of uranium give the same kind of phosphorescent light as that produced by the violet rays of the solar spectrum. A solution of the bisulphate of quinine emits a yellow phosphorescent light, whereas the fluorescent light of that liquid is blue. The colours of these two kinds of light are generally complementary to one another.

Phosphorescence is probably more or less concerned in some, at least, of a series of very curious experiments made by M. Niepcé de Saint-Victor, on what he calls the saturation of substances with light. It has long been known that, if a person in an intensely dark room should expose his arm to the sun through a hole in a window-shutter, it will shine on being drawn into the darkness. Now, M. de Saint-Victor found that if an engraving be exposed for a certain time to the sun, and instantly brought into darkness, it will make a photographic impression on a collodion or argentine surface, and that anything written or drawn with tartaric acid, or a solution of the salts of uranium, in large characters, is reproduced even at a small distance from a sensitive surface. It may be presumed that the light communicates its vibrations to the surfaces exposed to it with sufficient force to enable them to disturb the unstable equilibrium of such sensitive substances as collodion or the argentine salts. M. de Saint-Victor has shown that tartaric acid, which is readily impressed by sunlight, is neither fluorescent nor phosphorescent, whence he concludes that his experiments are independent of both of these modes of action. Uranium appears to have very peculiar properties: its salts are strongly luminous when exposed to the sun; they are very fluorescent; and the crystallized azitote of uranium becomes phosphorescent by percussion.

SECTION XXIX.

Voltaic Electricity—The Voltaic Battery—Intensity—Quantity—Static Electricity, and Electricity in Motion—Luminous Effects—Mr. Grove on the Electric Arc and Light—Decomposition of Water—Formation of Crystals by Voltaic Electricity—Photo-galvanic Engraving—Conduction—Heat of Voltaic Electricity—Electric Fish.

VOLTAIC or Dynamic electricity is elicited by the force of chemical action. It is connected with some of the most brilliant periods of British science, from the splendid discoveries to which it led Sir Humphry Davy and Dr. Faraday.

In 1790, while Galvani, Professor of Anatomy in Bologna, was making experiments on electricity, he was surprised to see convulsive motions in the limbs of a dead frog accidentally lying near the machine during an electrical discharge. Though a similar action had been noticed long before his time, he was so much struck with this singular phenomenon, that he examined all the circumstances carefully, and at length found that convulsions take place when the nerve and muscle of a frog are connected by a metallic conductor. This excited the attention of all Europe; and it was not long before Volta, Professor at Pavia, showed that the mere contact of different bodies is sufficient to disturb electrical equilibrium, and that a current of electricity flows in one direction through a circuit of three conducting substances. From this he was led, by acute reasoning and experiment, to the construction of the Voltaic pile, which, in its early form, consisted of alternate discs of zinc and copper, separated by pieces of wet cloth, the extremities being connected by wires. This simple apparatus, perhaps the most wonderful instrument that has been invented by the ingenuity of man, by divesting electricity of its sudden and uncontrollable violence, and giving in a continued stream a greater quantity at a diminished intensity, has exhibited that force under a new and manageable form, possessing powers the most astonishing and unexpected. The expression current has no relation to a fluid, which is now considered to be as inconsistent with the phenomena of dynamic as with static electricity. It was shown by Grotthus that the transmission of Voltaic electricity through liquids consists of a series of chemical affinities acting in definite directions; and Mr. Grove, from an examination of its action on the various kinds of matter, has come to the same conclusion. Indeed it is now the generally received opinion that a current of electricity is merely a continuous transmission of chemical affinity from particle to particle of the substance through which it is passing, and consequently that it is a continuous transmission of force. As the Voltaic battery has become one of the most important engines of physical research, some account of its present condition may not be out of place.

The disturbance of electric equilibrium, and a development of electricity, invariably accompany the chemical action of a fluid on metallic substances, and the electricity is most plentiful when that action occasions oxidation. Metals vary in the quantity of electricity afforded by their combination with oxygen. But the greatest abundance is developed by the oxidation of zinc by weak sulphuric acid. And, in conformity with the law that one kind of electricity cannot be evolved without an equal quantity of the other being brought into activity, it is found that the acid is positively, and the zinc negatively electric. It has not yet been ascertained why equilibrium is not restored by the contact of these two substances, which are both conductors, and in opposite electrical states. However, the electrical and chemical changes are so connected, that, unless equilibrium be restored, the action of the acid will go on languidly, or stop as soon as a certain quantity of electricity is accumulated in it. Equilibrium, nevertheless, will be restored, and the action of the acid will be continuous, if a plate of copper be placed in contact with the zinc, both being immersed in the fluid; for the copper, not being acted upon by the acid, will serve as a conductor to convey the positive electricity from the acid to the zinc, and will at every instant restore the equilibrium, and then the oxidation of the zinc will go on rapidly. Thus three substances are concerned in forming a Voltaic circuit, but it is indispensable that one of them should be a fluid. The electricity so obtained will be very feeble in overcoming resistances offered by imperfect conductors interposed in the circuit, or by very long wires, but it may be augmented by increasing the number of plates. In the common Voltaic battery, the electricity which the fluid has acquired from the first plate of zinc exposed to its action is taken up by the copper plate belonging to the second pair, and transferred to the second zinc plate, with which it is connected. The second plate of zinc, possessing equal powers, and acting in conformity with the first, having thus acquired a larger portion of electricity than its natural share, communicates a larger quantity to the fluid in the second cell. This increased quantity is again transferred to the next pair of plates; and thus every succeeding alternation is productive of a further increase in the quantity of the electricity developed. This action, however, would stop unless a vent were given to the accumulated electricity, by establishing a communication between the positive and negative poles of the battery by means of wires attached to the extreme plate at each end. When the wires are brought into contact, the Voltaic circuit is completed, the electricities meet and neutralize each other, producing the shock and other electrical phenomena; and then the electric current continues to flow uninterruptedly in the circuit, as long as the chemical action lasts. The stream of positive electricity flows from the zinc to the copper. The construction and power of the Voltaic battery have been much improved of late years, but the most valuable improvement is the constant battery of Professor Daniell. In all batteries of the ordinary construction, the power, however energetic at first, rapidly diminishes, and ultimately becomes very feeble. Professor Daniell found that this diminution of power is occasioned by the adhesion of the evolved hydrogen to the surface of the copper, and by the precipitation of the sulphate formed by the action of the acid on the zinc. He prevents the latter by interposing between the copper and the zinc, in the cell containing the liquid, a membrane which, without impeding the electric current, prevents the transfer of the salt; and the former, by placing between the copper and the membrane solution of sulphate of copper, which being reduced by the hydrogen prevents the adhesion of this gas to the metallic surface. Each element of the battery consists of a hollow cylinder of copper, in the axis of which is placed a cylindrical rod of zinc; between the zinc and the copper a membranous bag is placed, which divides the cell into two portions, the inner of which is filled with dilute acid, and the one nearer the copper is supplied with crystals of the sulphate of that metal. The battery consists of several of these elementary cells connected together by metallic wires, the zinc rod of one with the copper cylinder of that next to it. The zinc rods are amalgamated, so that local action, which, in ordinary cases, is so destructive of the zinc, does not take place, and no chemical action is manifested unless the circuit be completed. The rods are easily detached, and others substituted for them when worn out. This battery, which possesses considerable power, and is constant in its effects for a very long time, is greatly superior to all former arrangements, either as an instrument of research, or for exhibiting the ordinary phenomena of Voltaic electricity.

A battery charged with water alone, instead of acid, is constant in its action, but the quantity of electricity it develops is comparatively very small. Mr. Cross, of Broomfield in Somersetshire, kept a battery of this kind in full force during twelve months. M. Becquerel had invented an instrument for comparing the intensities of the different kinds of electricity by means of weights; but, as it is impossible to make the comparison with Voltaic electricity produced by the ordinary batteries, on account of the perpetual variation to which the intensity of the current is liable, he has constructed a battery which affords a continued stream of electricity of uniform power, but it is also of very feeble force. The current is produced by the chemical combination of an acid with an alkali.

Metallic contact is not necessary for the production of Voltaic electricity, which is entirely due to chemical action. The intensity of the Voltaic electricity is in proportion to the intensity of the affinities concerned in its production, and the quantity produced is in proportion to the quantity of matter which has been chemically active during its evolution. Dr. Faraday considers this definite production to be one of the strongest proofs that electricity is of chemical origin.

Galvanic or Voltaic electricity is manifested by two continuous forces or currents passing in opposite directions through the circuit: the zinc is the positive end or pole of the battery, and the copper the negative.

Voltaic electricity is distinguished by two marked characters. Its intensity increases with the number of plates, its quantity with the extent of their surfaces. The most intense concentration of force is displayed by a numerous series of large plates: light and heat are copiously evolved, and chemical decomposition is accomplished with extraordinary energy; whereas the electricity from one pair of plates, whatever their size may be, is so feeble that it gives no sign either of attraction or repulsion. Common or static electricity is of greater intensity and has a greater power of overcoming resistance than Voltaic electricity, but it acts upon a smaller quantity of matter. However, by diminishing the size of the plates, and increasing their number, the intensity of a battery may be increased till it becomes equal to that of the electrical machine.

The action of Voltaic electricity differs in some respects materially from that of the ordinary kind. When a quantity of common electricity is accumulated, the restoration of equilibrium is attended by an instantaneous violent explosion, accompanied by the development of light, heat, and sound. The concentrated power of the electricity forces its way through every obstacle, disrupting and destroying the cohesion of the particles of the bodies through which it passes, and occasionally increasing its destructive effects by the conversion of fluids into steam from the intensity of the momentary heat, as when trees are torn to pieces by a stroke of lightning. Even the vivid light which marks the path of the electricity is probably owing in part to the sudden compression of the air and the rapidity of its passage. But the instant equilibrium is restored by this energetic action the whole is at an end. On the contrary, when an accumulation takes place in a Voltaic battery, equilibrium is restored the moment the circuit is completed. But so far is the electric stream from being exhausted, that it continues to flow silently and invisibly in an uninterrupted current supplied by a perpetual reproduction. And, although its action on bodies is neither so sudden nor so intense as that of common electricity, yet it acquires such power from constant accumulation and continued action, that it ultimately surpasses the energy of the other. The two kinds of electricity differ in no circumstance more than in the development of heat. Instead of a momentary evolution, the circulation of the Voltaic electricity is accompanied by a continued development of heat, lasting as long as the circuit is complete, without producing either light or sound. Its intensity from a very powerful battery is greater than that of any heat that can be obtained by artificial means, so that it fuses substances which resist the action of the most powerful furnaces. The temperature of every part of a Voltaic battery itself is raised during its activity. With the greater number of metals Mr. Grove found that the positive terminal or pole is hotter than the negative.

According to Mr. Joule, the quantity of heat generated in a unit of time is proportional to the strength of the current, and when a galvanic current is employed in chemical analysis, the heat in the entire circuit generated in a unit of time is equal to the work expended in producing it, minus that employed in the analysis. In fact, a current of electricity cannot pass through a homogeneous conductor without generating heat in overcoming resistance, an effect proved by Mr. Joule to be proportional to the square of the force of the current, and the same in whatever direction the current may be flowing. Any other thermal action that can take place must depend upon the heterogeneousness of the circuit, and must be reversible with the current. For example, if a semicircle of bismuth be joined to a semicircle of antimony, an electric current in passing through it produces cold where it passes from the bismuth to the antimony by absorption, and heat where it passes from the antimony to the bismuth.

The transit of the electricity from pole to pole is accompanied by light, and in consequence of the continuous current sparks occur every time the contact of the wires is either broken or renewed; but considerable intensity is requisite to enable the electricity to force its way through atmospheric air or gas. Both its length and colour are affected by the density of the medium through which it passes. If the medium be gradually rarefied the discharge increases from a spark to a luminous glow, differing in colour in different gases, but white in air. When very much attenuated a discharge may be made to pass across 6 or 7 feet of space, while in air of the ordinary density it will not pass through an inch. In rarefied gas it resembles the Aurora by its continuous flashes. When the battery is powerful the luminous effects are very brilliant.

The most splendid artificial light known is produced by fixing pencils of charcoal at the extremities of the wires, and bringing them into contact. This light is the more remarkable as it is independent of combustion, since the charcoal suffers no apparent change, and, likewise, because it is equally vivid in such gases as do not contain oxygen. It depends upon the molecular arrangement of the charcoal; for Mr. Grove observes that “carbon in a transparent crystalline state, as diamond, is as perfect a non-conductor as we know, while in an opaque amorphous state, as graphite or charcoal, it is one of the best conductors: thus in one state it transmits light and stops electricity, in the other it transmits electricity and stops light. It is a circumstance worthy of remark, that the arrangement of molecules which renders a solid body capable of transmitting light is most unfavourable to the transmission of electricity, transparent solids being very imperfect conductors of electricity; so all gases readily transmit light, but are amongst the worst conductors of electricity, if indeed they can be said to conduct it at all. The fact that the molecular structure or arrangement of a body influences, indeed I may say determines, its conducting power, is by no means explained by the theory of a fluid; but if electricity be only a transmission of force or motion, the influence of the molecular state is just what would be expected.”

Professor Wheatstone, by fixing metallic points at the extremities of the wires or poles, has found that the appearance of the spectrum of the voltaic arc or vivid flame that is seen between the terminals of a battery, depends, as in static electricity, upon the metal from whence it is taken. The spectrum of that from mercury consists of seven definite rays, separated from each other by dark intervals; these visible rays are two orange lines close together, a bright green line, two blueish-green lines near each other, a very bright purple line, and, lastly, a blue line. It is the same when it passes through carbonic acid gas, oxygen gas, air, or vacuum. The light from zinc, cadmium, tin, bismuth, and lead, in a melted state, gives similar results; but the number, position, and colour of the lines vary so much in each case, and the appearances are so different, that the metals may easily be distinguished from one another by this mode of investigation. The electric spark is considered by M. Angström to be the overlapping of two spectra, one of which belongs to the metal, and the other to the gas through which the spark passes, and that the bright lines vary with the gas as well as with the metal. In an oxygen spectrum the greatest number of bright lines occur in the blue and violet, in nitrogen in the green and yellow, and in hydrogen in the red. These effects must necessarily be connected with the chemical and thermal properties of the gases.

Mr. Grove considers that the colour of the voltaic arc, or flame, which appears between the poles of a very powerful battery, depends upon the substance of the metal from whence it proceeds and on the medium through which it passes. The spark from zinc is blue, from silver it is green, from iron it is red and scintillating—precisely the colours afforded by these metals in their ordinary combustion. But the colour varies also with the medium through which the light passes, for when the medium is changed a change takes place in the colour, showing an affection of the intervening matter. A portion of the metal terminals or poles is actually transmitted with every electrical or Voltaic discharge, whence Mr. Grove concludes that the electrical discharge arises, at least in part, from an actual repulsion and severance of the electrified matter itself, which flies off at the points of least resistance. He observes that “the phenomena attending the electric spark or Voltaic arc tends to modify considerably our previous idea of the nature of the electric force as a producer of ignition and combustion. The Voltaic arc is perhaps, strictly speaking, neither ignition nor combustion. It is not simply ignition; because the matter of the terminals is not merely brought to a state of incandescence, but is physically separated, and partially transferred from one terminal to another, much of it being dissipated in a vaporous state. It is not combustion; for the phenomena will take place independently of atmospheric air, oxygen gas, or any of the bodies usually called supporters of combustion; combustion being in fact chemical union attended with heat and light. In the Voltaic arc we may have no chemical union, for if the experiment be performed in an exhausted receiver, or in nitrogen, the substance forming the terminals is condensed and precipitated upon the interior of the vessel, in, chemically speaking, an unaltered state. Thus, to take a very striking example, if the Voltaic discharge be taken between zinc terminals in an exhausted receiver, a fine black powder of zinc is deposited on the sides of the receiver; this can be collected, and takes fire readily in air by being touched with a match, or ignited wire, instantly burning into white oxide of zinc. To an ordinary observer the zinc would appear to be burned twice—first in the receiver, where the phenomenon presents all the appearance of combustion, and, secondly, in the real combustion in air. With iron the experiment is equally instructive. Iron is volatilized by the Voltaic arc in nitrogen, or in an exhausted receiver; and when a scarcely perceptible film has lined the receiver, if it be washed with an acid, it then gives, with ferrocyanide of potassium, the Prussian-blue precipitate. In this case we readily distil iron, a metal by ordinary means fusible only at a very high temperature.”

Another strong evidence that the Voltaic discharge consists of the material itself of which the terminals are composed, is the peculiar rotation which is observed in the light when iron is employed, the magnetic character of this metal causing its particles to rotate by the influence of the Voltaic current. In short, Mr. Grove concludes that, although it would be hasty to assert that the electrical disruptive discharge can in no case take place without the terminals being affected, yet he had met with no instance of such a result, provided the discharge had been sufficiently prolonged, and the terminals in such a state as could be expected to render manifest slight changes![15]

Some years ago Mr. Grove discovered that the electrical discharge possesses certain phases or fits of an alternate character, forming rings of alternate oxidation and deoxidation on metallic surfaces. A highly polished silver plate in an air-pump was connected with the pole of a powerful inductive battery, while a fine metallic wire, or even a common sewing needle, was fixed at the other pole, and so arranged as to be perpendicular to the silver plate, and very near, but not touching it. By means of this apparatus the electrical discharge could be sent through any kind of rarefied media. In some of the experiments a series of concentric coloured rings of oxide alternating with rings of polished or unoxidated silver were formed on the plate under the point of the needle or wire. When the plate was previously coated with a film of oxide, the oxide was removed in concentric spaces by the discharge, and increased on the alternate ones, showing an alternate positive and negative electricity, or electricity of an opposite character in the same discharge.

When the silver plate was polished the centre of the rings formed on it was yellow-green surrounded by blue-green; then a ring of polished silver, followed by a crimson ring with a slight orange tint on the inner side and deep purple on the outer; lastly the indication of a polished one. When the air-pump was filled with attenuated olefiant gas the rings were precisely the same with those seen in thin plates; hence the effect is the same as that produced by the interference of light. In these experiments the luminous appearance extended from three quarters of an inch to an inch round the point of the needle or wire.

When the silver plate was connected with the negative pole of the battery a polished point appeared upon it opposite the needle, surrounded by a dusky ill-defined areola of a brown colour tinged with purple when viewed in one direction, and greenish-white when seen in another.

In the present year Mr. Gassiot, Vice-President of the Royal Society, has shown that the stratified character of the electric discharge is remarkably developed in the Torricellian vacuum. Among the various experiments made by that gentleman two may be selected as strongly illustrative of this new and singular property of electrical light.

In a closed glass tube about an inch internal diameter and 38 inches long, in which a vacuum had been made, two platinum wires were hermetically sealed, 32 inches apart, and connected with the poles of an inductive battery. The luminous appearance at the two poles was very different when electricity passed through the wires. A glow surrounded the negative pole, and in close approximation to the glow a well-defined dark space appeared, while from the positive pole or wire the light proceeded in a stream; but unless the charge be great or the tube short, the stream will not extend to the black band, which is totally different from the intervening space. When discharges of electricity were sent through this vacuum tube a series of bands or stratifications were formed which were concave towards the positive pole; and as in the changes in making and breaking the circuit the electricity emanates from the different terminals or wires, their concavities were in opposite directions.

When instead of platinum wires narrow tinfoil coatings were placed round the exterior of the glass tube and connected with the wires of the battery, brilliant stratifications filled the interior of the tube between the foil coatings, but no dark band appeared. At present Mr. Gassiot is inclined to believe that the dark band is due to interference; but that the stratifications arise from pulsations or impulses of a force acting in a highly attenuated but resisting medium, for even with the best air-pumps it is impossible to make a perfect void; he is still occupied with experiments on this new subject, and no doubt will obtain very remarkable results, of which none can be more extraordinary than his discovery of the powerful influence of the magnet on this electric light. The stratifications are formed in rapid succession in the tube with platinum wires and are turned different ways, but they can be separated at any part of the tube by the pole of a magnet round which the whole stratifications have a tendency to revolve. In the second experiment, where the tinfoil was used, the discharge was divided in two by the pole of a magnet, and the two parts had a tendency to rotate round the magnet in opposite directions.

Voltaic electricity is a powerful agent in chemical analysis. When transmitted through conducting fluids, it separates them into their constituent parts, which it conveys in an invisible state through a considerable space or quantity of liquid to the poles, where they come into evidence. Numerous instances might be given, but the decomposition of water is perhaps the most simple and elegant. Suppose a glass tube filled with water, and corked at both ends; if one of the wires of an active Voltaic battery be made to pass through one cork, and the other through the other cork, into the water, so that the extremities of the two wires shall be opposite and about a quarter of an inch asunder, chemical action will immediately take place, and gas will continue to rise from the extremities of both wires till the water has vanished. If an electric spark be then sent through the tube, the water will reappear. By arranging the experiment so as to have the gas given out by each wire separately, it is found that water consists of two volumes of hydrogen and one of oxygen. The hydrogen is given out at the positive wire of the battery, and the oxygen at the negative. The oxides are also decomposed; the oxygen appears at the positive pole, and the metal at the negative. The decomposition of the alkalies and earths by Sir Humphry Davy formed a remarkable era in the history of science. Soda, potash, lime, magnesia, and other substances heretofore considered to be simple bodies incapable of decomposition, were resolved by electric agency into their constituent parts, and proved to be metallic oxides, by that illustrious philosopher. All chemical changes produced by electricity are accomplished on the same principle; and it appears that, in general, combustible substances, metals, and alkalies go to the negative wire, while acids and oxygen are evolved at the positive. The transfer of these substances to the poles is not the least wonderful effect of the Voltaic battery. Though the poles be at a considerable distance from one another, nay, even in separate vessels, if a communication be only established by a quantity of wet thread, as the decomposition proceeds the component parts pass through the thread in an invisible state, and arrange themselves at their respective poles. According to Dr. Faraday, electro-chemical decomposition is simply a case of the preponderance of one set of chemical affinities more powerful in their nature over another set which are less powerful. And in electro-chemical action of any kind produced by a continuous current, the amount of action in a given time is nearly, if not rigorously, proportional to the strength of the current. The great efficacy of Voltaic electricity in chemical decomposition arises not from its tension, but from the quantity set in motion and the continuance of its action. Its agency appears to be most exerted on fluids and substances which by conveying the electricity partially and imperfectly impede its progress. But it is now proved to be as efficacious in the composition as in the decomposition or analysis of bodies.

It had been observed that, when metallic solutions are subjected to galvanic action, a deposition of metal, sometimes in the form of minute crystals, takes place on the negative wire. By extending this principle, and employing a very feeble Voltaic action, M. Becquerel has succeeded in forming crystals of a great proportion of the mineral substances, precisely similar to those produced by nature. The electric state of metallic veins makes it possible that many natural crystals may have taken their form from the action of electricity bringing their ultimate particles, when in solution, within the narrow sphere of molecular attraction. Both light and motion favour crystallization. Crystals which form in different liquids are generally more abundant on the side of the jar exposed to the light; and it is well known that still water, cooled below 32°, starts into crystals of ice the instant it is agitated. A feeble action is alone necessary, provided it be continued for a sufficient time. Crystals formed rapidly are generally imperfect and soft, and M. Becquerel found that even years of constant Voltaic action were necessary for the crystallization of some of the hard substances. If this law be general, how many ages may be required for the formation of a diamond!

The deposition of metal from a metallic solution by galvanic electricity has been most successfully applied to the arts of plating and gilding, as well as to the more delicate process of copying medals and copper plates. Indeed, not medals only, but any object of art or nature, may be coated with precipitated metal, provided it be first covered with the thinnest film of plumbago, which renders a non-conductor sufficiently conducting to receive the metal. Photo-galvanic engraving depends upon this. Gelatine mixed with bichromate of potash, nitrate of silver, and iodide of potassium, is spread over a plate of glass, and when dry a positive print is laid upon it with its face downwards, which, when exposed to the sun, leaves its impression. When soaked in water the gelatine swells around all those parts where the light had fallen, thus forming an intaglio, a cast of which is taken in gutta-percha, which is then coated with copper by the electro process, whence a copper plate in relief is obtained.

Static electricity, on account of its high tension, passes through water and other liquids as soon as it is formed, whatever the length of its course may be. Voltaic electricity, on the contrary, is weakened by the distance it has to traverse. Pure water is a very bad conductor; but ice absolutely stops a current of Voltaic electricity altogether, whatever be the power of the battery, although static or common electricity has sufficient power to overcome its resistance. Dr. Faraday has discovered that this property is not peculiar to ice; that, with a few exceptions, bodies which do not conduct electricity when solid acquire that property, and are immediately decomposed, when they become fluid, and, in general, that decomposition takes place as soon as the solution acquires the capacity of conduction, which has led him to suspect that the power of conduction may be only a consequence of decomposition.

Heat increases the conducting power of some substances for Voltaic electricity, and of the gases for both kinds. Dr. Faraday has given a new proof of the connexion between heat and electricity, by showing that, in general, when a solid, which is not a metal, becomes fluid, it almost entirely loses its power of conducting heat, while it acquires a capacity for conducting electricity in a high degree. M. Becquerel regards the production of heat and that of electricity to be concomitant; their dependence being such, that when one is increased the other diminishes, and vice versâ, so that one may altogether disappear with the increase of the other. For instance, when electricity circulates in a metallic wire, the greater the heat produced, the less the quantity of electricity which passes, and the contrary, so that the affair proceeds as if electricity were converted into heat, and heat into electricity. Again, in a closed galvanic circuit the sum of the heat produced in the chemical action of the acidulated water upon the zinc and in the conducting wire is constant, so that the quantity of heat disengaged in the reaction is greater in proportion as less electricity passes through the wire. These, and other circumstances, prove such an intimate connexion between the production of heat and electricity, that in the change of condition of substances the electrical effects might disappear or be annulled by the calorific effects.

The galvanic current affects all the senses: nothing can be more disagreeable than the shock, which may even be fatal if the battery be very powerful. A bright flash of light is perceived with the eyes shut, when one of the wires touches the face, and the other the hand. By touching the ear with one wire, and holding the other, strange noises are heard; and an acid taste is perceived when the positive wire is applied to the tip of the tongue, and the negative wire touches some other part of it. By reversing the poles the taste becomes alkaline. It renders the pale light of the glow-worm more intense. Dead animals are roused by it, as if they started again into life, and it may ultimately prove to be the cause of muscular action in the living.

Several fish possess the faculty of producing electrical effects. The most remarkable are the gymnotus electricus, found in South America; and the torpedo, a genus of ray, frequent in the Mediterranean. The electrical action of the torpedo depends upon an apparatus apparently analogous to the Voltaic pile, which the animal has the power of charging at will, consisting of membranous columns filled throughout with laminæ, separated from one another by a fluid. The absolute quantity of electricity brought into circulation by the torpedo is so great, that it effects the decomposition of water, has power sufficient to make magnets, gives very severe shocks and the electric spark. It is identical in kind with that of the galvanic battery, the electricity of the under surface of the fish being the same with the negative pole, and that in the upper surface the same with the positive pole. Its manner of action is, however, somewhat different; for, although the evolution of the electricity is continued for a sensible time, it is interrupted, being communicated by a succession of discharges.

SECTION XXX.

Discovery of Electro-magnetism—Deflection of the Magnetic Needle by a Current of Electricity—Direction of the Force—Rotatory Motion by Electricity—Rotation of a Wire and a Magnet—Rotation of a Magnet about its Axis—Of Mercury and Water—Electro-Magnetic Cylinder or Helix—Suspension of a Needle in a Helix—Electro-Magnetic Induction—Temporary Magnets—The Galvanometer.

THE disturbing effects of the aurora and lightning on the mariner’s compass had been long known. In the year 1819 M. Oersted, Professor of Natural Philosophy at Copenhagen, discovered that a current of Voltaic electricity exerts a powerful influence on a magnetized needle. This observation has given rise to the theory of electro-magnetism—one of the most interesting sciences of modern times, whether it be considered as leading us a step farther in generalization, by identifying two agencies hitherto referred to different causes, or as developing a new force, unparalleled in the system of the world, which, overcoming the retardation from friction, and the obstacle of a resisting medium, maintains a perpetual motion as long as the action of a Voltaic battery is continued.

When the two poles of a Voltaic battery are connected by a metallic wire, so as to complete a circuit, the electricity flows without ceasing. If a straight portion of that wire be placed parallel to, and horizontally above, a magnetized needle at rest in the magnetic meridian, but freely poised like the mariner’s compass, the action of the electric current flowing through the wire will instantly cause the needle to change its position. Its extremity will deviate from the north towards the east or west, according to the direction in which the current is flowing; and, on reversing the direction of the current, the motion of the needle will be reversed also. The numerous experiments that have been made on magnetism and electricity, as well as those on the various relative motions of a magnetic needle under the influence of galvanic electricity, arising from all possible positions of the conducting wire, and every direction of the Voltaic current, together with all the other phenomena of electro-magnetism, are explained by Dr. Roget in some excellent articles on these subjects in the Library of Useful Knowledge.

All experiments tend to prove that the force emanating from the electric current, which produces such effects on the magnetic needle, acts at right angles to the current. The action of an electrical current upon either pole of a magnet has no tendency to cause the pole to approach or recede, but to rotate about it. If the stream of electricity be supposed to pass through the centre of a circle whose plane is perpendicular to the current, the direction of the force exerted by the electricity will always be in the tangent to the circle, or at right angles to its radius (N. 223). Consequently, the tangential force of the electricity has a tendency to make the pole of a magnet move in a circle round the wire of the battery.

Rotatory motion was suggested by Dr. Wollaston. Dr. Faraday was the first who actually succeeded in making the pole of a magnet rotate about a vertical conducting wire. In order to limit the action of the electricity to one pole, about two-thirds of a small magnet were immersed in mercury, the lower end being fastened by a thread to the bottom of the vessel containing the mercury. When the magnet was thus floating almost vertically with its north pole above the surface, a current of positive electricity was made to descend perpendicularly through a wire touching the mercury, and immediately the magnet began to rotate from left to right about the wire. The force being uniform, the rotation was accelerated till the tangential force was balanced by the resistance of the mercury, when it became constant. Under the same circumstances the south pole of the magnet rotates from right to left. It is evident, from this experiment, that the wire may also be made to perform a rotation round the magnet, since the action of the current of electricity on the pole of the magnet must necessarily be accompanied by a corresponding reaction of the pole of the magnet on the electricity in the wire. This experiment has been accomplished by a vast number of contrivances, and even a small battery, consisting of two plates, has performed the rotation. Dr. Faraday produced both motions at the same time in a vessel containing mercury; the wire and the magnet revolved in one direction about a common centre of motion, each following the other.

The next step was to make a magnet, and also a cylinder, revolve about their own axes, which they do with great rapidity. Mercury has been made to rotate by means of Voltaic electricity, and Professor Ritchie exhibited in the Royal Institution the singular spectacle of the rotation of water by the same means, while the vessel containing it remained stationary. The water was in a hollow double cylinder of glass, and, on being made the conductor of electricity, was observed to revolve in a regular vortex, changing its direction as the poles of the battery were alternately reversed. Professor Ritchie found that all the different conductors hitherto tried by him, such as water, charcoal, &c., give the same electro-magnetic results when transmitting the same quantity of electricity, and that they deflect the magnetic needle in an equal degree when their respective axes of conduction are at the same distance from it. But one of the most extraordinary effects of this force is exhibited by coiling a copper wire, so as to form a helix or corkscrew, and connecting the extremities of the wire with the poles of a galvanic battery. If a magnetized steel bar or needle be placed within the screw, so as to rest upon the lower part, the instant a current of electricity is sent through the wire of the helix, the steel bar starts up by the influence of this invisible power, and remains suspended in the air in opposition to the force of gravitation (N. 224). The effect of the electro-magnetic power exerted by each turn of the wire is to urge the north pole of the magnet in one direction, and the south pole in the other. The force thus exerted is multiplied in degree and increased in extent by each repetition of the turns of the wire, and in consequence of these opposing forces the bar remains suspended. This helix has all the properties of a magnet while the electrical current is flowing through it, and may be substituted for one in almost every experiment. It acts as if it had a north pole at one extremity and a south pole at the other, and is attracted and repelled by the poles of a magnet exactly as if it were one itself. All these results depend upon the course of the electricity; that is, on the direction of the turns of the screw, according as it is from right to left, or from left to right, being contrary in the two cases.

The action of Voltaic electricity on a magnet is not only precisely the same with the action of two magnets on one another, but its influence in producing temporary magnetism in iron and steel is also the same with magnetic induction. The term induction, when applied to electric currents, expresses the power which these currents possess of inducing a particular state upon matter in their immediate neighbourhood, otherwise neutral or indifferent. For example, the connecting wire of a galvanic battery holds iron filings suspended like a magnet as long as the current continues to flow through it: the iron becomes magnetic by the induction of the current. The most powerful temporary magnets are obtained by bending a thick cylinder of soft iron into the form of a horseshoe, and surrounding it with a coil of thick copper wire covered with silk to prevent communication between its coils. When this wire forms part of a galvanic circuit the iron becomes so highly magnetic by the induction of the current flowing through the wire that a temporary magnet of this kind made by Professor Henry of the Albany Academy in the United States sustained a weight of nearly a ton. Another by Mr. Gage has been applied with considerable success as a moving power: its spark is a bright flash, and the snap as loud as a pistol. But the most powerful known is that employed by Mr. Joule in his experiments, which sustains a weight of 2080 lbs. The iron loses its magnetism the instant the electricity ceases to flow, and acquires it again as instantaneously when the circuit is renewed.

The action of an electric current causes a deviation of the compass from the plane of the magnetic meridian. In proportion as the needle recedes from the meridian, the intensity of the force of terrestrial magnetism increases, while at the same time the electro-magnetic force diminishes; the number of degrees at which the needle stops, showing where the equilibrium between these two forces takes place, will indicate the intensity of the galvanic current. The galvanometer, constructed upon this principle, is employed to measure the intensity of galvanic currents collected and conveyed to it by wires. This instrument is rendered much more sensible by neutralizing the effects of the earth’s magnetism on the needle, which is accomplished by placing a second magnetised needle so as to counteract the action of the earth on the first—a precaution requisite in all delicate magnetical experiments.

It has been ascertained by means of this instrument that the action of an electrical current upon a magnet is inversely as the square of the distance, and the energy with which an electro magnet acts is directly as the power of the galvanic battery and the number of coils round the core, and inversely as the resistance of the wire.

SECTION XXXI.

Electro-Dynamics—Reciprocal Action of Electric Currents—Identity of Electro-Dynamic Cylinders and Magnets—Differences between the Action of Voltaic Electricity and Electricity of Tension—Effects of a Voltaic Current—Ampère’s Theory—Dr. Faraday’s Experiment of Electrifying and Magnetising a Ray of Light.

THE science of electro-magnetism, which must render the name of M. Oersted ever memorable, relates to the reciprocal action of electrical and magnetic currents: M. Ampère, by discovering the mutual action of electrical currents on one another, has added a new branch to the subject, to which he has given the name of electro-dynamics.

When electric currents are passing through two conducting wires, so suspended or supported as to be capable of moving both towards and from one another, they show mutual attraction or repulsion, according as the currents are flowing in the same or in contrary directions; the phenomena varying with the relative inclinations and positions of the streams of electricity. The mutual action of such currents, whether they flow in the same or in contrary directions, whether they be parallel, perpendicular, diverging, converging, circular, or heliacal, all produce different kinds of motion in a conducting wire, both rectilineal and circular, and also the rotation of a wire helix, such as that described, now called an electro-dynamic cylinder on account of some improvements in its construction (N. 225). And, as the hypothesis of a force varying inversely as the square of the distance accords perfectly with all the observed phenomena, these motions come under the same laws of dynamics and analysis as any other branch of physics.

Electro-dynamic cylinders act on each other precisely as if they were magnets during the time the electricity is flowing through them. All the experiments that can be performed with the cylinder might be accomplished with a magnet. That end of the cylinder in which the current of positive electricity is moving in a direction similar to the motion of the hands of a watch, acts as the south pole of a magnet, and the other end, in which the current is flowing in a contrary direction, exhibits northern polarity.

The phenomena mark a very decided difference between the action of electricity in motion or at rest, that is, between Voltaic and static electricity; the laws they follow are in many respects of an entirely different nature, though the electricities themselves are identical. Since Voltaic electricity flows perpetually, it cannot be accumulated, and consequently has no tension, or tendency to escape from the wires which conduct it. Nor do these wires either attract or repel light bodies in their vicinity, whereas static or ordinary electricity can be accumulated in insulated bodies to a great degree, and in that state of rest the tendency to escape is proportional to the quantity accumulated and the resistance it meets with. In ordinary electricity, the law of action is, that dissimilar electricities attract and similar electricities repel one another. In Voltaic electricity, on the contrary, similar currents, or such as are moving in the same direction, attract one another, while a mutual repulsion is exerted between dissimilar currents, or such as flow in opposite directions. Common electricity escapes when the pressure of the atmosphere is removed, but the electro-dynamical effects are the same whether the conductors be in air or in vacuo.

The effects produced by a current of electricity depend upon the celerity of its motion through a conducting wire. Yet we are ignorant whether the motion be uniform or varied, but the method of transmission has a marked influence on the results; for, when it flows without intermission, it occasions a deviation in the magnetic needle, but it has no effect whatever when its motion is discontinuous or interrupted, like the current produced by the common electrical machine when a communication is made between the positive and negative conductors.

M. Ampère has established a theory of electro-magnetism suggested by the analogy between electro-dynamic cylinders and magnets, founded upon the reciprocal attraction of electro-currents, to which he reduces all the phenomena of magnetism and electro-magnetism, by assuming that the magnetic properties which bodies possess derive these properties from currents of electricity, circulating about every part in one uniform direction. Although every particle of a magnet possesses like properties with the whole, yet the general effect is the same as if the magnetic properties were confined to the surface. Consequently, Ampère concludes that the internal electro-currents must compensate one another, and that the magnetism of a body must therefore arise from a superficial current of electricity constantly circulating in a direction perpendicular to the axis of the magnet; so that the reciprocal action of magnets and all the phenomena of electro-magnetism are reduced to the action and reaction of superficial currents of electricity, acting at right angles to their direction.

Notwithstanding the experiments made by Ampère to elucidate the subject, there is still an uncertainty in the theory of the induction of magnetism by an electric current in a body near it. It does not appear whether electric currents which did not previously exist are actually produced by induction, or if its effect be only to give one uniform direction to the infinite number of electric currents previously existing in the particles of the body, and thus rendering them capable of exhibiting magnetic phenomena, in the same manner as polarization reduces the undulations of light to one plane, which had previously been performed in every plane. Possibly both may be combined in producing the effect; for the action of the electric current may not only give a common direction to those already existing, but may also increase their intensity. However that may be, by assuming that the attractions and repulsions of the elementary portions of electric currents vary inversely as the square of the distance, the actions being at right angles to the direction of the current, it is found that the attraction and repulsion of a current of indefinite length on the elementary portion of a parallel current at any distance from it are in the simple ratio of the shortest distance between them: consequently, the reciprocal action of electric currents is reduced to the composition and resolution of forces, so that the phenomena of electro-magnetism are brought under the laws of mechanics by the theory of Ampère. It appears that Dr. Faraday’s very remarkable experiment of electrifying and magnetising a ray of polarized light may possibly afford a demonstration of the reality of Ampère’s explanation of the ultimate nature of magnetism.

In this experiment a copper wire 501 feet long was arranged in four concentric spirals, the extremities of which were connected with the poles of a powerful galvanic battery, and a polished prism of heavy glass, or silicated borate of lead, was placed in the axis of the spiral as a core, through the length or axis of which a ray of polarized light was sent. This ray, viewed through a piece of tourmaline or a Nichol’s eye-piece, vanished and reappeared as usual at each quarter revolution of the eye-piece; but when a current of electricity was sent through the spiral at the time the ray had vanished, it instantly reappeared, and remained as long as the electric current continued to flow; but the instant the electricity ceased the light vanished, and as often as the electric current flowed through the spiral, or was interrupted, so often did the polarized ray appear and vanish.

The character of the force thus impressed on the heavy glass is that of rotation, for the stopping and renewing of the electric current had the same effect as the revolving motion of the eye-piece in making the light alternately appear and vanish. Accordingly, Dr. Faraday found that, when the electricity flowed through the spiral in one direction, the rotation of the plane of polarization was right-handed; and when it flowed in the other direction, the rotation of the plane of polarization was left-handed, the rotation increasing with the length of the prism and the intensity of the electricity. The same phenomena were produced by a very powerful magnet when a ray of polarized light was sent through the heavy glass parallel to the line of magnetic force.

Heavy glass or silico-borate of lead has the property more than any other substance of making light rotate under electric and magnetic influence; but many substances have the property more or less, as flint and crown glass, rock salt, all the fixed and essential oils, water, and many other liquids, but none of the gases possess it. In those substances that have the power of circular polarization naturally, the magnetic and electric influences increase or diminish the rotation according to its direction.

Polarized heat is made to revolve in the same manner, when the medium through which it passes is subject to magnetic influence.

Mr. Grove observes that if light and heat be merely modes of force, which there is every reason to believe that they are, it may be fairly stated that in these experiments magnetism affects these forces directly; for light and heat being, in that view, motions of ordinary matter, magnetism in affecting these movements affects the forces which occasion them. If, however, this effect of magnetism be a molecular change of the matter transmitting the light and heat, then it follows that the light and heat are indirectly affected by the electricity or magnetism. Dr. Faraday says that the magnetic forces do not act on the ray of light directly, without the intervention of matter, but through the mediation of the substance in which they and the ray have a simultaneous existence; the substances and the forces giving to and receiving from each other the power of acting on the light. Dr. Thomson has shown, by a mathematical investigation of the subject, that Dr. Faraday’s discovery seems to prove the truth of Ampère’s explanation of the ultimate nature of magnetism. However, in Ampère’s theory, the current of electricity flowing round the iron makes it a permanent magnet, but it does not make the heavy glass or the other bodies, which have the same property, either temporary magnets when the light is rotating within them, or permanent magnets when the inductive action of the current of electricity ceases. Hence the molecular condition of the substances, when the light is rotating in them, must be specifically distinct from that of magnetised iron: it must therefore be a new magnetic condition, and the force which the matter in this state possesses must be a new magnetic force.

After describing his admirable experiment, Dr. Faraday observes that “it has established for the first time a true, direct relation and dependence between light and the magnetic and electric forces; and thus a great addition is made to the facts and considerations which tend to prove that all natural forces are tied together, and have one common origin. It is no doubt difficult, in the present state of our knowledge, to express our expectations in exact terms; and though I have said that another of the powers of nature is in these experiments directly related to the rest, I ought perhaps rather to say that another form of the great power is distinctly and directly related to the other forms; or that the great power manifested by particular phenomena in particular forms is here further identified and recognised by the direct relation of its form of light to its forms of electricity and magnetism. The relation existing between polarized light and magnetism and electricity is even more interesting than if it had been shown to exist with common light only. It cannot but extend to common light; and, as it belongs to light made in a certain respect more precise in its character and properties by polarization, it collates and connects it with these powers in that duality of character which they possess, and yields an opening, which before was wanting to us, for the appliances of these to the investigation of the nature of this and other radiant agencies.” Thus Dr. Faraday’s experiment not only shows the increasing connexion between the sciences, but the tendency of all the forces of nature to merge in one great and universal power.

In the action of a magnet upon the stratifications of an electrical discharge Mr. Gassiot has discovered a new instance of the connexion between magnetism and light.

SECTION XXXII.

Magneto-Electricity—Volta-Electric Induction—Magneto-Electric Induction—Identity in the Action of Electricity and Magnetism—Description of a Magneto-Electric Apparatus and its Effects—Identity of Magnetism and Electricity—The Submarine Telegraph.

FROM the law of action and reaction being equal and contrary, it might be expected that, as electricity powerfully affects magnets, so, conversely, magnetism ought to produce electrical phenomena. By proving this very important fact from the following series of interesting and ingenious experiments, Dr. Faraday has added another branch to the science which he has named magneto-electricity. A great quantity of copper wire was coiled in the form of a helix round one half of a ring of soft iron, and connected with a galvanic battery; while a similar helix connected with a galvanometer was wound round the other half of the ring, but not touching the first helix. As soon as contact was made with the battery, the needle of the galvanometer was deflected. But the action was transitory; for, when the contact was continued, the needle returned to its usual position, and was not affected by the continual flow of the electricity through the wire connected with the battery. As soon, however, as the contact was broken, the needle of the galvanometer was again deflected, but in the contrary direction. Similar effects were produced by an apparatus consisting of two helices of copper wire coiled round a block of wood, instead of iron, from which Dr. Faraday infers that the electric current passing from the battery through one wire induces a similar current through the other wire, but only at the instant of contact, and that a momentary current is induced in a contrary direction when the passage of the electricity is suddenly interrupted. These brief currents or waves of electricity were found to be capable of magnetizing needles, of passing through a small extent of fluid, and, when charcoal points were interposed in the current of the induced helix, a minute spark was perceived as often as the contacts were made or broken, but neither chemical action nor any other electric effects were obtained. A deviation of the needle of the galvanometer took place when common magnets were employed instead of the Voltaic current; so that the magnetic and electric forces are identical in their effects in this experiment. Again, when a helix formed of 220 feet of copper wire, into which a cylinder of soft iron was introduced, was placed between the north and south poles of two bar magnets, and connected with the galvanometer by means of wires from each extremity, as often as the magnets were brought into contact with the iron cylinder it became magnetic by induction, and produced a deflection in the needle of the galvanometer. On continuing the contact the needle resumed its natural position, and, when the contact was broken, deflection took place in the opposite direction; when the magnetic contacts were reversed, the deflection was reversed also. With strong magnets, so powerful was the action, that the needle of the galvanometer whirled round several times successively; and similar effects were produced by the mere approximation or removal of the helix to the poles of the magnets. Thus it was proved that magnets produce the very same effects on the galvanometer that electricity does. Though at that time no chemical decomposition was effected by these momentary currents which emanate from the magnets, they agitated the limbs of a frog; and Dr. Faraday justly observes, that “an agent which is conducted along metallic wires in the manner described, which, whilst so passing, possesses the peculiar magnetic actions and force of a current of electricity, which can agitate and convulse the limbs of a frog, and which finally can produce a spark by its discharge through charcoal, can only be electricity.” Soon after he completely established the identity of the two powers by producing the spark, heating metallic wires, and accomplishing chemical decomposition. Hence it appears that electrical currents are evolved by magnets, which produce the same phenomena with the electrical currents from the Voltaic battery: they, however, differ materially in this respect—that time is required for the exercise of the magnetico-electric induction, whereas Volta-electric induction is instantaneous.

Thus the effect of induction or the influence of the spiral wire in increasing the electric and magnetic power is very great indeed, and to that we are indebted for the electric telegraph, for Voltaic electricity alone is too feeble to overcome the resistance of a long wire.

Electric currents, whatever their tension may be, produce the phenomena of induction; these again induce other currents in bodies capable of induction, and so on indefinitely; the first and second flow in the same direction, the others alternately opposite and direct. They all give the shock and can decompose water, but with Volta-electric currents the elevation of temperature as well as their physiological and magnetic effects are produced by instantaneous actions, which only depend upon the quantity and tension of the current, and by no means on its duration, for induced currents only exist for a moment when the circuit of the battery is broken. The most energetic physiological effects are produced by a small quantity of electricity moving with great velocity. The apparatus first employed by Dr. Faraday is in effect a battery, where the agent is the magnetic instead of the Voltaic force, or, in other words, electricity, and is thus constructed:—

A very powerful horseshoe magnet, formed of twelve steel plates in close approximation, is placed in a horizontal position. An armature, consisting of a bar of the purest soft iron, has each of its ends bent at right angles, so that the faces of those ends may be brought directly opposite and close to the poles of the magnet when required. Ten copper wires—covered with silk, in order to insulate them—are wound round one half of the bar of soft iron, as a compound helix: ten other wires, also insulated, are wound round the other half of the bar. The extremities of the first set of wires are in metallic connexion with a circular disc, which dips into a cup of mercury, while the ends of the other ten wires in the opposite direction are soldered to a projecting screw-piece, which carries a slip of copper with two opposite points. The steel magnet is stationary; but when the armature, together with its appendages, is made to rotate vertically, the edge of the disc always remains immersed in the mercury, while the points of the copper slip alternately dip in it and rise above it. By the ordinary laws of induction, the armature becomes a temporary magnet while its bent ends are opposite the poles of the steel magnet, and ceases to be magnetic when they are at right angles to them. It imparts its temporary magnetism to the helices which concentrate it; and, while one set conveys a current to the disc, the other set conducts the opposite current to the copper slip. As the edge of the revolving disc is always immersed in the mercury, one set of wires is constantly maintained in contact with it, and the circuit is only completed when a point of the copper slip dips in the mercury also; but the circuit is broken the moment that point rises above it. Thus, by the rotation of the armature, the circuit is alternately broken and renewed; and as it is only at these moments that electric action is manifested, a brilliant spark takes place every time the copper point leaves the surface of the mercury. Platinum wire is ignited, shocks smart enough to be disagreeable are given, and water is decomposed with astonishing rapidity, by the same means; which proves, beyond a doubt, the identity of the magnetic and electric agencies, and places Dr. Faraday, whose experiments established the principle, in the first rank of experimental philosophers.

A magneto-electric machine has been recently constructed by Mr. Henley, of enormous power. It consists of two permanent magnets, from which the induction is obtained; each of these is formed of thirty horseshoe steel magnets, two feet and a half long, and from four to five inches broad, and each is surrounded by a coil of wire six miles long, coated with silk to insulate the coils. A shock from these wires would be instantaneous death. This apparatus will ultimately be employed to send a stream of electricity through long submarine and subterraneous wires; but a Volta-electric machine has hitherto been used, in which the electricity is generated by a galvanic battery instead of magnets.

Induction, or the effect of the spiral wires in augmenting the power of Voltaic electricity, is admirably illustrated in the Atlantic telegraph.

Wires that are to convey electricity under ground, or through water, must be defended from injury and insulated to prevent the lateral escape of the electricity. For that purpose the cable that is laid at the bottom of the Atlantic, from near Valentia in Ireland to Trinity Bay in Newfoundland, is formed of seven fine copper wires which convey the electricity, bound together by a coating of gutta percha, over which there are layers of cloth dipped in pitch, and then the whole is covered by steel wires twisted together in strands and twined round in long close spirals, forming a cord or cable not more than an inch and a quarter in diameter, and 2100 miles long. The use of the gutta percha is to insulate the wires; the other coatings are merely for protection.

The Voltaic battery which generates the electricity consists of 40 cells, the plates of which are alternately of zinc and platinized silver, each about nine inches square, the exciting fluid being dilute sulphuric acid. Although the force developed by this battery is so great that a piece of iron three inches long and three eighths of an inch in diameter placed in contact with the poles may be consumed in a few minutes, it is absolutely incapable of sending a current of electricity through wires 2500 miles long, on account of their resistance, without the aid of Dr. Faraday’s inductive action. It is only the primary agent for inducing a current of sufficient strength.

To accomplish that, many thousand yards of fine copper wire coated with silk are wound round a hollow soft iron cylinder; the whole is then coated by gutta percha, and the end of the wire is joined to the wires in the cable so as to form a continuous line from Valentia to Newfoundland. A second copper wire, shorter but thicker than the preceding, and also insulated by a coating of silk, is wound round the cylinder above the gutta percha: when the ends of this thick wire are brought into contact with the poles of the battery, currents of electricity flow through it, between pole and pole, and in their passage temporarily convert the hollow iron cylinder into a powerful electro-magnet, which by its reaction induces a current of electricity in the fine wire of sufficient power to cross the Atlantic. The efficiency of the electric telegraph depends upon the power we possess of breaking and renewing the current at pleasure, since by that means distinct and successive signals are made from station to station. In the Atlantic cable positive and negative electricity are transmitted alternately; the electricity is sent to America from alternate poles, and the current returns again through the water, which completes the circuit.

The passage of electricity through a cable or telegraphic wire in air is sensibly instantaneous; that through a cable, whether extended in water or under ground, requires time on account of lateral induction through the gutta percha; for the electricity, in passing through the wires, induces the opposite electricity on the surface of the water or moist earth in contact with the cable, and in that respect it is precisely like a Leyden jar, the gutta percha representing the glass. As the power of induction is proportional to the tension of the electricity, and as the tension is continually diminished by the resistance of the wires, the induction is continually diminished and requires a longer time. Electricity took two seconds to pass through a cable 768 miles long, laid under ground from London to Manchester, and back again twice; while in air it was all but instantaneous, because the inductive capacity of air is very much less than that of water or moist earth. In the experiment with the cable under ground it took two-thirds of a second to overcome the resistance of the wires, and then the velocity of the electricity was 1000 miles in a second, and it was the same whatever the intensity of the electricity.

It has already been mentioned that the efficiency of the electric telegraph depends upon the breaking and renewing the current of electricity by means of which a succession of waves of electricity are sent through the conducting wires. Now it has been ascertained that three electric waves may travel simultaneously through the wires of the Atlantic telegraph with sufficient intervals between them to record the indications they are intended to convey; that is, three signals can be intelligibly and practically transmitted in two seconds.

The original design, structure, and difficulty of depositing the cable are only equalled by the talent and perseverance with which it has been done. The 5th of August, 1858, will be memorable for the accomplishment of the boldest enterprise that ever was undertaken by man, and which is only the beginning of a vast submarine communication that will ultimately encircle the globe. It has been granted to British genius thus to annihilate time and space, in order to connect all mankind into one great family for their moral and religious advancement; and, whatever may be the fate of the British Islands in the course of ages, to their energetic race the glory will remain of having been the chief instruments in the hands of Providence for the civilization of the world—a civilization which will extend with the development of their numerous colonies into great independent Christian states, like those of the Union in North America. The thunderbolt snatched from heaven by Franklin now passes through the depths of the Atlantic as a messenger of peace between the kindred nations.[16]

In telegraphs on land the intensity of the battery or magnets is increased by induction on the same principle. It is by intensity that the electric current is enabled to pass through the wires, and that is augmented by increasing the number of coils round the cylinder: however, it is only advantageous when the distance between the stations is great, for then the resistance in the additional coils bears a small proportion to the resistance offered by very long wires, but a very great proportion to that opposed in very short ones. The nice adjustment for each case has been determined by the experiments of eminent electricians, and all the arrangements have been brought to great perfection in this wonderful triumph of science, which is due to Volta, who called into existence the fiery stream, and to Faraday, who has given it the energy of the lightning.

When the length of the wire in the helices of an electro-magnet is very great, it offers increasing resistance to the passage of the electricity, so that the cessation of magnetism is not instantaneous when the contact with the Voltaic battery is broken. To remedy that defect an instrument has been invented which instantaneously deprives the apparatus of the remaining electricity. A great length of fine wire gives the severest shocks, while a shorter and thicker wire gives the longest sparks and ignites the greatest quantity of platinum wire.

Ruhmkorff’s electro-inductive apparatus has either been improved, or new machines constructed, by Messrs. Grove, Gassiot, and Joule, of intense energy. Indeed, so great is the energy of electro-induction, that hopes were entertained of its superseding steam as a motive power. For the current of electricity from an electro-magnet can be made to flow in opposite directions, so as to produce alternate attractions and repulsions, and consequently a continued motion, which might be applied as a motive force to machinery. However, Mr. Joule has proved that the power developed by one pound of coal in combustion is to that produced by one pound of zinc consumed in Mr. Grove’s powerful electro-magnetic apparatus as nine to one, so that, even if zinc were as cheap as coal, and a Voltaic battery as easily kept in order as an engine-furnace, electricity will not supersede steam as a motive power.

A current of electricity traversing a conductor gives out a quantity of heat determined by fixed laws, the amount of which is invariable as long as the machine to which it is applied remains at rest; but the instant the machine is set in motion a reaction takes place in the intensity of the current, causing a diminution in the quantity of heat, because the heat that disappears is converted into the mechanical force exerted by the engine.

Mr. Joule’s experiments prove that, whenever a current of electricity is generated by a magneto-electric machine, the quantity of heat evolved by that current has a constant relation to the power required to work the machine; and on the other hand, whenever an engine is worked by a Voltaic battery, that the power developed is at the expense of the calorific force of the battery for a given consumption of zinc, the mechanical effect produced having a fixed relation to the heat lost in the Voltaic current. The obvious conclusion Mr. Joule draws from these experiments is, that heat and mechanical power are convertible into one another, and it becomes evident, therefore, that heat is either the vis viva or living force of ponderable particles, or a state of attraction and repulsion capable of generating vis viva (N. 222).

SECTION XXXIII.

Electricity produced by Rotation—Direction of the Currents—Electricity from the Rotation of a Magnet—M. Arago’s Experiment explained—Rotation of a Plate of Iron between the Poles of a Magnet—Relation of Substances to Magnets of three Kinds—Thermo-Electricity.

M. ARAGO discovered a source of magnetism in rotatory motion. If a circular plate of copper be made to revolve immediately above or below a magnetic needle or magnet, suspended in such a manner that it may rotate in a plane parallel to that of the copper plate, the magnet tends to follow the circumvolution of the plate; or, if the magnet revolves, the plate tends to follow its motion; so powerful is the effect, that magnets and plates of many pounds weight have been carried round. This is quite independent of the motion of the air, since it is the same when a pane of glass is interposed between the magnet and the copper. When the magnet and the plate are at rest, not the smallest effect, attractive, repulsive, or of any kind, can be perceived between them. In describing this phenomenon, M. Arago states that it takes place not only with metals, but with all substances, solids, liquids, and even gases, although the intensity depends upon the kind of substance in motion. Experiments made by Dr. Faraday explain this singular action. He found that, if a piece of metal or a metallic wire forming a circuit of any form be moved from right to left across the lines of force proceeding from the pole of a bar magnet, these lines of force induce a current of electricity flowing in one direction; and when the motion of the metal or wire is reversed, the direction of the current is reversed also: the rotation of the magnet about its axis has no effect on these results, and no current is induced when the metal or wire is at rest. A plate of copper, twelve inches in diameter and one fifth of an inch thick, was placed between the poles of a powerful horseshoe magnet, consequently crossing the magnetic lines of force at right angles, and connected at certain points with a galvanometer by copper wires. When the plate was at rest no effect was produced; but as soon as the plate was made to revolve rapidly the galvanometer needle was deflected sometimes as much as 90°, and by a uniform rotation the deflection was constantly maintained at 45°. When the motion of the copper plate was reversed, the needle was deflected in the contrary direction, and thus a permanent current of electricity was evolved by an ordinary magnet. The intensity of the electricity collected by the wires, and conveyed by them to the galvanometer, varied with the position of the plate relatively to the poles of the magnet.

The motion of the electricity in the copper plate may be conceived by considering that, merely by moving a single wire, like the spoke of a wheel, before a magnetic pole, a current of electricity tends to flow through it from one end to the other. Hence, if a wheel be constructed of a great many such spokes, and revolved near the pole of a magnet in the manner of the copper disc, each radius or spoke will tend to have a current produced in it as it passes the pole. Now, as the circular plate is nothing more than an infinite number of radii or spokes in contact, the currents will flow in the direction of the radii if a channel be open for their return; and, in a continuous plate, that channel is afforded by the lateral portions on each side of the particular radius close to the magnetic pole. This hypothesis is confirmed by observation; for the currents of positive electricity set from the centre to the circumference, and the negative from the circumference to the centre, and vice versâ, according to the position of the magnetic poles and the direction of rotation; so that a collecting wire at the centre of the copper plate conveys positive electricity to the galvanometer in one case, and negative in another; that collected by a conducting wire in contact with the circumference of the plate is always the opposite of the electricity conveyed from the centre. It is evident that, when the plate and magnet are both at rest, no effect takes place, since the electric currents which cause the deflection of the galvanometer are only induced by motion across the magnetic lines of force. When the plate is placed edgewise so as to be parallel to these lines of force, no revolution of it with the most powerful magnet produces the slightest signs of a current at the galvanometer. The same phenomena may be produced by electro-magnets. The effects are similar when the magnet rotates and the plate remains at rest. When the magnet revolves uniformly about its own axis, electricity of the same kind is collected at its poles, and the opposite electricity at its equator.

The phenomena which take place in M. Arago’s experiments may be explained on this principle. When both the copper plate and the magnet are revolving, the action of the induced electric current tends continually to diminish their relative motion, and to bring the moving bodies into a state of relative rest; so that, if one be made to revolve by an extraneous force, the other will tend to revolve about it in the same direction, and with the same velocity.

When a plate of iron, or of any substance capable of being made either a temporary or permanent magnet, revolves between the poles of a magnet, it is found that dissimilar poles on opposite sides of the plate neutralize each other’s effects, so that no electricity is evolved; while similar poles on each side of the revolving plate increase the quantity of electricity, and a single pole end-on is sufficient. But when copper, and substances not sensible to ordinary magnetic impressions, revolve, similar poles on opposite sides of the plate neutralize each other; dissimilar poles on each side exalt the action; and a single pole at the edge of the revolving plate, or end-on, does nothing. This forms a test for distinguishing the ordinary magnetic force from that produced by rotation. If unlike poles, that is, a north and south pole, produce more effect than one pole, the force will be due to electric currents; if similar poles produce more effect than one, then the power is not electric. These investigations show that there are really very few bodies magnetic in the manner of iron. Dr. Faraday therefore arranges substances in three classes, with regard to their relation to magnets:—those affected by the magnet when at rest, like iron, steel, and nickel, which possess ordinary magnetic properties; those affected when in motion, in which electric currents are evolved by the inductive force of the magnet, such as copper; and, lastly, those which are perfectly indifferent to the magnet, whether at rest or in motion.

It has already been observed that three bodies are requisite to form a galvanic circuit, one of which must be fluid. But, in 1822, Professor Seebeck, of Berlin, discovered that electric currents may be produced by the partial application of heat to a circuit formed of two solid conductors. For example, when a semicircle of bismuth, joined to a semicircle of antimony, so as to form a ring, is heated at one of the junctions by a lamp, a current of electricity flows through the circuit from the antimony to the bismuth; and such thermo-electric currents produce all the electro-magnetic effects. A compass needle, placed either within or without the circuit, and at a small distance from it, is deflected from its natural position, in a direction corresponding to the way in which the electricity is flowing. If such a ring be suspended so as to move easily in any direction, it will obey the action of a magnet brought near it, and may even be made to revolve. According to the researches of M. Seebeck, the same substance, unequally heated, exhibits electrical currents; and M. Nobili observed, that in all metals, except zinc, iron, and antimony, the electricity flows from the hot part towards that which is cold. That philosopher attributes terrestrial magnetism to a difference in the action of heat on the various substances of which the crust of the earth is composed; and, in confirmation of his views, he has produced electrical currents by the contact of two pieces of moist clay, of which one was hotter than the other.

M. Becquerel constructed a thermo-electric battery of one kind of metal, by which he has determined the relation between the heat employed and the intensity of the resulting electricity. He found that, in most metals, the intensity of the current increases with the heat to a certain limit, but that this law extends much farther in metals that are difficult to fuse, and which do not rust. The experiments of Professor Cumming show that the mutual action of a magnet and a thermo-electric current is subject to the same laws as those of magnets and galvanic currents; consequently all the phenomena of repulsion, attraction, and rotation may be exhibited by a thermo-electric current. M. Botto, of Turin, has decomposed water and some solutions by thermo-electricity; and the Cav. Antinori of Florence succeeded in obtaining a brilliant spark with the aid of an electro-dynamic coil.

The principle of thermo-electricity has been employed by MM. Nobili and Melloni for measuring extremely minute quantities of heat in their experiments on the instantaneous transmission of radiant heat. The thermo-multiplier, which they constructed for that purpose, consists of a series of alternate bars, or rather fine wires of bismuth and antimony, placed side by side, and the extremities alternately soldered together. When heat is applied to one end of this apparatus, the other remaining at its natural temperature, currents of electricity flow through each pair of bars, which are conveyed by wires to a delicate galvanometer, the needle of which points out the intensity of the electricity conveyed, and consequently that of the heat employed. This instrument is so delicate that the comparative warmth of different insects has been ascertained by means of it.

The conservation of force is strictly maintained throughout the whole science and different forms of electricity. In static electricity the positive and negative forces exactly balance one another; they are always simultaneous, and related often by curved lines of force; there is no defect or surplus, and the existence of one kind without the other is utterly impossible—it is absolutely a dual force. The very same may be said of electric currents, whether produced by the Voltaic battery or in any other way—the current in one part of the circuit is absolutely the same in amount and dual character as the other; and in the insulated Voltaic battery, where the sustaining power is internal, not the slightest development of the forces of either of these can occur till the circuit is completed or induction allowed at the extremities; for if when there is no circuit the induction be prevented, not merely no current, but no quantity of electricity at the poles ready to produce a current, can be evolved in the slightest degree.[17]

SECTION XXXIV.

Magnetism a Dual Power—Antithetic Character of Paramagnetism and Diamagnetism—The Earth Paramagnetic—Properties of Paramagnetic Bodies—Polarity—Induction—Lines of Magnetic Force—Currents of Electricity induced by them—Proved to be Closed Curves—Analogy and Identity of Electricity and Magnetism—Terrestrial Magnetism—Mean Values of the Three Magnetic Elements—Their Variations in Double Progression proved to consist of Two Superposed Variations—Discovery of the Periodicity of the Magnetic Storms—The Decennial Period of the Magnetic Elements the same with that of the Solar Spots—Magnetism of the Atmosphere—Diamagnetism—Action of Electro-Magnetism on Paramagnetic, Diamagnetic Bodies, and on Copper, very different—Proof of Diamagnetic Polarity and Induction—Magnecrystallic Action—Effects of Compression, Heat, and Cleavage on Magnetic Bodies—Mutual Dependence of Light, Heat, Electricity, &c. &c.—The Conservation of Force and the Permanency of Matter Primary Laws of Nature—Definition of Gravity not according to that Law—Gravity only the Residual Force of a Universal Power—Magnetism of the Ethereal Medium.

MAGNETISM may be regarded as a new science in consequence of the profound researches and admirable discoveries of Dr. Faraday. Since the magnetism of matter is only known by the action of a magnet or of electricity upon it, by using an extremely energetic magnet or electro-magnet he has proved that all known substances, whether solid, liquid, or aëriform, are more or less magnetic, but that the magnetism is very different in different substances. For example, if a bar of iron be freely suspended between the poles of a very powerful magnet or electro-magnet, it will be attracted by both poles, and will set or rest in the direction of a straight line joining them; but if a similar bar of bismuth be freely suspended in the same manner, it will rest in a direction at right angles to that which the iron bar assumed. Thus the direction in which the iron sets is axial or in the line of force, while that which the bismuth assumes is equatorial or perpendicular to the line of force. Substances that are magnetic after the manner of iron are said to be paramagnetic, those that are magnetic after the manner of bismuth are diamagnetic. As far as we know, all matter comes under one or other of these laws. Many bodies are paramagnetic besides iron, as the loadstone, which consists of the peroxide and protoxide of iron mixed with small portions of silica and alumina; also some of the gems and metals, as cobalt, nickel, &c. A substance is often paramagnetic if it contains only the 130,000th part of its weight of iron; but by far the greater number are diamagnetic, as all animal and vegetable matter, acids, oils, sugar, starch, bread, &c., and all the gases except oxygen, which is highly paramagnetic; and its force increases with its density: but notwithstanding the predominance of diamagnetic matter at the surface, the terrestrial globe is paramagnetic—in fact it is a powerful magnet.

Besides the substances which are paramagnetic naturally, that property may be imparted by a variety of methods, as by friction with magnets or even juxtaposition with them; and a bar of hard steel held at the angle of the dip will become a magnet on receiving a few strokes with a hammer on its upper end.

Polarity is one of the most distinguishing characters of magnetism: it is the property which a magnet possesses when freely suspended of resting spontaneously in the magnetic meridian, or nearly north and south, and always returning to that position when disturbed in consequence of the mean magnetic attraction of the earth; yet the magnet has no tendency to move to the north or south even when floating on water, because the same pole that attracts one end repels the other. Both poles of a magnet attract iron, which in return attracts either pole of the magnet with an equal and contrary force. The action of a magnet on unmagnetised iron is confined to attraction, whereas the reciprocal agency of magnets is characterised by a repulsive as well as by an attractive force; for a north pole repels a north pole, and a south pole repels a south pole; but a north and south pole mutually attract one another—which proves that paramagnetism is a dual power in which the conservation of force is perfectly maintained, for the force of attraction is exactly equal to the force of repulsion. One kind of polarity cannot exist without the other: they are absolutely simultaneous, dependent, and of equal intensity.

Induction is the power which a magnet possesses of exciting temporary or permanent paramagnetism in such bodies in its vicinity as are capable of receiving it. By this property the mere approach of a magnet renders iron and steel paramagnetic, the more powerfully the less the distance, but the induced force is always exactly equal to the force which produces it. When the north end of a magnet is brought near to, and in the line with, an unmagnetised iron bar, the bar acquires all the properties of a perfect magnet; the end next the north pole of the magnet becomes a south pole, while the remote end becomes a north pole. Exactly the reverse takes place when the south end is presented to the bar, so that each pole of a magnet induces the opposite polarity in the adjacent end of the bar, and the same polarity in the remote extremity; consequently the nearest extremity of the bar is attracted, and the farther repelled; but as the action is greater on the adjacent than on the distant part, the resulting force is that of attraction. By induction the iron bar not only acquires polarity, but the power of inducing paramagnetism in a third body; and although all these properties vanish from the iron as soon as the magnet is removed, a lasting increase of intensity is generally imparted to the magnet itself by the reaction of the temporary paramagnetism of the iron. Iron acquires the inductive force more rapidly than steel, yet it loses it as quickly on the removal of the magnet, whereas the steel is impressed with a lasting polarity.

A certain time is requisite for induction, and it may be accelerated by anything that excites a vibratory motion in the particles of the steel; such as the smart stroke of a hammer, or heat succeeded by sudden cold. A steel bar may be converted into a magnet by the transmission of an electric discharge through it; and as its efficacy is the same in whatever direction the electricity passes, the effect arises from its mechanical operation exciting a vibration among the particles of the steel. It has been observed that the particles of iron easily resume their neutral state after induction, while those of steel resist the restoration of equilibrium, or a return to the neutral state: it is therefore evident that any cause which removes or diminishes the resistance of the particles will tend to destroy the paramagnetism of the steel; consequently the same mechanical means which develop the power will also destroy it. On that account a steel bar may lose its paramagnetism by any mechanical concussion, such as by falling on a hard substance, a blow with a hammer, and heating to redness, which makes the steel soft. The circumstances which determine whether it shall gain or lose are its position with respect to the magnetic equator, and the higher or lower intensity of its previous magnetic state.

A comparison of the number of vibrations accomplished by the same magnetised needle during the same time at different distances from a magnet gives the law of paramagnetic intensity, which follows the inverse ratio of the square of the distance—a law that is not affected by the intervention of any substance whatever between the magnet and the needle, provided the substance be not itself susceptible of magnetism. Induction and the reciprocal action of magnets are therefore subject to the laws of mechanics; but the composition and resolution of the forces are complicated in consequence of four forces being constantly in activity, two in each magnet. Mr. Were Fox discovered that the law of the paramagnetic force changes from the inverse square of the distance to the simple inverse ratio when the distance between two magnets is as small as from the fourth to the eighth of an inch, or even as much as half an inch when the magnets are large; and in the case of repulsion, that the change takes place at a still greater distance, especially when the two magnets differ materially in intensity.

Without assuming any hypothesis of what magnetism is, or how that force is originated or sustained, Dr. Faraday regards a magnet as a source of power surrounded by curved lines of force which are not only representants of the magnetic power in quality and direction, but also in quantity—an hypothesis which accords perfectly with experiment, and with the action both of electricity and magnetism. The nature and form of these lines may be seen by placing a bar magnet upon a table, spreading a sheet of stiff paper over it so as to be perfectly level and free from creases, and then sifting very clean iron filings through a fine sieve equably over it. The filings will instantly assume the form of the curved lines represented by fig. 1, plate 7, in consequence of the action of the magnet. These lines are the true representatives of the magnetic forces, and being related to a polar power, they have opposite qualities in opposite directions. When a magnet is broken across the middle, each part is at once converted into a perfect magnet; the part that originally had a south pole acquires a north pole at the fractured end; the part that had originally a north pole gets a south pole; and as far as mechanical division can be carried, it is found that each fragment is a perfect magnet. Fig. 2, plate 7, shows the lines of force in a fractured magnet when the ends are not yet separated; fig. 3 shows them when they are.

Currents of electricity are produced in conducting bodies moved across these lines of magnetic force. If a copper wire at a little distance above the north pole of a bar magnet be moved from left to right, at any angle across the lines of magnetic force, they will induce a current of electricity in the wire flowing from right to left; if the wire be moved with the same velocity in the contrary direction, the induced current will be of equal intensity, but it will flow from left to right. Similar results are obtained from the south pole, and the phenomena are the same when the magnet is moved and the wire is at rest; in both cases the intensity is greater the swifter the motion. It appears that the quantity of electricity induced is directly as the amount of the magnetic curves intersected, and when a wire is moving uniformly in a field of equal magnetic force, the current of electricity generated is proportional to the time, and also to the velocity of motion; for when a metallic disc is made to revolve through the lines of force, the current induced is strongest near the edge where the velocity is greatest; and in different substances moving across the lines of force the intensity of the induced current is directly as the conducting power of the substance. Thus bodies moved near a magnet have an electrical current developed in them, and conversely bodies affected by an electric current are definitely moved by a magnet near them.

By the preceding experiments it appears that magnetic polarity is manifested in two ways; in the magnetised needle, by attraction and repulsion, and in a wire moving across lines of magnetic force it is shown by the opposite directions in which the induced current flows according as the body is moved from the right to the left, or left to right. Hence polarity consists in the opposite and antithetical actions manifested at the opposite ends or opposite sides of a limited or unlimited line of force. Antithesis is the true and most general character of magnetism, whatever may be its mode of action.

It was by the induction of electric currents in copper wires moving across the lines of magnetic force that Dr. Faraday proved that the lines of force issuing from a magnet are closed curves which return again and pass through the interior of the magnet. He placed two bar magnets of the same length, size, and intensity with their similar poles together, so that they might act as one magnet. A copper wire was then passed between their axes, which after extending through half their length was bent up equatorially and turned back along the outside, so that the whole wire formed a loop, the two ends being connected with a galvanometer. When the whole wire was made to revolve, no effect was produced, although it crossed the lines of magnetic force; but when it was cut in two, so as to separate the external from the internal part, electrical currents of equal intensity, but in contrary directions, were induced in each portion of the wire as they were made separately to cross the lines of force, for the apparatus was so constructed that that could be done. The exterior wire crossed the lines of force which issued from the magnets at right angles to their axes, while the equatorial part of the interior wire traversed the returning lines of force. It is evident that these forces neutralized each other when the whole wire revolved: consequently the internal and external lines of force must have been of equal intensity and opposite in direction, so as to balance one another. By this and a very great number of other experiments Dr. Faraday has proved that the magnetic lines of force are continuous closed curves alike in shape, size, and power. They extend indefinitely beyond the magnet, and undergo no change by distance.

Thus the magnetic force pervades the interior of the mass; if electricity does the same, a compensation must either take place, or it also must move in lines of force, sensible only at the surface. Electricity has a perpetual tendency to escape, and does escape, when not prevented by the coercive power of the air, and other non-conducting substances. Such a tendency does not exist in magnetism, which never leaves the substance containing it under any circumstances whatever. There must be some coercive force, analogous to friction, which arrests the magnetic forces, so as first to oppose their separation, and then to prevent their reunion. In soft iron the coercive force is either wanting or extremely feeble, since iron is easily rendered paramagnetic by induction, and as easily loses that quality; whereas in steel the coercive force is extremely energetic, because it prevents the steel from acquiring the paramagnetic properties rapidly, and entirely hinders it from losing them when acquired. The feebleness of the coercive force in iron, and its energy in steel, with regard to the paramagnetic force, is perfectly analogous to the facility of transmission afforded to electricity by non-electrics, and the resistance it experiences in electrics. At every step the analogy between electricity and magnetism becomes more striking. The agency of attraction and repulsion is common to both; the positive and negative electricities are similar to the northern and southern polarities, and are governed by the same laws—namely, that between like powers there is repulsion, and between unlike powers there is attraction. Each of these four forces is capable of acting most energetically when alone; but as the electric equilibrium is restored by the union of the two electric states, and magnetic neutrality by the combination of the two polarities, they respectively neutralise each other when joined. All these forces vary inversely as the square of the distance, and consequently come under the same mechanical laws.

A like analogy extends to magnetic and electric induction. Iron and steel are in a state of equilibrium when neutral; but this equilibrium is immediately disturbed on the approach of the pole of a magnet, which by induction transfers one kind of polarity to one end of an iron or steel bar, and the opposite kind to the other—effects exactly similar to electrical induction. There is even a correspondence between the fracture of a magnet and that of an electric conductor; for if an oblong conductor be electrified by induction, its two extremities will have opposite electricities; and if in that state it be divided across the middle, the two portions, when removed to a distance from one another, will each retain the electricity that has been induced upon it. The analogy, however, does not extend to transference. A body may transfer a redundant quantity of positive electricity to another, or deprive another of its electricity—the one gaining at the expense of the other; but a body cannot possess only one kind of polarity. With that exception, there is such perfect correspondence between the theories of magnetic attractions and repulsions, and electric forces in conducting bodies, that they not only are the same in principle, but are determined by the same formulæ. Experiment concurs with theory in proving the identity of these two influences. Hence, if the electrical phenomena be due to a modification of the ethereal medium, the magnetic phenomena must be owing to an analogous cause.

Curved lines of magnetic force issue from every point of the earth’s surface where there is sensible dip, and bending round enter the earth again at the magnetic equator. They induce electric currents in conducting-wires, moving across them exactly the same as in artificial magnets; and when a hollow helix, or coil of copper wire, whose extremities are connected with a galvanometer, is placed in the magnetic dip, and suddenly moved across the lines of force, the needle of the galvanometer will vibrate through an arc of 80° or 90°, in consequence of the electric current induced by these lines of magnetic force in the wire, and the action is greater when a core of soft iron is placed in the helix, which becomes a temporary magnet by induction. Again, if a copper plate be connected with a galvanometer by two copper wires, one from the centre, and another from the circumference, in order to collect and convey the electricity, it is found that, when the plate is made to revolve in a plane passing through the line of the dip, the galvanometer is not affected. But as soon as the plate is inclined to that plane, electricity begins to be developed by its motion across the lines of magnetic force; it becomes more powerful as the inclination increases, and arrives at a maximum when the plate revolves at right angles to the line of dip. When the revolution is in the same direction with that of the hands of a watch, the current of electricity flows from its centre to the circumference; and when the rotation is in a contrary direction, the current sets the opposite way. Thus a copper plate, revolving at right angles to the line of the dip, becomes a new electrical machine, differing from the common plate-glass machine by the copper being the most perfect conductor, whereas glass is the most perfect non-conductor; besides insulation, which is essential to the glass machine, is fatal to the copper one. The quantity of electricity evolved by the metal does not appear to be inferior to that devolved by the glass, though very different in intensity. Even a ship crossing the lines of force must have electric currents running through her. Dr. Faraday observes that such is the facility with which electricity is generated by the magnetic lines of force, that scarcely any piece of metal can be moved without a development of it; consequently, among the arrangements of steam-engines and metallic machinery, curious electro-magnetic combinations probably exist which have never yet been noticed. Thus magnetic lines of force certainly issue from the surface of the globe.

No doubt the earth is a magnet on a vast scale, but it differs from all others in having four poles of maximum magnetic force of different intensities, the two in the northern hemisphere having a secular motion in a contrary direction from the two in the southern. They are not even symmetrically placed; hence the magnetic intensity varies so much in the different points on the earth’s surface, that the dynamic equator, or line passing through all the points of least intensity, is a very irregular curve surrounding the globe, but by no means coinciding with the terrestrial equator. In consequence of the mean action of these four forces, the north end of a magnetised needle, arranged so as to revolve in a vertical plane, dips or inclines beneath the horizon in the northern hemisphere, and the south end in the southern. The two hemispheres are separated by a line encircling the earth, called the magnetic equator, or line of no dip, in which the dipping or inclination needle is horizontal. On each side of this line the inclination increases till at last the needle becomes perpendicular to the horizon in two points, or rather small spaces, in each hemisphere, known as the magnetic poles, which are quite different from the poles of the earth’s rotation. The mean action of the four poles of magnetic intensity causes the mariner’s compass, or a magnetic needle suspended so as to revolve in a horizontal plane, to remain at rest when pointing to the two magnetic poles. It is then in the magnetic meridian of the place of observation, which is thus determined by the mean action of all the four magnetic forces.

These mean values of the three magnetic elements, namely, the declination, inclination or dip, and magnetic intensity, are well known to be subject to secular, annual, and diurnal variations. The secular only become sensible after some years, but the annual and diurnal variations have a double progression—that is to say, two maximum and two minimum values in their respective periods of a year and twenty-four hours; for example, the declination needle makes two deviations to the west and two to the east in the course of twenty-four hours, and that with great regularity. Now General Sabine discovered that the double progression arises from two combined or superposed variations having different hours of maxima and minima, and that they are due to two distinctly different causes—the one being the difference in the sun’s position relatively to the place of observation at the different seasons of the year, and hours of the day and night; the other being a mean annual and diurnal variation proved by General Sabine to exist in those great magnetic storms or casual disturbances which affect the magnetic elements simultaneously over enormously extensive tracts of the globe.

Moreover the General discovered that, besides these annual and diurnal variations, the magnetic storms have a variation which accomplishes its vicissitudes in ten or more nearly eleven years, the increase from year to year being gradual, till its maximum becomes twice as great as its minimum value. In consequence of this inequality in the storms or casual disturbances, each of the magnetic elements has a variation of similar period and similar maxima and minima. Now the number and magnitude of the spots on the sun had been observed by M. Schwabe, of Dessau, to increase to a maximum, and decrease again to a minimum, regularly in the very same period of between ten and eleven years; and General Sabine found that this variation in the solar spots, and that in the magnetic elements, not only have the same periods of maxima and minima, but that they correspond in all their minutest vicissitudes. Thus a very remarkable and unexpected connexion exists between terrestrial and solar magnetism. The dual and antagonist principle is perfectly maintained in the earth’s magnetism, all the phenomena and their variations being in opposite directions in the two hemispheres. (N. 226.)

No doubt the magnetic lines of force in the earth are closed curves, as in artificial magnets; but in their circuitous courses they may extend to any distance in space, or rather in the ethereal medium, even to thousands or tens of thousands of miles; for the ethereal medium is permeable to lines of magnetic force, or rather transmits them, otherwise the solar spots could not affect the variations of terrestrial magnetism; besides, they pass through the Torricellian vacuum, which is nearly a void with respect to air, but not to the ethereal medium.

The atmosphere which surrounds the earth to the height of about fifty miles with sensible density, consists of three and a half parts by weight of nitrogen gas and one part of oxygen, uniformly mixed. The nitrogen is neutral whether dense or rare, hot or cold, while the oxygen is highly paramagnetic; but it loses a great part of its force when rarefied by heat; consequently the magnetic force of the atmosphere must increase from the equator to the poles of maximum cold; it must vary summer and winter, night and day. Its effect upon terrestrial magnetism is unknown; but it can hardly be without some influence. M. E. Becquerel observes—“If we reflect that the earth is encompassed by a mass of air equivalent in weight to a layer of mercury of 30 inches, we may inquire whether such a mass of magnetic gas, continually agitated, and submitted to the regular and irregular variations of pressure and temperature, does not intervene in some of the phenomena dependent upon terrestrial magnetism. If we calculate, in fact, what is the magnetic force of this fluid mass, we find that it is equivalent to an immense plate of iron, of a thickness little more than 1/250 of an inch, which covers the whole surface of the globe.” Both the conducting power of the air and its density are increased by cold; and as the sum of the magnetic forces which issue from the earth on one side of the line of no dip is equal to their sum on the other side, the intensity and concentration in our winter are coincident with a diffusion and feebleness in the opposite hemisphere, so that the line of no dip will move annually from north to south and back again. The same holds with regard to day and night. Thus the law of the conservation of force is rigorously maintained; and it is equally so in the effect of the atmosphere on the magnetic lines of force, which refracts them as they pass through it, in one direction in summer, and in the opposite direction in winter—in one direction in the enlightened hemisphere, in the other in that which is dark. The whole of the magnetic lines about the earth are held by their mutual tension in one connected, sensitive system, which feels in every part, even to the antipodes, a change in any particular place.

It may be mentioned as a well-known fact, that apparent anomalies have been found in the diurnal variation of the declination in the high magnetic latitudes of the northern hemisphere when compared with their great regularity in other parts of the same hemisphere, and that the magnetic storms are of much greater magnitude there than in lower latitudes. Moreover, although Captain Maguire’s observations at Cape Barrow, in the North Polar Ocean, show that the annual and diurnal variations of the casual disturbances or magnetic storms, as well as those of the decennial period, are maintained, yet it appears that at certain hours of the day the disturbance in the declination may be easterly at Point Barrow, and westerly at the Magnetic Observatory at Toronto, in Upper Canada, and vice versâ: in fact, the magnetic storms are simultaneous at these two stations, but in opposite directions—a circumstance not yet accounted for, and may possibly be due to the increased magnetism of the air in these cold regions. The heat of the sun has no effect upon terrestrial magnetism unless possibly by its indirect action on the oxygen of the atmosphere; but hitherto it has been imperceptible. It is hardly possible that the aurora can be independent of the magnetic character of the air, since it occurs in the high latitudes, where the atmospheric magnetism is most powerful. Captain Maguire remarked that it frequently appeared at Point Barrow when the magnetic storms were at a maximum.

We are totally ignorant of the cause of terrestrial magnetism, though the powerful influence of the solar spots renders it highly probable that it will ultimately be found to originate in the sun himself. Mr. Barlow’s theory of electric currents revolving round the globe is borne out by Mr. Fox’s observations in the Cornish mines, which show that electro-magnetism is extremely active in metallic veins; that not only the nature of the metalliferous deposits must have been determined by their relative electrical conditions, but that the direction of the metallic veins must have been influenced by the direction of the magnetic meridians, and in fact almost all the metallic deposits in the world tend from east to west, or from north-east to south-west. However, these currents of electricity may be regarded as magnetic lines of force, and are more likely to be the effect than the cause of terrestrial magnetism. They are found to have a powerful inductive effect on the Atlantic telegraph, disturbing the needles and galvanometers at each end of the line to a considerable degree, and on the night of the 6th of September, 1858, a magnetic storm passed over the cable, which violently agitated the reflecting galvanometer in connection with the telegraphic wires.

We are equally ignorant of the cause of the secular magnetic variations, but we have no reason to believe that the earth is alone magnetic; on the contrary, the planets are probably magnets, and we know that the sun and moon are magnetic; hence, as the magnetic, like the gravitating force, is transmitted through the ethereal medium, the induction of the sun, moon, and planets, in all their secular and periodic changes, may cause perpetual variations in terrestrial magnetism, and it may not be beyond the delicacy of modern observation to ascertain whether a planet, when nearest to the earth, has any sensible magnetism.

Diamagnetism is also a dual power, but in complete antithesis to paramagnetism under the same circumstances. Dr. Faraday first discovered this property in heavy glass, or silico-borate of lead, a piece of which was repelled by the pole of a powerful electro-magnet, and an elongated prism of the same heavy glass, when freely suspended between the poles, set equatorially. He then found that so great a number of substances followed the same law, that it established the very remarkable fact of a hitherto unknown force having acted upon the substances submitted to its influence, a discovery which he subsequently confirmed by many experiments, all of which proved the antithesis between the two modes of magnetic action. He also discovered that magnetic bodies differ exceedingly in their magnetic power: of paramagnetic bodies iron is the most powerful; then follow nickel, cobalt, and a long gradation down to osmium and a vacuum. The body that seems to have the lowest diamagnetic power is arsenic, and the series ascends to heavy glass, antimony, phosphorus, and bismuth; so iron and bismuth are the most powerful in their respective classes, and both have a small conducting power for electricity. It may be presumed that many remarkable instances of diamagnetism are to be met with in nature; among others, Dr. Faraday has suggested the idea that Saturn’s ring, from its position, may be diamagnetic with regard to the planet.

With very powerful magnets or electro-magnets, which are absolutely necessary for all these experiments, it is found that no simple substance is neutral, but that such may be compounded by mixing in due proportion a diamagnetic and paramagnetic liquid, as water and protosulphate of iron.

Professor Tyndall proved diamagnetic polarity by placing two bismuth bars within two vertical coils or spirals of insulated copper wire, through which electric currents were transmitted from a galvanic battery, and caused to act upon a steel magnet freely suspended without the spirals. Now, when the excited magnetism is merely by induction, the electric current, being momentary, only causes a shock or momentary deviation in the magnet, which returns to its original position when the current ceases. When, on the contrary, the magnetism is permanent, the suspended magnet does not return to its original position when the current ceases. In Professor Tyndall’s experiment the deviation was permanent, and it was equally so when a bismuth bar was freely suspended and the cores within the spirals were steel magnets. Had the effect been from currents induced in the mass of the bar of bismuth, division of the bar would have stopped them, but the result was the same with powdered bismuth as with the solid mass. Moreover, since the strength of induced currents depends upon the conducting power of the substance, and as the conducting power of copper is forty times as great as that of bismuth, had the polarity been induced and not real, the effect ought to have been forty times greater when copper instead of bismuth cores were put in the spirals, whereas it was scarcely sensible. Besides these proofs, Dr. Tyndall made experiments with eleven different diamagnetic substances, of which water was one, with similar results. He then determined the polarity of twelve paramagnetic bodies by the same method, whence it appeared that the same action which produced a north pole in the paramagnetic bodies produced a south pole in those that were diamagnetic, and vice versâ, whence he concludes that diamagnetic polarity is one of the most firmly established truths of science. It follows from this that, when a man is standing, his head is a north pole and his feet a south, and the top of an iron railing on which he may be leaning is a south pole and the lower end a north. Diamagnetic bodies thus possess a polarity, the same in kind but opposite in direction to that possessed by paramagnetic ones.[18] They are both dual powers, and the two diamagnetic forces like the two paramagnetic being coexistent, simultaneous, and mutually dependent, there can be no doubt that the diamagnetic forces also are represented, or rather consist of curved and closed lines of force passing through the interior of the substance. Dr. Tyndall has proved that the attraction of iron, and the repulsion of bismuth, are as the square of the electro-magnetic current producing them, and that diamagnetic substances are capable of induction.

The molecular structure of substances freely suspended between the poles of a magnet has a decided effect upon the position they assume.

It has already been mentioned that the optic axis is a symmetrical line in a doubly refracting crystal in which there is no double refraction, and that in some crystals there are two such symmetrical lines. Now, Professor Plücker of Bonn discovered, when such crystals are submitted to powerful magnetic influence, that the single optic axis in the one, and the resultant or mean line between the double optic axes in the other, set diametrically or at right angles to the line of magnetic force; and so powerful did the Professor find the action of magnetism on crystalline form, that the mineral cyanite, when suspended, arranges itself so definitely with regard to terrestrial magnetism, that it might be used as a compass needle.

Dr. Faraday afterwards observed that amorphous substances, cut in the form of a sphere, have no tendency to set or be attracted or repelled in one direction in preference to any other; but if the sphere be formed of a crystallized substance, it is a general fact that, whether it be paramagnetic or diamagnetic, it is more powerfully attracted or repelled in one direction than in any other—a property named by Dr. Faraday magnecrystallic action. For example, a sphere of calcareous spar, which is a diamagnetic crystal, is most strongly repelled in the direction of its principal optic axis, and least strongly in the direction of its least axis. In a sphere of carbonate of iron, which has exactly the same crystalline form and is highly paramagnetic, the line which in carbonate of lime sets equatorially, in this case sets axially, and more strongly in that direction than in any other. The law according to which the attraction of the carbonate of iron increases from the least to its greatest or principal optic axis, is precisely the same as that according to which the repulsion of the calcareous spar increases from the least to the principal optic axis. These relations are not altered by the immersion of the spheres in liquids of either magnetism. Dr. Faraday observed that a line at right angles to the planes of principal cleavage in crystals takes the axial position, and on that account he called it the magnecrystallic axis. Its position was proved by MM. Tyndall and Knoblauch to depend upon the general fact, that the mass is most strongly repelled in the direction of the planes of principal cleavage, and that the elective position of crystals depends more upon the direction of these planes with respect to the electric force, than upon the optic axis. The planes of principal cleavage set themselves equatorially in diamagnetic, and axially in paramagnetic substances: it was thence inferred that the phenomena offered by crystals in the magnetic field is a particular case of the general law, that the superior action of magnets upon matter in a particular direction is due to the particles of the body being closer together in that direction than in any other: in short, the line of maximum density; the force exerted being attractive or repulsive according as the particles are paramagnetic or diamagnetic.

It appears, however, that the set of crystals with regard to the line of magnetic force does not depend solely upon their density in particular directions. Professor Matteucci, of Pisa, has proved that the diamagnetic force is inversely as the conducting power of substances for electricity, that the conducting power is a maximum in the planes of principal cleavage, and that a needle of crystallized bismuth, in which the planes of cleavage are parallel to its length, places itself equatorially with more force when these planes are vertical, or at right angles to the force, than when they are horizontal or parallel to it. Experiments had hitherto been made only with diamagnetic or slightly paramagnetic bodies, which induced M. le Roux to try the effect of magnetism on pulverized iron compressed by the hydraulic press, which reduced the grains of iron to lamellæ equivalent to planes of cleavage. Cubes of this substance, suspended by a thread over a horseshoe magnet, oscillated for a longer time when the lamellæ were perpendicular than when they were horizontal; that is, the force was stronger when the lamellæ were equatorial than when they were axial, exactly the same result as in Professor Matteucci’s experiment with the needle of bismuth. Thus the vertical position of the cleavages, which increases the diamagnetism of the bismuth, increases also the paramagnetism of the iron. M. le Roux observes that these results are independent of the influence of the currents of electricity induced in the oscillating body, for the fundamental character of the phenomena of Arago’s discovery of rotation by induction is, that the oscillations diminish rapidly in extent without any sensible diminution in their duration, while in his experiments the time of the oscillations varied. He concludes that the arrangement of the molecules must be intimately connected with paramagnetism or diamagnetism itself, since the effect of that arrangement is equally sensible in bismuth and iron, although the diamagnetism of the former is 25,000 times weaker than the paramagnetism of the latter.

The diamagnetism of conducting substances and metals, such as gold, silver, and copper, is augmented by division. Compression has also a great effect on magnetic action. For example, a bar of soft iron sets with its longest dimensions from pole to pole of a magnet, but a bar of compressed carbonate of iron-dust, whose shortest dimensions coincide with the line of pressure, sets equatorially. A bar of bismuth whose plane of principal cleavage is parallel to its length sets equatorially, but a bar of compressed bismuth dust, whose shortest dimensions coincide with the line of pressure, or a bar of bismuth whose principal planes of cleavage are transverse to its length, sets with its length axially. The antithesis is perfect whether the bars are under the influence of a magnet or electro-magnet. For since the diamagnetic force is inversely as the conducting power of a body for electricity, and that the latter is a maximum in the direction of the planes of principal cleavage, therefore when these planes are parallel to the axis of the bismuth bar it sets equatorially; but as the conducting power is augmented when the bismuth dust is compressed in the direction of the force, the diamagnetic power is diminished, and the bar sets axially. Again, since the paramagnetic force augments with the conducting power, the action of the magnet on the iron is antithetic to that on the bismuth.

The action of an electro-magnet on copper is strongly contrasted with that which it exerts on iron or bismuth. For when a copper bar suspended by a thread revolves before its pole, it is brought to a dead halt as soon as the electric current acts upon it, and maintains its position with considerable tenacity, for it does not return when pushed out of it, but keeps its new place with stiffness; however, as soon as the electric current ceases, there is a strong revulsion, the bar revolving the contrary way. Even when swinging with considerable force it may be caught and retained in any position at pleasure, but there is no revulsion when it is arrested either in the axial or equatorial position; at any angle between these two, but especially midway, the electricity will make it move towards the axis, but it is arrested before it comes to it. The action depends much on the form and dimensions of the bar and the magnetic pole, which ought to be flat. The phenomena are due to the high electro-conducting power of the copper, and are met with in some of the other pure metals, though in a far inferior degree.

Great magnetic power is requisite for all these experiments. Dr. Faraday employed a magnet that could sustain a weight of 450 lbs. at each pole, and the poles were either pointed or flat surfaces at pleasure, as the kind of experiment required.

Heat strongly affects the magnetic properties of bodies. Dr. Faraday found that, when the temperature of nickel is increased, its magnetic force diminishes; when that of iron is increased its magnetic force remains the same, while that of cobalt increases; which seems to indicate that there is a temperature at which the magnetic force is a maximum, above and below which it diminishes. Nickel loses its magnetism at the temperature of boiling oil, iron at a red heat, and cobalt near the temperature at which copper melts. Calcareous spar retains its magnetic character at a very high temperature; but the same substance when it contains iron, and also oxide of iron, loses it entirely at a dull red heat. A crystal of the ferrocarbonate of lime was absolutely reversed by change of temperature, for at a low heat the optic axis pointed axially, and at a high temperature equatorially. With the exception of these substances, magnecrystals, whether paramagnetic or diamagnetic, are generally all affected alike by heat. The difference between the forces in any two different directions, as for instance the greatest and least principal axes, diminishes as the temperature is raised, increases as the temperature is lowered, and is constant for a given temperature. No unmixed or pure substance has as yet passed by heat from the paramagnetic to the diamagnetic state. No simple magnecrystal has shown any inversion of this kind, nor have any of the chief axes of power changed their characters or relations to one another.

It appears that, as the molecules of crystals and compressed bodies affect magnetism, so magnetism acts upon the molecules of matter, for torsion diminishes the magnetic force, and the elasticity of iron and steel is altered by magnetism. M. Matteucci has found that the mechanical compression of glass alters the rotatory power of a polarized ray of light transmitted through it, and that a change takes place in the temper of glass under the influence of powerful magnetism.

Even from the limited view of the powers of nature which precedes, it is evident that the progress of science based upon experiment tends to show that the various forces of light, heat, motion, chemical affinity, electricity, and magnetism will ultimately be traced to one common origin; that they are so directly related, and mutually dependent, that they are convertible, motion producing heat, and heat motion; chemical affinity producing electricity, and electricity chemical action, &c., each mediately or immediately producing the other. These forces are transmitted through substances; they act upon matter, causing changes in the molecular structure of bodies either momentary or permanent, and reciprocally the changes indicate the action of these forces. Matter and force are only known to us as manifestations of Almighty power: we are assured that we can neither create nor destroy them—that their amount is the same now as in the beginning. In chemical attraction the powers with which a molecule of matter is endowed, and which give rise to various qualities, never change; even when passing through a thousand combinations, the molecule and its power are ever the same.

Machinery does not create force; it only enables us to turn the forces of nature to the best advantage; it is by the force of wind or falling water that our corn is ground, and the steam engine owes its power to the force of heat and chemical action. As force cannot be created, neither can it be annihilated. It may be dispersed in various directions, and subdivided so as to become evanescent to our perceptions; it may be balanced so as to be in abeyance, or become potential as in static electricity; but the instant the impediment is removed the force is manifested by motion; it may also be turned into heat by friction, but it is never lost. Every motion we make, every breath, every word we utter, is a force that produces pulsations which are communicated to continually increasing particles of air, and conveyed through countless channels so as to become indeed imperceptible to our senses, yet they are demonstrated to exist as witnesses of the words we have spoken or the actions we have performed, by analysis, that all-powerful instrument of human reason.[19]

A body acquires heat in the exact proportion that the adjacent substances become cold, and when heat is absorbed by a body it becomes an expansive force at the expense of those around that contract, but it is not lost. In chemical action at a distance the principle of the conservation of force is maintained, for a chemical action may be produced miles away from an electro-magnet, perfectly equivalent to the dominant chemical action in the battery. The two electricities are developed in equal proportions, which may be combined so as to produce many changes in their respective relations, yet the sum of the force of one kind can never be made in the smallest degree either to exceed or to come short of the sum of the other. Experimental research proves that the conservation of force is an unalterable law of nature—“a principle in physics as large and sure as that of the indestructibility of matter or the invariability of gravity. No hypothesis should be admitted, nor any assertion of a fact credited, that denies this principle. No view should be inconsistent or incompatible with it. Many of our hypotheses in the present state of science may not comprehend it, and may be unable to suggest its consequences, but none should oppose or contradict it.”

Having thus expressed his conviction of the truth of this great principle, Dr. Faraday considers the case of gravity, and concludes that “the definition of gravity as an attractive force between the particles of matter varying inversely as the square of the distance, while it stands as a full definition of the power, is inconsistent with the principle of the conservation of force.” For while in this definition the principle is maintained of the constancy of the force at the same distance, it implies a creation of force to an enormous amount when the distance is diminished, and an equal amount annihilated when the distance is increased,—“an effect,” he says, “which is equal in its infinity and its consequences with creation, and only within the power of Him who creates.” He continues, “It will not be imagined for a moment that I am opposed to what may be called the law of gravitating action, that is, the law by which all the known effects of gravity are governed; what I am considering is the definition of the force of gravitation. That the result of one exercise of a power may be inversely as the square of the distance, I believe and admit; and I know that it is so in the case of gravity, and has been verified to an extent that could hardly have been within the conception of Newton himself when he gave utterance to the law; but that the totality of a force can be employed according to that law I do not believe either in relation to gravitation, or electricity, or magnetism, or any other supposed form of power. That there should be a power of gravitation existing by itself, having no relation to the other natural powers, and no respect to the law of the conservation of force, is as little likely as that there should be a principle of levity as well as gravity. Gravity may be only the residual part of the other forces of nature, as Mossotti has tried to show; but that it should fall out from the law of all other forces, and should be outside the reach either of farther experiment or philosophical conclusions, is not probable. So we must strive to learn more of this outstanding power, and endeavour to avoid any definition of it which is incompatible with the principles of force generally, for all the phenomena of nature lead us to believe that the great and governing law is one. Thus gravitation can only be considered as part of a more general force whose law has yet to be discovered.”

The definition of the gravitating force immediately suggests the question of how it is transmitted; the full force of that question was felt by Newton himself when, in his third letter to Bentley, he wrote, “That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophic matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers.”

Since Newton’s time the continual decrease in the periodic times of the comets belonging to our system, and the undulatory theory of light and heat, have proved the existence of an extremely rare elastic medium filling space even to the most distant regions of which we are cognizant. But, rare as it may be, it has inertia enough to resist the motion of comets, and therefore must be material, whether considered to be ether or, according to Mr. Grove, the highly attenuated atmospheres of the celestial bodies. Professor William Thomson of Glasgow has computed that in the space traversed by the earth in its annual revolution, a cube whose side is 1000 miles would contain not less than a pound weight of the ethereal medium, and that the earth, in moving through it, would not displace the ·250th part of that pound of matter. Yet that is enormously more dense than the continuation of the earth’s atmosphere would be in interplanetary space, if rarefied according to Bayle’s law. But whatever be the density or nature of the ether, there is every reason to believe that it is the medium which transmits the gravitating force from one celestial object to another, or possibly it may possess a higher attribute with regard to gravity than its mere transmission.

Dr. Faraday, who discovered the magnetism of the atmosphere, is led to believe that the ethereal medium too is magnetic by the following experiment. Three solutions of the protosulphate of iron, l, m, n, the first of which contained 4 grains of the salt dissolved in a cubic inch of water, the second 8 grains, and the third 16 grains—these were respectively enclosed in three glass globules, all of which were attracted by the pole of a magnet. A quantity of the mean solution m was then put into a vessel, and the globule containing the strongest solution n was immersed in it, which was attracted as before, but the globule l, containing the weakest solution, was repelled when plunged into the same liquid. Here there was a diamagnetic phenomenon, although the glass globules and the liquid in which they were immersed contained iron. The effect was evidently differential, for when the liquid was less attracted than the globule, the globule approached the pole, and when the liquid was more attracted than the globule, the latter appeared to recede from the pole. In fact, the effect is the same as that of gravity on a body immersed in water; if it be more forcibly attracted than the water, it sinks; if less forcibly attracted, it rises, the effect being the same as if it were repelled by the earth. Hence the question, are all magnetic phenomena the result of a differential action of this kind, and is the ethereal medium less strongly attracted than soft iron, and more strongly attracted than bismuth, thus permitting the approach of the iron, but causing the bismuth to recede from the pole of a magnet? If such a medium exist, that is, if the ethereal medium be magnetic, then diamagnetism is the same with paramagnetism, and the polarity of the magnetic force in iron and bismuth is one and the same.

The ethereal medium may be presumed to transmit the gravitating force; it transmits the magnetism of the solar spots, its undulations constitute light, heat, and all the influences bound up in the solar beam; and the most perfect vacuum we can make is capable of transmitting mechanical energy in enormous quantities, some of which differ but little from that of air or oxygen at an ordinary barometric pressure; and why not thus admit, says Mr. Thomson, the magnetic property, of which we know so little that we have no right to pronounce a negative?

Mr. Waterstone is also of opinion that it would be taking too narrow a view if we limited the function of the luminiferous ether to the conveying of physical pulses only. The atmosphere also conveys physical pulses, but that is the least important of its functions in the economy of nature. There is nothing that should hinder us attributing to the media concerned in the radiation of light and heat the higher functions of electrical polarity and gravitation. The special dynamic arrangements by which this is effected may ever elude our research; but as there is no limit to the vis viva (N. 222) which such media may conserve in their minutest parts, so there is no physical impossibility in that vis viva being suddenly transferred to the molecules of ordinary matter in the proportion and sequence required to carry out the order and system of nature.

The fundamental principle of action in such media must be in accordance with elastic impact, for upon that the dynamic theory of heat and conservation of force rests as a foundation. The statical and dynamical characteristics of gravitation and transfusion of force conform to it, so that all the forces that hold the molecules of bodies together must also be in subjection to it.[20]

SECTION XXXV.

Ethereal Medium—Comets—Do not disturb the Solar System—Their Orbits and Disturbances—M. Faye’s Comet probably the same with Lexel’s—Periods of other three known—Acceleration in the mean Motions of Encke’s and Biela’s Comets—The Shock of a Comet—Disturbing Action of the Earth and Planets on Encke’s and Biela’s Comets—Velocity of Comets—The Comet of 1264—The great Comet of 1343—Physical Constitution—Shine by borrowed Light—Estimation of their Number.

IN considering the constitution of the earth, and the fluids which surround it, various subjects have presented themselves to our notice, of which some, for aught we know, are confined to the planet we inhabit; some are common to it and to the other bodies of our system. But an all-pervading ether must fill the whole visible creation, since it conveys, in the form of light, tremors which may have been excited in the deepest recesses of the universe thousands of years before we were called into being. The existence of such a medium, though at first hypothetical, is proved by the undulatory theory of light, and rendered certain by the motion of comets, and by its action upon the vapours of which they are chiefly composed. It has often been imagined that the tails of comets have infused new substances into our atmosphere. Possibly the earth may attract some of that nebulous matter, since the vapours raised by the sun’s heat, when the comets are in perihelio, and which form their tails, are scattered through space in their passage to their aphelion; but it has hitherto produced no effect, nor have the seasons ever been influenced by these bodies. The light of the comet of the year 1811, which was so brilliant, did not impart any heat even when condensed on the bulb of a thermometer of a structure so delicate that it would have made the hundredth part of a degree evident. In all probability, the tails of comets may have passed over the earth without its inhabitants being conscious of their presence; and there is reason to believe that the tail of the great comet of 1843 did so. M. Valz observed that the light of a brilliant comet was eclipsed as it passed over a star of the 7th magnitude, whence M. Babinet computed that the light of the comet must have been sixty times less than that of the star, and that matter so attenuated could not penetrate the earth’s atmosphere, but the constitution of these bodies is still a matter of conjecture.

The passage of comets has never sensibly disturbed the stability of the solar system; their nucleus, being in general only a mass of vapour, is so rare, and their transit so rapid, even when they had a solid part, that the time has not been long enough to admit of a sufficient accumulation of impetus to produce a perceptible action. Indeed, M. Dusejour has shown that, under the most favourable circumstances, a comet cannot remain longer than two hours and a half at a less distance from the earth than 10,500 leagues. The comet of 1770 passed within about six times the distance of the moon from the earth, without even affecting our tides. According to La Place, the action of the earth on the comet of 1770 augmented the period of its revolution by more than two days; and, if comets had any perceptible disturbing energy, the reaction of the comet ought to have increased the length of our year. Had the mass of that comet been equal to the mass of the earth, its disturbing action would have increased the length of the sidereal year by 2^h 53^m; but, as Delambre’s computations from the Greenwich observations of the sun show that the length of the year has not been increased by the fraction of a second, its mass could not have been equal to the 1/5000th part of that of the earth. This accounts for the same comet having twice swept through the system of Jupiter’s satellites without deranging the motion of these moons. M. Dusejour has computed that a comet, equal in mass to the earth, passing at the distance of 12,150 leagues from our planet, would increase the length of the year to 367^d 16^h 5^m, and the obliquity of the ecliptic as much as 2°. So the principal action of comets would be to alter the calendar, even if they were dense enough to affect the earth.

Comets traverse all parts of the heavens; their paths have every possible inclination to the plane of the ecliptic, and, unlike the planets, the motion of more than half of those that have appeared has been retrograde, that is, from east to west. They are only visible when near their perihelia; then their velocity is such, that its square is twice as great as that of a body moving in a circle at the same distance: they consequently remain but a very short time within the planetary orbits. And, as all the conic sections of the same focal distance sensibly coincide, through a small arc, on each side of the extremity of their axis, it is difficult to ascertain in which of these curves the comets move, from observations made, as they necessarily must be, near their perihelia (N. 227). Probably they all move in extremely excentric ellipses; although, in most cases, the parabolic curve coincides most nearly with their observed motions. Some few seem to describe hyperbolas; such, being once visible to us, would vanish for ever, to wander through boundless space, to the remote systems of the universe. If a planet be supposed to revolve in a circular orbit, whose radius is equal to the perihelion distance of a comet moving in a parabola, the areas described by these two bodies in the same time will be as unity to the square root of two, which forms such a connexion between the motion of comets and planets, that, by Kepler’s law, the ratio of the areas described during the same time by the comet and the earth may be found; so that the place of a comet may be computed at any time in its parabolic orbit, estimated from the instant of its passage at the perihelion. It is a problem of very great difficulty to determine all the other elements of parabolic motion—namely, the comet’s perihelion distance, or shortest distance from the sun, estimated in parts of the mean distance of the earth from the sun; the longitude of the perihelion; the inclination of the orbit on the plane of the ecliptic; and the longitude of the ascending node. Three observed longitudes and latitudes of a comet are sufficient for computing the approximate values of these quantities; but an accurate estimation of them can only be obtained by successive corrections, from a number of observations, distant from one another. When the motion of a comet is retrograde, the place of the ascending node is exactly opposite to what it is when the motion is direct. Hence the place of the ascending node, together with the direction of the comet’s motion, show whether the inclination of the orbit is on the north or south side of the plane of the ecliptic. If the motion be direct, the inclination is on the north side; if retrograde, it is on the south side.

The identity of the elements is the only proof of the return of a comet to our system. Should the elements of a new comet be the same, or nearly the same, with those of any one previously known, the probability of the identity of the two bodies is very great, since the similarity extends to no less than four elements, every one of which is capable of an infinity of variations. But, even if the orbit be determined with all the accuracy the case admits of, it may be difficult, or even impossible, to recognize a comet on its return, because its orbit would be very much changed if it passed near any of the large planets of this or of any other system, in consequence of their disturbing energy, which would be very great on bodies of so rare a nature.

By far the most curious and interesting instance of the disturbing action of the great bodies of our system is found in the comet of 1770. The elements of its orbit, determined by Messier, did not agree with those of any comet that had hitherto been computed, yet Lexel ascertained that it described an ellipse about the sun, whose major axis was only equal to three times the length of the diameter of the terrestrial orbit, and consequently that it must return to the sun at intervals of five years and a half. This result was confirmed by numerous observations, as the comet was visible through an arc of 170°; yet this comet had never been observed before the year 1770, nor has it ever again been seen till 1843, though very brilliant. The disturbing action of the larger planets affords a solution of this anomaly, as Lexel ascertained that in 1767 the comet must have passed Jupiter at a distance less than the fifty-eighth part of its distance from the sun, and that in 1779 it would be 500 times nearer Jupiter than the sun; consequently the action of the sun on the comet would not be the fiftieth part of what it would experience from Jupiter, so that Jupiter became the primum mobile. Assuming the orbit to be such as Lexel had determined in 1770, La Place found that the action of Jupiter, previous to the year 1770, had so completely changed the form of it, that the comet which had been invisible to us before 1770 was then brought into view, and that the action of the same planet, producing a contrary effect, has subsequently to that year removed it from our sight, since it was computed to be revolving in an orbit whose perihelion was beyond the orbit of Ceres. However, the action of Jupiter during the summer of 1840 must have been so great, from his proximity to that singular body, that he seems to have brought it back to its former path as he had done in 1767, for the elements of the orbit of a comet which was discovered in November 1843, by M. Faye, agree so nearly with those of the orbit of Lexel’s comet that the two bodies were supposed to be identical; by the subsequent computation of M. le Verrier, it appears, however, that they are not the same, that they were both brought to our system by Jupiter’s attraction, and that they have been in it more than a century, and have frequently come near the earth without having been seen. From the smallness of the excentricity of Lexel’s comet, the orbit resembles those of the planets, but this comet is liable to greater perturbations than any other body in the system, because it comes very near the orbit of Mars when in perihelion, and very near that of Jupiter when in aphelion; besides, it passes within a comparatively small distance of the orbits of the minor planets; and as it will continue to cross the orbit of Jupiter at each revolution till the two bodies meet, its periodic time, now about seven years, will again be changed, but in the mean time it ought to have returned to its perihelion in the year 1851. This comet might have been seen from the earth in 1776, had its light not been eclipsed by that of the sun. There is still so much doubt with regard to Lexel’s comet that during the present year, 1858, M. le Verrier has constructed a table of all the orbits in which the comet may have moved after leaving Jupiter in 1770, which will enable astronomers to recognise the comet even should the elements of its orbit be much altered. He thinks it possible that its path may have become hyperbolic, but that it is more likely an augmentation of its periodic time may have taken place. It is quite possible that comets frequenting our system may be turned away, or others brought to the sun, by the attraction of planets revolving beyond the orbit of Neptune, or by bodies still farther removed from the solar influence.

Other comets, liable to less disturbance, return to the sun at stated intervals. Halley computed the elements of the orbit of a comet that appeared in the year 1682, which agreed so nearly with those of the comets of 1607 and 1531, that he concluded it to be the same body returning to the sun at intervals of about seventy-five years. He consequently predicted its reappearance in the year 1758, or in the beginning of 1759. Science was not sufficiently advanced in the time of Halley to enable him to determine the perturbations this comet might experience; but Clairaut computed that, in consequence of the attraction of Jupiter and Saturn, its periodic time would be so much shorter than during its revolution between 1607 and 1682, that it would pass its perihelion on the 18th of April, 1759. The comet did arrive at that point of its orbit on the 12th of March, which was thirty-seven days before the time assigned. Clairaut subsequently reduced the error to twenty-three days; and La Place has since shown that it would only have been thirteen days if the mass of Saturn had been as well known as it is now. It appears, from this, that the path of the comet was not quite known at that period; and, although many observations were then made, they were far from attaining the accuracy of those of the present day. Besides, since the year 1759, the orbit of the comet has been altered by the attraction of Jupiter in one direction, and that of Saturn, Uranus, and Neptune in the other; yet, notwithstanding these sources of uncertainty, and our ignorance of all the possible causes of derangement from unknown bodies on the confines of our system, or in the regions beyond it, the comet appeared exactly at the time, and not far from the place assigned to it by astronomers; and its actual arrival at its perihelion a little before noon on the 16th of November, 1835, only differed from the computed time by a very few days, which was probably owing to the attraction of Neptune.

The fulfilment of this astronomical prediction is truly wonderful, if it be considered that the comet is seen only for a few weeks during its passage through our system, and that it wanders from the sun for seventy-five years to twice the distance of Uranus. This enormous orbit is four times longer than it is broad; its length is about 3420 millions of miles, or about thirty-six times the mean distance of the earth from the sun. At its perihelion the comet comes within nearly fifty-seven millions of miles of the sun, and at its aphelion it is sixty times more distant. On account of this extensive range it must experience 3600 times more light and heat when nearest to the sun than in the most remote point of its orbit. In the one position the sun will seem to be four times larger than he appears to us, and at the other he will not be apparently larger than a star (N. 228.)

On the first appearance of Halley’s comet, early in August 1835, it seemed to be merely a globular mass of dim vapour, without a tail. A concentration of light, a little on one side of the centre, increased as the comet approached the sun and earth, and latterly looked so like the disc of a small planet, that it might have been mistaken for a solid nucleus. M. Struve, however, saw a central occultation of a star of the ninth magnitude by the comet, at Dorpat, on the 29th of September. The star remained constantly visible, without any considerable diminution of light; and, instead of being eclipsed, the nucleus of the comet disappeared at the moment of conjunction from the brilliancy of the star. The tail increased as the comet approached its perihelion, and shortly before it was lost in the sun’s rays it was between thirty and forty degrees in length.

According to the observations of M. Valz, the nebulosity increased in magnitude as it approached the sun; but no other comet on record has exhibited such sudden and unaccountable changes of aspect. It was invisible for two months when near its perihelion passage, and when it reappeared on the 24th of January, 1836, its aspect was completely changed; it had no tail, and to the naked eye was like a hazy star; but with a powerful telescope it presented a small, round, planetary-looking nucleus 2ʺ in diameter, surrounded by an extensive coma, and in the centre it had a small, bright, solid part. The nucleus, clear and well defined, like the disc of a planet, was observed on one occasion to become obscure and enlarged in the course of a few hours. But by far the most remarkable circumstance was the sudden appearance of certain luminous brushes or sectors, diverging from the centre of the nucleus through the nebulosity. M. Struve describes the nucleus of the comet, in the beginning of October, as elliptical, and like a burning coal, out of which there issued, in a direction nearly opposite to the tail, a divergent flame, varying in intensity, form, and direction, appearing occasionally even double, and suggesting the idea of luminous gas bursting from the nucleus. On one occasion M. Arago saw three of these divergent flames on the side opposite the tail, rising through the nebulosity, which they greatly exceeded in brilliancy: after the comet had passed its perihelion, it acquired another of these luminous fans, which was observed by Sir John Herschel at the Cape of Good Hope. Hevelius describes an appearance precisely similar, which he had witnessed in this comet at its approach to the sun in the year 1682, and something of the kind seems to have been noticed in the comet of 1744. Possibly the second tail of the comet of 1724, which was directed towards the sun, may have been of this nature.

The influence of the ethereal medium on the motions of Halley’s comet will be known after another revolution, and future astronomers will learn, by the accuracy of its returns, whether it has met with any unknown cause of disturbance in its distant journey. Undiscovered planets, beyond the visible boundary of our system, may change its path and the period of its revolution, and thus may indirectly reveal to us their existence, and even their physical nature and orbit. The secrets of the yet more distant heavens may be disclosed to future generations by comets which penetrate still farther into space, such as that of 1763, which, if any faith may be placed in the computation, goes nearly forty-three times farther from the sun than Halley’s does, and shows that the sun’s attraction is powerful enough, at the enormous distance of 15,500 millions of miles, to recall the comet to its perihelion. The periods of some comets are said to be of many thousand years, and even the average time of the revolution of comets generally is about a thousand years; which proves that the sun’s gravitating force extends very far. La Place estimates that the solar attraction is felt throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun.

Authentic records of Halley’s comet do not extend beyond the year 1456, yet it may be traced, with some degree of probability, even to a period preceding the Christian era. But as the evidence only rests upon coincidences of its periodic time, which may vary as much as eighteen months from the disturbing action of the planets, its identity with comets of such remote times must be regarded as extremely doubtful.

This is the first comet whose periodicity has been established. It is also the first whose elements have been determined from observations made in Europe; for, although the comets which appeared in the years 240, 539, 565, and 837, are the most ancient of those whose orbits have been traced, their elements were computed from Chinese observations.

Besides Halley’s and Lexel’s comets, ten or twelve others are now known to form part of the solar system; that is to say, they return to the sun at stated periods. Six of them have periods of less than eight years. That generally called Encke’s comet, or the comet of the short period, was first seen by MM. Messier and Mechain in 1786, again by Miss Herschel in 1805, and its returns, in the years 1805 and 1819, were observed by other astronomers, under the impression that all four were different bodies. However, Professor Encke not only proved their identity, but determined the circumstances of the comet’s motion. Its reappearance in the years 1825, 1828, and 1832, accorded with the orbit assigned by M. Encke, who thus established the length of its period to be 1204 days, nearly. This comet is very small, of feeble light, and invisible to the naked eye, except under very favourable circumstances, and in particular positions. It has no tail, it revolves in an ellipse of great excentricity inclined at an angle of 13° 22ʹ to the plane of the ecliptic, and is subject to considerable perturbations from the attraction of the planets, which occasion variations in its periodic time. Among the many perturbations to which the planets are liable, their mean motions, and therefore the major axes of their orbits, experience no change; while, on the contrary, the mean motion of the moon is accelerated from age to age—a circumstance at first attributed to the resistance of an ethereal medium pervading space, but subsequently proved to arise from the secular diminution of the excentricity of the terrestrial orbit. Although the resistance of such a medium has not hitherto been perceived in the motions of such dense bodies as the planets and satellites, its effects on the revolutions of the comets leave no doubt of its existence. From the numerous observations that have been made on each return of the comet of the short period, the elements have been computed with great accuracy on the hypothesis of its moving in vacuo. Its perturbations occasioned by the disturbing action of the planets have been determined; and, after everything that could influence its motion had been duly considered, M. Encke found that an acceleration of about two days in each revolution has taken place in its mean motion, precisely similar to that which would be occasioned by the resistance of an ethereal medium. And, as it cannot be attributed to a cause like that which produces the acceleration of the moon, it must be concluded that the celestial bodies do not perform their revolutions in an absolute void, and that, although the medium be too rare to have a sensible effect on the masses of the planets and satellites, it nevertheless has a considerable influence on so rare a body as a comet. Contradictory as it may seem that the motion of a body should be accelerated by the resistance of an ethereal medium, the truth becomes evident if it be considered that both planets and comets are retained in their orbits by two forces which exactly balance one another; namely, the centrifugal force producing the velocity in the tangent, and the attraction of the gravitating force directed to the centre of the sun. If one of these forces be diminished by any cause, the other will be proportionally increased. Now, the necessary effect of a resisting medium is to diminish the tangential velocity, so that the balance is destroyed, gravity preponderates, the body descends towards the sun till equilibrium is again restored between the two forces; and, as it then describes a smaller orbit, it moves with increased velocity. Thus, the resistance of an ethereal medium actually accelerates the motion of a body; but, as the resisting force is confined to the plane of the orbit, it has no influence whatever on the inclination of the orbit, or on the place of the nodes. In computing its effect, M. Encke assumed the increase to be inversely as the square of the distance, and that its resistance acts as a tangential force proportional to the squares of the comet’s actual velocity in each point of its orbit. Another comet belonging to our system, which returns to its perihelion after a period of 6-3/4 years, has been accelerated in its motion by a whole day during one revolution, which puts the existence of ether beyond a doubt, and confirms the undulatory theory of light. Since this comet, which revolves nearly between the orbits of the earth and Jupiter, is only accelerated one day at each revolution, while Encke’s, revolving nearly between the orbits of Mercury and Pallas, is accelerated two, the ethereal medium must increase in density towards the sun. The comet in question was discovered by M. Biela at Josephstadt on the 27th of February, 1826, and ten days afterwards it was seen by M. Gambart at Marseilles, who computed its parabolic elements, and found that they agreed with those of the comets which had appeared in the years 1789 and 1795, whence he concluded them to be the same body moving in an ellipse, and accomplishing its revolution in 2460 days. The perturbations of this comet were computed by M. Damoiseau, who predicted that it would cross the plane of the ecliptic on the 29th of October, 1832, a little before midnight, at a point nearly 18,484 miles within the earth’s orbit; and as M. Olbers of Bremen, in 1805, had determined the radius of the comet’s head to be about 21,136 miles, it was evident that its nebulosity would envelop a portion of the earth’s orbit,—a circumstance which caused some alarm in France, from the notion that, if any disturbing cause had delayed the arrival of the comet for one month, the earth must have passed through its head. M. Arago dispelled these fears by his excellent treatise on comets, in the Annuaire of 1832, where he proves that, as the earth would never be nearer the comet than 18,000,000 British leagues, there could be no danger of collision. The earth is in more danger from these two small comets than from any other. Encke’s crosses the terrestrial orbit sixty times in a century, and may ultimately come into collision, but both are so extremely rare, that little injury is to be apprehended.

The earth would fall to the sun in 64-1/2 days, if it were struck by a comet with sufficient impetus to destroy its centrifugal force. What the earth’s primitive velocity may have been it is impossible to say. Therefore a comet may have given it a shock without changing the axis of rotation, but only destroying part of its tangential velocity, so as to diminish the size of the orbit—a thing by no means impossible, though highly improbable. At all events, there is no proof of this having occurred; and it is manifest that the axis of the earth’s rotation has not been changed, because, as the ether offers no sensible resistance to so dense a body as the earth, the libration would to this day be evident in the variation it must have occasioned in the terrestrial latitudes. Supposing the nucleus of a comet to have a diameter only equal to the fourth part of that of the earth, and that its perihelion is nearer to the sun than we are ourselves, its orbit being otherwise unknown, M. Arago has computed that the probability of the earth receiving a shock from it is only one in 281 millions, and that the chance of our coming in contact with its nebulosity is about ten or twelve times greater. Only comets with retrograde motions can come into direct collision with the earth, and if the momentum were great the event might be fatal; but in general the substance of comets is so rare, that it is likely they would not do much harm if they were to impinge; and even then the mischief would probably be local, and the equilibrium soon restored, provided the nucleus were gaseous, or very small. It is, however, more probable that the earth would only be deflected a little from its course by the approach of a comet, without being touched by it. The comets that have come nearest to the earth were that of the year 837, which remained four days within less than 1,240,000 leagues from our orbit: that of 1770, which approached within about six times the distance of the moon. The celebrated comet of 1680 also came very near to us; and the comet whose period is 6-3/4 years was ten times nearer the earth in 1805 than in 1832, when it caused so much alarm.

Encke’s and Biela’s comets are at present far removed from the influence of Jupiter, but they will not always remain so, because, the aphelia and nodes of the orbits of these two comets being the points which approach nearest to the orbit of Jupiter at each meeting of the planet and comets, the major axis of Encke’s comet will be increased and that of Biela’s diminished, till in the course of time, when the proximity has increased sufficiently, the orbits will be completely changed, as that of Lexel’s was in 1770. Every twenty-third year, or after seven revolutions of Encke’s comet, its greatest proximity to Jupiter takes place, and at that time his attraction increases the period of its revolution by nine days—a circumstance which took place in the end of the years 1820 and 1843. But from the position of the bodies there is a diminution of three days in the six following revolutions, which reduces the increase to six days in seven revolutions. Thus, before the year 1819, the periodic time of Encke’s comet was 1204 days, and it was 1219 days in accomplishing the revolution that ended in 1845. By this progressive increase the orbit of the comet will reach that of Jupiter in seven or eight centuries, and then by the very near approach of the two bodies it will be completely changed.

At present the Earth and Mercury have the most powerful influence on the motions of Encke’s and Biela’s comets; and have had for so long a time that, according to the computation of Mr. Airy, the present orbit of the latter was formed by the attraction of the Earth, and that of Encke’s by the action of Mercury. With regard to the latter comet, that event must have taken place in February 1776. In 1786 Encke’s comet had both a tail and a nucleus, now it has neither; a singular instance of the possibility of their disappearance. It was in perihelio in 1855.

In 1846 Biela’s comet was divided into two distinct bodies, by what strange accident is altogether a mystery. The nuclei of the two comets were separated by about 150,000 miles, and they travelled together with their tails parallel, and an arch of light over their heads. Till that time Biela’s comet never had been seen with a tail. The new head was dull at first, but increased in size and brightness till it surpassed its companion in both; besides, it had a bright flashing diamond-like point in its centre—gradually it resumed its dull appearance, and its period was computed to be eight days longer than that of the original head. They had separated to a greater distance from one another in 1853, but were still travelling together, one having become smaller than the other.

A comet discovered by M. Brorsen of Kiel, on the 26th of February, 1846, came, on the 20th of April following, nearly as close to Jupiter as his fourth satellite, when Jupiter’s attraction must have been ten times greater than that of the sun; so there is every reason to believe that the comet’s orbit will be as much altered as that of Lexel’s; and another discovered by Padre de Vico at Rome, on the 22nd of August, will, in all probability, be as much disturbed by the same cause. One of the comets found by that astronomer has a period which varies, according to different computations, from 55 to 99 years; it certainly has an elliptical orbit. That discovered at Naples by Mr. Peters revolves about the sun in 16 years; but Olbers’s comet of 1815 must go nearly the same distance into space with Halley’s, since its period is 74 years. Two discovered by M. Brorsen have periods, one of 500 and the other of 28 years; but of the latter there is some uncertainty.

The comet which appeared in 1596 and 1845 has a period of 249 years; and should M. Argelander’s computation be accurate, the orbit which has hitherto been assigned to the great comet of 1811 must be erroneous, since he has ascertained its period to be 3066 years.

The great comet of 1264, which had a tail that extended over 100° of the celestial vault, was observed and recorded by the Chinese, and was ascertained to be the same that had appeared in 1556, and of whose motions observations were taken at Vienna in the reign of the Emperor Charles V., but it was then less brilliant. In consequence of the discovery of the original observations of the comet of 1556, by Fabricius at Vienna, and by Heller at Nuremburg, Mr. Hind was induced to compute its orbit for that year; but after much labour, aided by all the improved methods of calculation, he found Heller’s observations so confused, and even erroneous, that he could not determine the curve described by the comet at that time with any precision, and therefore could only predict that the epoch of its return would be some time between 1848 and 1861. Before comets reach the sun they are rarely conspicuous; but if after passing their perihelion they come near the earth, then they have tails, and become brilliant in consequence of the sun’s action upon the matter of which they are formed. Now if the comet in question should pass its perihelion between the months of March and October, it possibly may be as remarkable as ever; but should it come nearest to the sun in winter, such is the position of its orbit with regard to the earth, that it may pass unnoticed—which is very unlikely, as search is being made for it at almost all the observatories in Europe and in the United States. Nearly the whole of its orbit lies below the plane of the ecliptic, and far from the paths of the larger planets, but it extends into space more than twice the distance of Neptune, or nearly six thousand millions of miles from the sun.

Comets in or near their perihelion move with prodigious velocity. That of 1680 appears to have gone half round the sun in ten hours and a half, moving at the rate of 880,000 miles an hour. If its enormous centrifugal force had ceased when passing its perihelion, it would have fallen to the sun in about three minutes, as it was then less than 147,000 miles from his surface. So near the sun, it would be exposed to a heat 27,500 times greater than that received by the earth; and as the sun’s heat is supposed to be in proportion to the intensity of his light, it is probable that a degree of heat so intense would be sufficient to convert into vapour every terrestrial substance with which we are acquainted. At the perihelion distance the sun’s diameter would be seen from the comet under an angle of 73°, so that the sun, viewed from the comet, would nearly cover the whole extent of the heavens from the horizon to the zenith. As this comet is presumed to have a period of 575 years, the major axis of its orbit must be so great, that at the aphelion the sun’s diameter would only subtend an angle of about fourteen seconds, which is not so great by half as the diameter of Mars appears to us when in opposition. The sun would consequently impart no heat, so that the comet would then be exposed to the temperature of the ethereal regions, which is 239° below the zero point of Fahrenheit. A body of such tenuity as the comet, moving with such velocity, must have met with great resistance from the dense atmosphere of the sun, while passing so near his surface at its perihelion. The centrifugal force must consequently have been diminished, and the sun’s attraction proportionally augmented, so that it must have come nearer to the sun in 1680 than in its preceding revolution, and would subsequently describe a smaller orbit. As this diminution of its orbit will be repeated at each revolution, the comet will infallibly end by falling on the surface of the sun, unless its course be changed by the disturbing influence of some large body in the unknown expanse of creation. Our ignorance of the actual density of the sun’s atmosphere, of the density of the comet, and of the period of its revolution, renders it impossible to form any idea of the number of centuries which must elapse before this event takes place.

The same cause may affect the motions of the planets, and ultimately be the means of destroying the solar system. But, as Sir John Herschel observes, they could hardly all revolve in the same direction round the sun for so many ages without impressing a corresponding motion on the ethereal medium, which may preserve them from the accumulated effects of its resistance. Should this material medium revolve about the sun like a vortex, it will accelerate the revolutions of such comets as have direct motions, and retard those that have retrograde motions.

The comet which appeared unexpectedly in the beginning of the year 1843 was one of the most splendid that ever visited the solar system. It was in the constellation of Antinous in the end of January, at a distance of 115 millions of miles from the earth, and it passed through its perihelion on the 27th of February, when it was lost in the sun’s rays; but it began to be visible about the 3rd of March, at which time it was near the star Iota Cetæ, and its tail extended towards the Hare. Before the passage at the perihelion it had no tail; but at that epoch the tail suddenly darted out, and extended to a distance of 1826 millions of miles in about an hour and a half—a most inexplicable speed of development, which indicates some powerful repulsive force at the moment of the greatest proximity to the sun, at which time the tails are formed. The brightness of the comet and the length of its tail continued to increase till the latter stretched far beyond the constellation of the Hare towards a point above Sirius. Stars were distinctly seen through it, and when near perihelion the comet was so bright that it was seen in clear sunshine, in the United States, like a white cloud. The motion was retrograde, and on leaving the solar system it retreated so rapidly at once from the sun and earth that it was soon lost sight of for want of light. On the 1st of April it was between the sun and the earth, and only 40 millions of miles from the latter; and as its tail was at least 60 millions of miles long, and 20 millions of miles broad, we probably passed through it without being aware of it. There is some discrepancy in the different computations of the elements of the orbit, but in the greater number of cases the perihelion distance was found to be less than the semidiameter of the sun, so that the comet must have grazed his surface, if it did not actually impinge obliquely on him.

The perihelion distance of this comet differs little from that of the great comet of 1668, which came so near the sun. The motion of both was retrograde, and a certain resemblance in the two orbits makes it probable that they are the same body performing a revolution in 175 years.

Though already so well acquainted with the motions of comets, we know nothing of their physical constitution. A vast number, especially of telescopic comets, are only like clouds or masses of vapour, often without tails. The head commonly consists of a concentrated mass of light, like a planet, surrounded by a very transparent atmosphere, and the whole, viewed with a telescope, is so diaphanous, that the smallest star may be seen even through the densest part of the nucleus; in general their solid parts, when they have any, are so minute, that they have no sensible diameter, like that of the comet of 1811, which appeared to Sir William Herschel like a luminous point in the middle of the nebulous matter. The nuclei, which seem to be formed of the denser strata of that nebulous matter in successive coatings, are sometimes of great magnitude. Those comets which came to the sun in the years 1799 and 1807 had nuclei whose diameters measured 180 and 275 leagues respectively, and the second comet of 1811 had a nucleus 1350 leagues in diameter.

It must, however, be stated that, as comets are generally at prodigious distances from the earth, the solid parts of the nuclei appear like mere points of light, so minute that it is impossible to measure them with any kind of accuracy, so that the best astronomers often differ in the estimation of their size by one-half of the whole diameter. The transit of a comet across the sun would afford the best information with regard to the nature of the nuclei. It was computed that such an event was to take place in the year 1827; unfortunately the sun was hid by clouds from the British astronomers, but it was examined at Viviers and at Marseilles at the time the comet must have been projected on its disc, but no spot or cloud was to be seen, so that it must have had no solid part whatever. The nuclei of many comets which seemed solid and brilliant to the naked eye have been resolved into mere vapour by telescopes of high powers; in Halley’s comet there was no solid part at all.

The nebulosity immediately round the nucleus is so diaphanous, that it gives little light; but at a small distance the nebulous matter becomes suddenly brilliant, so as to look like a bright ring round the body. Sometimes there are two or three of these luminous concentric rings separated by dark intervals, but they are generally incomplete on the part next the tail.

These annular appearances are an optical effect, arising from a succession of envelopes of the nebulous matter with intervals between them, of which the first is sometimes in contact with the nucleus and sometimes not. The thickness of these bright diaphanous coatings in the comets of 1799 and 1807 was about 7000 and 10,000 leagues respectively; and in the first comet of 1811 the luminous ring was 8000 leagues thick, and the distance between its interior surface and the centre of the head was 10,000 leagues. The latter comet was by much the most brilliant that has been seen in modern times; it was first discovered in this country by Mr. James Vietch of Inchbonny, and was observed in all its changes by Sir William Herschel and M. Olbers. To the naked eye, the head had the appearance of an ill-defined round mass of light, which was resolved into several distinct parts when viewed with a telescope. A very brilliant interior circular mass of nebulous matter was surrounded by a black space having a parabolic form, very distinct from the dark blue of the sky. This dark space was of a very appreciable breadth. Exterior to the black interval there was a luminous parabolic contour of considerable thickness, which was prolonged on each side in two diverging branches, which formed the bifid tail of the comet. Sir William Herschel found that the brilliant interior circular mass lost the distinctness of its outline as he increased the magnifying power of the telescope, and presented the appearance of a more and more diffuse mass of greenish or blueish green light, whose intensity decreased gradually, not from the centre, but from an eccentric brilliant speck, supposed to be the truly solid part of the comet. The luminous envelope was of a decided yellow, which contrasted strongly with the greenish tint of the interior nebulous mass. Stars were nearly veiled by the luminous envelope, whilst, on the contrary, Sir William Herschel saw three extremely small stars shining clearly in the black space, which was singularly transparent. As the envelopes were formed in succession as the comet approached the sun, Sir William Herschel conceived them to be vapours raised by his heat at the surface of the nucleus, and suspended round it like a vault or dome by the elastic force of an extensive and highly transparent atmosphere. In coming to the sun, the coatings began to form when the comet was as distant as the orbit of Jupiter, and in its return they very soon entirely vanished; but a new one was formed after it had retreated as far as the orbit of Mars, which lasted for a few days. Indeed, comets in general are subject to sudden and violent convulsions in their interior, even when far from the sun, which produce changes that are visible at enormous distances, and baffle all attempts at explanation—probably arising from electricity, or even causes with which we are unacquainted. The envelopes surrounding the nucleus of the comet on the side next to the sun diverge on the opposite side, where they are prolonged into the form of a hollow cone, which is the tail. Two repulsive forces seem to be concerned in producing this effect; one from the comet and another from the sun, the latter being the most powerful. The envelopes are nearer the centre of the comet on the side next to the sun, where these forces are opposed to one another; but on the other side the forces conspire to form the tail, conveying the nebulous particles to enormous distances.

The lateral edges of the tail reflect more light than the central part, because the line of vision passes through a greater depth of nebulous matter, which produces the effect of two streams somewhat like the aurora. Stars shine with undiminished lustre through the central part of the tail, because their rays traverse it perpendicularly to its thickness; but, though distinctly seen through its edges, their light is weakened by its oblique transmission. The tail of the great comet of 1811 was of wonderful tenuity; stars which would have been entirely concealed by the slightest fog were seen through 64,000 leagues of nebulous matter without the smallest refraction. Possibly some part of the changes in the appearance of the tails arises from rotation. Several comets have been observed to rotate about an axis passing through the centre of the tail. That of 1825 performed its rotation in 20-1/2 hours, and the rapid changes in the luminous sectors which issued from the nucleus of Halley’s comet in all probability were owing to rotatory motion.

The two streams of light which form the edges of the tail in most cases unite at a greater or less distance from the nucleus, and are generally situate in the plane of the orbit. The tails follow comets in their descent towards the sun, but precede them in their return, with a small degree of curvature; their apparent extent and form vary according to the positions of the orbits with regard to the ecliptic. In some cases the tail has been at right angles to the line joining the sun and comet. The curvature is in part owing to the resistance of the ether, and partly to the velocity of the comet being greater than that of the particles at the extremity of its tail, which lag behind. The tails are generally of enormous lengths; the comet of 1811 had one no less than a hundred millions of miles in length, and those which appeared in the years 1618, 1680, and 1769, had tails which extended respectively over 104, 90, and 97 degrees of space. Consequently, when the heads of these comets were set, a portion of the extremity of their tails was still in the zenith. Sometimes the tail is divided into several branches, like the comet of 1744, which had six, separated by dark intervals, each of them about 4° broad, and from 30° to 44° long. They were probably formed by three hollow cones of the nebulous matter proceeding from the different envelopes, and enclosing one another, with intervals between; the lateral edges of these cones would give the appearance of six streams of light. The tails do not attain their full magnitude till the comet has left the sun. When comets first appear, they resemble round films of vapour, with little or no tail. As they approach the sun, they increase in brilliancy, and their tail in length, till they are lost in his rays; and it is not till they emerge from the sun’s more vivid light that they assume their full splendour. They then gradually decrease, their tails diminish, and they disappear, nearly or altogether, before they are beyond the sphere of telescopic vision. Many comets have no tails, as, for example, Encke’s comet. Those which appeared in the years 1585, 1763, and 1682, were also without tails, though the latter is recorded to have been as bright as Jupiter. The matter of the tail must be extremely buoyant to precede a body moving with such velocity: indeed, the rapidity of its ascent cannot be accounted for. It has been attributed to that power in the sun which produces those vibrations of ether which constitute light; but as this theory will not account for the comet of 1824, which is said to have had two tails, one directed towards the sun, and a very short one diametrically opposite to it, our ignorance on this subject must be confessed. In this case the repelling power of the comet seems to have been greater than that of the sun. Whatever that unknown power may be, there are instances in which its effects are enormous; for, immediately after the great comet of 1680 had passed its perihelion, its tail was 100,000,000 miles in length, and was projected from the comet’s head in the short space of two days. A body of such extreme tenuity as a comet is most likely incapable of an attraction powerful enough to recall matter sent to such an enormous distance; it is therefore, in all probability, scattered in space or absorbed by the zodiacal light or nebula that surrounds the sun, which may account for the rapid decrease observed in the tails of comets every time they return to their perihelia. Should the great comet of 1843 prove to be the same with that of 1668, its tail must have diminished considerably.

It is remarkable that, although the tails of comets increase in length as they approach their perihelia, there is reason to believe that the real diameter of the head contracts on coming near the sun, and expands rapidly on leaving him. Hevelius first observed this phenomenon, which Encke’s comet has exhibited in a very extraordinary degree. On the 28th of October, 1828, this comet was about three times as far from the sun as it was on the 24th of December; yet at the first date its apparent diameter was twenty-five times greater than at the second, the decrease being progressive. M. Valz attributes the circumstance to a real condensation of volume from the pressure of the ethereal medium, which increases most rapidly in density towards the surface of the sun, and forms an extensive atmosphere around him. It did not occur to M. Valz, however, that the ethereal fluid would penetrate the nebulous matter instead of compressing it. Sir John Herschel, on the contrary, conjectures that it may be owing to the alternate conversion of evaporable materials in the upper regions of the transparent atmosphere of comets into the states of visible cloud and invisible gas by the effects of heat and cold; or that some of the external nebulous envelopes may come into view when the comet arrives at a darker part of the sky, which were overpowered by the superior light of the sun while in his vicinity. The first of these hypotheses he considers to be perfectly confirmed by his observations on Halley’s comet, made at the Cape of Good Hope, after its return from the sun. He thinks that, in all probability, the whole comet, except the densest part of its head, vanished, and was reduced to a transparent and invisible state during its passage at its perihelion: for when it first came into view, after leaving the sun, it had no tail, and its aspect was completely changed. A parabolic envelope soon began to appear, and increased so much and so rapidly that its augmentation was visible to the eye. This increase continued till it became so large and so faint, that at last it vanished entirely, leaving only the nucleus and a tail, which it had again acquired, but which also vanished; so that at last the nucleus alone remained. Not only the tails, but the nebulous part of comets, diminishes every time they return to their perihelia; after frequent returns they ought to lose it altogether, and present the appearance of a fixed nucleus: this ought to happen sooner to comets of short periods. M. de la Place supposes that the comet of 1682 must be approaching rapidly to that state. Should the substances be altogether, or even to a great degree, evaporated, the comet would disappear for ever. Possibly comets may have vanished from our view sooner than they would otherwise have done from this cause.

The comet discovered at Florence by Signore Donati, on the 2nd of June, 1858, was one of the most beautiful that has been seen from our planet for many years, whether for the brightness of the nucleus, or the length and graceful form of the coma; when first discovered it was near the star λ in the constellation of the Lion, being then at a distance of 288,000,000 miles from the earth; during the month of August its nucleus assumed an almost planetary aspect from the concentration of its light; on the 27th of September the head appeared almost as bright as Mercury, but smaller; when near its perihelion passage, on September 30th, its diameter, as ascertained by Signore Donati, was 3ʺ; during the early part of October it continued to increase in brilliancy, the tail becoming more elongated, and describing a beautiful arc in the heavens, occupying a space of nearly 40°, or a length of 40,000,000 miles in the solar system. On the evening of the 5th of October it was seen from most parts of Britain, within 20ʹ of Arcturus, the brightest star in the northern heavens, across which the densest part nearly of the tail passed, and through which notwithstanding the star shone with undiminished brilliancy. On the 30th of October, when in perihelio, the comet was only 55,000,000 miles from the sun; on the 10th it approached nearest to the earth, from which it was then distant 51,000,000 miles; and on the 15th of the same month near to Venus, being at that time less than one-tenth the distance of the earth from the Sun; if the comet had reached its perihelion a few days earlier, Venus might have passed through its nucleus, the consequences of which to the planet it would be very difficult to imagine. The motion of Donati’s comet is what astronomer’s call retrograde, or from east to west. It ceased to be visible in our northern latitudes in the last week in October, having passed into the southern heavens, where it will traverse the constellations of Sagittarius, Telescopium, and Indus, approaching the large star of Toucan; after which it will disappear until it has nearly completed its revolution round the sun. The observed orbit of this remarkable comet coincides more nearly with an ellipse than a parabola; the longer diameter of the ellipse being 184 times that of the earth’s orbit, or the immense distance of 35,100,000,000 miles—a space which, however great, is less than the thousandth of the distance of the nearest fixed star. According to the calculations of M. Loewy, and adopting an elliptic orbit, Donati’s comet will not return to the same places in the heavens for 2495 years, being 500 less than the period of revolution of the great comet of 1811.

Signore Donati observed that between the 25th and 30th September two concentric, luminous, semicircular envelopes, with a dark space between them, were formed in the head. From the extremities of these the cone of the tail extended, and a non-luminous or dark space stretched for 20° from the nucleus into the tail. On the 1st October the two envelopes were combined into one. This comet, like Halley’s, has shown some singular irregularities, supposed to arise from the action of the sun when near its perihelion. At different periods of its apparition a violent agitation was observed in its nucleus, with luminous jets, spiral offshoots, &c., as in the great comets of 1680, 1744, 1811. A ray of light was thrown out from one side of the nucleus towards the sun, while a gas-like jet proceeded from the other side, which appeared to form the origin of a second tail within the great tail, and which was traced for half a degree by Mr. Hind on the 19th September. He observed decided spiral convolutions in the tail, which show that this comet has a rotatory motion about an axis passing through the tail.

If comets shine by borrowed light, they ought, in certain positions, to exhibit phases like the moon; but no such appearance has been detected, except in one instance, when they are said to have been observed by Hevelius and La Hire, in the year 1682. In general, the light of comets is dull—that of the comet of 1811 was only equal to the tenth part of the light of the full moon—yet some have been brilliant enough to be visible in full daylight, especially the comet of 1744, which was seen without a telescope at one o’clock in the afternoon, while the sun was shining. Hence it may be inferred that, although some comets may be altogether diaphanous, others seem to possess a solid mass resembling a planet. But whether they shine by their own or by reflected light has never been satisfactorily made out till now. Even if the light of a comet were polarized, it would not afford a decisive test, since a body is capable of reflecting light, though it shines by its own. M. Arago, however, has, with great ingenuity, discovered a method of ascertaining this point, independent both of phases and polarization.

Since the rays of light diverge from a luminous point, they will be scattered over a greater space as the distance increases, so that the intensity of the light on a screen two feet from the object is four times less than at the distance of one foot; three feet from the object it is nine times less; and so on, decreasing in intensity as the square of the distance increases. As a self-luminous surface consists of an infinite number of luminous points, it is clear that, the greater the extent of surface, the more intense will be the light; whence it may be concluded that the illuminating power of such a surface is proportional to its extent, and decreases inversely as the square of the distance. Notwithstanding this, a self-luminous surface, plane or curved, viewed through a hole in a plate of metal, is of the same brilliancy at all possible distances as long as it subtends a sensible angle, because, as the distance increases, a greater portion comes into view; and, as the augmentation of surface is as the square of the diameter of the part seen through the whole, it increases as the square of the distance. Hence, though the number of rays from any one point of the surface which pass through the hole decreases inversely as the square of the distance, yet, as the extent of surface which comes into view increases also in that ratio, the brightness of the object is the same to the eye as long as it has a sensible diameter. For example—Uranus is about nineteen times farther from the sun than we are, so that the sun, seen from that planet, must appear like a star with a diameter of a hundred seconds, and must have the same brilliancy to the inhabitants that he would have to us if viewed through a small circular hole having a diameter of a hundred seconds. For it is obvious that light comes from every point of the sun’s surface to Uranus, whereas a very small portion of his disc is visible through the hole; so that extent of surface exactly compensates distance. Since, then, the visibility of a self-luminous object does not depend upon the angle it subtends as long as it is of sensible magnitude, if a comet shines by its own light, it should retain its brilliancy as long as its diameter is of a sensible magnitude; and, even after it has lost an apparent diameter, it ought to be visible, like the fixed stars, and should only vanish in consequence of extreme remoteness. That, however, is far from being the case—comets gradually become dim as their distance increases, and vanish merely from loss of light, while they still retain a sensible diameter, which is proved by observations made the evening before they disappear. It may therefore be concluded that comets shine by reflecting the sun’s light. The most brilliant comets have hitherto ceased to be visible when about five times as far from the sun as we are. Most of the comets that have been visible from the earth have their perihelia within the orbit of Mars, because they are invisible when as distant as the orbit of Saturn: on that account there is not one on record whose perihelion is situate beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last appearance, remained five whole years within the ellipse described by Saturn without being once seen. More than a hundred and forty comets have appeared within the earth’s orbit during the last century that have not again been seen. If a thousand years be allowed as the average period of each, it may be computed, by the theory of probabilities, that the whole number which range within the earth’s orbit must be 1400; but, Uranus being about nineteen times more distant, there may be no less than 11,200,000 comets that come within the orbit of Uranus. M. Arago makes a different estimate; he considers that, as thirty comets are known to have their perihelion distance within the orbit of Mercury, if it be assumed that comets are uniformly distributed in space, the number having their perihelion within the orbit of Uranus must be to thirty as the cube of the radius of the orbit of Uranus to the cube of the radius of the orbit of Mercury, which makes the number of comets amount to 3,529,470. But that number may be doubled, if it be considered that, in consequence of daylight, fogs, and great southern declination, one comet out of two must be hid from us. According to M. Arago, more than seven millions of comets come within the orbit of Uranus.

The different degrees of velocity with which the planets and comets were originally propelled in space is the sole cause of the diversity in the form of their orbits, which depends only upon the mutual relation between the projectile force and the sun’s attraction.

When the two forces are exactly equal to one another, circular motion is produced; when the ratio of the projectile to the central force is exactly that of 1 to the square root of 2, the motion is parabolic; any ratio between these two will cause a body to move in an ellipse, and any ratio greater than that of 1 to the square root of 2 will produce hyperbolic motion (N. 229).

The celestial bodies might move in any one of these four curves by the law of gravitation: but, as one particular velocity is necessary to produce either circular or parabolic motion, such motions can hardly be supposed to exist in the solar system, where the bodies are liable to such mutual disturbances as would infallibly change the ratio of the forces, and cause them to move in ellipses in the first case, and hyperbolas in the other. On the contrary, since every ratio between equality and that of 1 to the square root of 2 will produce elliptical motion, it is found in the solar system in all its varieties, from that which is nearly circular to such as borders on the parabolic from excessive ellipticity. On this depends the stability of the system; the mutual disturbances only cause the orbits to become more or less excentric without changing their nature.

For the same reason the bodies of the solar system might have moved in an infinite variety of hyperbolas, since any ratio of the forces, greater than that which causes parabolic motion, will make a body move in one of these curves. Hyperbolic motion is however very rare; only two comets appear to move in orbits of that nature, those of 1771 and 1824; probably all such comets have already come to their perihelia, and consequently will never return.

The ratio of the forces which fixed the nature of the celestial orbits is thus easily explained; but the circumstances which determined these ratios, which caused some bodies to move nearly in circles and others to wander towards the limits of the solar attraction, and which made all the heavenly bodies to rotate and revolve in the same direction, must have had their origin in the primeval state of things; but as it pleases the Supreme Intelligence to employ gravitation alone in the maintenance of this fair system, it may be presumed to have presided at its creation.

SECTION XXXVI.

The Fixed Stars—Their Number—The Milky Way—Double Stars—Binary Systems—Their Orbits and Periodic Times—Colours of the Stars—Stars that have vanished—Variable Stars—Variation in Sun’s Light—Parallax and Distances of the Fixed Stars—Masses of the Stars—Comparative Light of the Stars—Proper Motions of the Stars—Apparent Motions of the Stars—Motion and Velocity of the Sun and Solar System—The Nebulæ—Their Number—Catalogue of them—Consist of Two Classes—Diffuse Nebulæ—Definitely formed Nebulæ—Globular Clusters—Splendour of Milky Way—Distribution of the Nebulæ—The Magellanic Clouds—Nebulæ round η Argûs—Constitution of Nebulæ, and the Forces that maintain them—Meteorites and Shooting Stars.

GREAT as the number of comets appears to be, it is absolutely nothing in comparison of the multitude of the fixed stars. About 2000 only are visible to the naked eye; but when the heavens are viewed through a telescope, their number seems to be limited only by the imperfection of the instrument. The number registered amounts to 200,000; their places are determined with great precision, and they are formed into a catalogue, not only for the purpose of ascertaining geographical positions by the occultations of the brightest among them, but also to serve as points of reference for marking the places of comets and other celestial phenomena. Sirius, α Centauri, and Arcturus are the brightest stars in the heavens; the others are classed according to their apparent lustre, from the first to the seventeenth magnitudes. Capella, α Lyræ, Procyon, and twenty or twenty-one more, are of the first magnitude; α Persei, γ Orionis, α Cygni, and in all fifty or sixty, are of the second; and of the third there are about 200, such as η Bootis and η Draconis, the numbers increasing as the magnitude diminishes. Those of the eighth magnitude are scarcely visible to the naked eye, and it requires a very good telescope to see stars of the seventeenth. This sequence is perfectly arbitrary; but Sir John Herschel has ascertained by actual measurement the comparative lustre of a great many—for example, he found that the light of a star of the sixth magnitude is 100 times less than that of one of the first magnitude, and that Sirius would make between three and four hundred of such little stars. Were the photometric scale completed, it would be of the greatest importance with regard to the variable stars.

The three or four brightest classes of stars are scattered pretty equably over the sky, with the exception of a zone or belt following the course of the great circle passing through ε Orionis and α Crucis, where they are very numerous, especially in the southern hemisphere. The stars of all magnitudes visible to the naked eye increase in numbers towards the borders of the Milky Way, which derives its lustre and name from the diffused light of myriads of stars; so numerous are they in some parts of it that more than 50,000 passed through the field of Sir William Herschel’s telescope in the course of an hour, in a zone only two degrees broad; in many places they are numerous beyond estimation, and most of them are extremely small on account of their enormous distances.

The Milky Way, which forms so conspicuous a part of the firmament, is a vast and somewhat flattened stratum or congeries of stars, encircling the heavens in a broad band, split through one part of its circumference into two streams of stars, bearing a strong resemblance to fig. 5, plate 5. It is contorted and broken in some places, and occasionally lengthened into branches stretching far into space. Its thickness is small compared with its length and breadth; yet in some places it is unfathomable even with the best telescopes; in others there is reason to believe that it is possible to see through it, and even beyond it, in its own plane. There is a gradual but rapid increase in the crowding of the stars on each side of the flat stratum towards the centre.

The solar system is deeply though excentrically plunged into this mass of stars, near that point where the circular stratum splits into two streams. Sir John Herschel’s description of the stars of the southern hemisphere shows that the Milky Way is a most magnificent object there. “The general aspect of the southern circumpolar regions (including in that expression 60° or 70° of south polar distance) is in a high degree rich and magnificent, owing to the superior brilliancy and large development of the Milky Way, which, from the constellation of Orion to that of Antinous, is a blaze of light, strangely interrupted, however, with vacant and entirely starless patches, especially in Scorpio, near α Centauri and the Cross, while to the north it fades away pale and dim, and is in comparison hardly traceable. I think it is impossible to view this splendid zone, with the astonishingly rich and evenly distributed fringe of stars of the 3rd and 4th magnitude, which forms a broad skirt to its southern border like a vast curtain, without an impression amounting almost to conviction, that the Milky Way is not a mere stratum, but annular, or at least that our system is placed within one of the poorer or almost vacant parts of its general mass, and that eccentrically, so as to be much nearer to the region about the Cross than to that diametrically opposite to it.”

Those dark vacuities called “Coal Sacks” by the ancient navigators, which are so numerous between α Centauri and α Antaris, are among the most extraordinary phenomena in the southern hemisphere; they are of intense blackness, though by no means void of extremely small telescopic stars; the darkness arises from the contrast these nearly vacant spaces form with the excessive brilliancy of the surrounding part of the Milky Way, and the sudden sharp transition from light to darkness. The largest and most conspicuous of them is a pear-shaped vacuity close to the Southern Cross. That portion of the Milky Way that is split longitudinally through its centre lies between α Centauri and the constellation of Cygnus: the two bands are joined here and there by narrow bridges of condensed stars, stretching across the darker space between them. In Scorpio and Sagittarius Sir John Herschel describes the Milky Way as composed of definite clouds of light running into clusters of extremely minute stars like sand, not strewed evenly as with a sieve, but as if thrown down by handfuls, and by both hands at once, leaving dark intervals. In this astonishing profusion the stars are of all sizes, from the 14th to the 20th magnitude, and even down to nebulosity. After an interval the same profusion is renewed, the stars being inconceivably minute and numerous beyond description—they are in millions and millions. Thus there is great irregularity in their diffusion as well as magnitude—in some places intensely crowded, in others the deep blackness of the sky, over which they are thinly scattered, irresistibly led to believe that in these regions the power of our telescopes fairly penetrates through the starry stratum, and beyond it. Sometimes we look through a sheet of stars nearly of the same size, of no great thickness compared with their distance from us, and not unfrequently there is a double stratum, one of large stars spread over another of very small ones.

The most southerly of the two streams of stars which form the Milky Way in this part of the firmament maintains an unbroken course of extreme brilliancy, containing some of the finest clusters of stars in the heavens. One round γ Sagittarii is an intense aggregate of stars, in some parts of which they are so crowded as to exceed enumeration; at a very moderate estimate Sir John Herschel thinks this group cannot contain fewer than a hundred thousand stars. Other two groups between the constellations of the Shield and Ophiuchus stand out like promontories of intense brilliancy in the dark space that separates the starry streams of the Milky Way.

The distance of the fixed stars is too great to admit of their exhibiting a sensible disc, but they must be spherical if gravitation pervades all space, as there is every reason to believe it does. With a powerful telescope the stars are like points of light: their occultations by the moon are therefore instantaneous. Their twinkling arises from sudden changes in the refractive power of the air, which would not be sensible if they had discs like planets. Thus nothing can be known of their distance from us or from one another by their apparent diameters. Although from the appearance of the stars no inference can be drawn as to their distance, yet among the multitudes in the heavens a few are found near enough to exhibit distinct parallactic motions arising from the revolution of the earth in its orbit, from whence their distance from the sun has been computed: α Centauri, the brightest star in the southern hemisphere, is a very remarkable instance. Professor Henderson at the Cape of Good Hope determined its parallax to be 1ʺ by a series of observations on its position at opposite periods of the year, that is, from opposite points in the earth’s orbit. The result was afterwards confirmed by Mr. Maclear, who found the amount to be 0ʺ·913. The difference between the two is wonderfully small, considering the many unavoidable sources of error in the determination of such minute quantities (N. 230).

Since no star in the northern hemisphere has so great an amount of parallax, an arc of 1ʺ is assumed as the parallactic unit. Now radius is to the sine of 1ʺ as 206,265 is to 1; hence, α Centauri is 206,265 times more distant from the sun than the sun is from the earth. Light flying at the rate of 192,000 miles in a second must take 3 years and 83 days to come to us from that star.

One or two tenths of a second becomes a very great error when the maximum amount of parallax is only 1ʺ, and on that account, with the exception of α Centauri, it has been found impracticable to determine the annual changes in the apparent motions of single stars affected by precession, nutation, aberration, and the variations of temperature of the instruments used in observing. However, as two stars in juxtaposition are equally affected by all of these; the difference in their motions is independent of them. Of two stars apparently in close approximation, one may be far behind the other in space. They may seem near to one another when viewed from the earth in one part of its orbit, but may separate widely when seen from the earth in another position, just as two terrestrial objects appear to be one when viewed in the same straight line, but separate as the observer changes his position. In this case the stars would not have real, but only apparent motion. One of them would seem to oscillate annually to and fro in a straight line on each side of the other, a motion that could not be mistaken for that of a binary system where one star describes an ellipse about the other; or if the edge of the orbit be turned towards the earth, where the oscillations require years for their accomplishment. The only circumstances that can affect the stars unequally, and which must be eliminated, are the proper motion of the stars in space, and specific aberration, a very minute quantity arising from peculiarities in the star’s light. This method of finding the distances of the fixed stars was proposed by Galileo and attempted by Dr. Long without success. Sir William Herschel afterwards applied it to some of the binary groups; and although he did not find the thing he sought for, it led to the discovery of the orbital motions of the double stars.

M. Struve was the first to apply this method, and that in a very difficult case. He perceived that a very small star is close to α Lyræ, and by a series of most accurate differential measurements from 1835 to 1838 he found that α Lyræ has a parallax of 0ʺ·261, which was afterwards corroborated by the observations of M. Peters; hence α Lyræ is 789,600 times more distant from the sun than the earth is.

It was natural to suppose that in general the large stars are nearer to the earth than the small ones; but there is now reason to believe that some stars, though by no means brilliant, are nearer to us than others which shine with greater splendour. This is inferred from the comparative velocity of their proper motions; all the stars have a general motion of translation, which tends ultimately to mix those of the different constellations; but none that we know of moves so rapidly as 61 Cygni, and on that account it was reckoned to be nearer to us than any other, for an object seems to move more quickly the nearer it is. Now M. Bessel saw that two minute and probably very remote stars are very near 61 Cygni, their directions from that star being at right angles to one another; so that, during the revolution of the earth, one of these distances was a maximum and the other a minimum alternately every three months. This alternation, although it indicated a parallax or difference of parallaxes of only 0ʺ·348, was maintained with such perfect regularity every three months, that it leaves not a doubt of its accuracy, which was afterwards confirmed by the observations of M. Peters at Polkova. It follows from that small parallax that 61 Cygni must be 592,700 times farther from the earth than the sun is—a distance that light would not pass over in less than nine years and three months.

Mr. Henderson found the parallax of Sirius, the brightest of all the stars, to be only 0ʺ·230; it is consequently more distant than 61 Cygni, though the latter is but of the 6th magnitude.

M. Argelander has calculated that the apparent magnitude of the stars depends upon their distance. Supposing them all to be of the same size, the smallest visible in Sir William Herschel’s 20 feet reflecting telescope, namely those of the 17th magnitude, would be 228 times farther off than those of the first magnitude; and M. Peters of Polkova from the annual parallax of thirty-five, seven of which are now very accurately determined, has ascertained the distance of the nearest of them to be such, that light flying at the rate of 95 millions of miles in a second would take 15 years and a half to come from them to the earth, and that a star of the 17th magnitude might be extinguished for 3541 years before we should be aware of it. (N. 231.)

The great gulfs that separate the stars from the sun, and probably from one another, no doubt maintain the stability of the stellar system, in the same manner that in the solar system the distances of the planets from the sun and the satellites from their primaries are so arranged as to preserve their mutual disturbances within due limits. The stars supposed to be nearest the sun are probably in a great zone which crosses the Milky Way between η Argûs and α Crucis. It comprises the bright stars of the constellations Orion, Canis Major, the Southern Cross, Centaur, Lupus, and Scorpio. The axis of the zone is inclined at an angle of 20° to the medial line, or circle, passing through the centre of the Milky Way.

A very great number of stars undergo periodical changes of lustre, varying in some cases from complete extinction to their original brilliancy, strongly suggesting the idea that they are temporarily obscured, and sometimes completely hid, by opaque bodies revolving round them in regular periodic times, as the planets do about the sun.

The star Mira, or ω Ceti, which was first noticed to be periodical by Fabricius, in 1596, appears about twelve times in eleven years, or in periods of 331^d 8^h 4^m 16^s; it remains at its greatest brightness about a fortnight, being then on some occasions equal to a large star of the second magnitude; then it decreases during about three months, till it becomes completely invisible to the naked eye, in which state it remains about five months; after that it continues increasing during the remainder of its period. Such is the general course of its changes; but it does not always return to the same degree of brightness, nor increase and diminish by the same gradations, neither are the successive intervals of its maxima equal. From the observations and investigations of M. Argelander, the mean period given is subject to fluctuation, embracing 88 such periods, and having the effect of gradually lengthening and shortening alternately those intervals to the extent of 25 days one way and the other. The irregularities in the degree of brightness attained at the maximum are probably also periodical. For four years previous to 1676 it did not appear at all; and on October 5, 1839, it exceeded α Ceti, and equalled β Aurigæ, in lustre. These irregularities may be occasioned by periodical perturbations among opaque bodies revolving about the star. Algol, or β Persei, is another very remarkable instance of a variable star. It has the size of a star of the second magnitude for two days and thirteen and a half hours, and then suddenly begins to diminish in splendour, till, in about three hours and a half, it is reduced to the size of a star of the fourth magnitude; it then begins again to increase, and in three hours and a half more regains its brightness, going through all these vicissitudes in 2^d 20^h 48^m 54^s·7. Sir John Herschel and Mr. Goodricke, by whom the variable nature of this star was discovered in 1782, considered this to be a case strongly indicative of the revolution of an opaque body, which, coming between us and Algol, cuts off a large portion of the light. This star has been constantly observed, and the more recent observations, compared with the ancient ones, indicated a diminution in the periodic time. It is even proved that this decrease is not uniformly progressive, but is actually proceeding with accelerated rapidity, which, however, will probably not continue, but will by degrees relax, and then be changed into increase, according to the laws of periodicity, which, as well as their causes, remain to be discovered. The first minimum of this star, in 1844, happened on January 3rd, at 4^h 14^m Greenwich time. γ Hydræ also vanishes and reappears every 494 days. β Lyræ was discovered to be variable, in 1784, by Mr. Goodricke, and its period was ascertained by Argelander to be 12^d 21^h 53^m 10^s, in which time a double maximum and minimum takes place, the two maxima being nearly equal, but the two minima unequal; besides these semi-periods, there is a slow aberration of period, which appears to be periodical itself: from its discovery to 1840 the time was continually lengthening, but more and more slowly, till, in 1840, it ceased to increase, and has since been slowly on the decrease.

The stars δ Cephei and η Aquilæ, or Antinoi, were discovered to be variable in 1784; their respective periods, being 5^d 8^h 47^m 39^s and 7^d 4^h 13^m 53^s, have since been accurately determined. Besides these, the variations of between 30 and 40 have been approximately ascertained, and a great many more among the smaller stars have been discovered to be variable by Mr. Hind, who has remarked that many of those stars which continue visible at their minimum appear hazy and indistinct, as though some cloudy or nebulous medium intervened. Some of the variable stars are red, and others present successive changes through blue, yellow, and red. When the brightness is increasing the star has a blueish tinge, when it is past its maximum lustre it assumes a yellow tint, and while on its decrease it becomes ruddy with flashes of bright red light. These changes are very marked in a small star near the star 77, at the extremity of the south wing of Virgo.

Sir John Herschel, after having described the glory of the starry heavens, asks, “For what purpose are we to suppose such magnificent bodies scattered through the abyss of space? Surely not to illuminate our nights, which an additional moon of the thousandth part the size of our own would do much better, nor to sparkle as a pageant void of meaning and reality, and bewilder us with vain conjectures. Useful, it is true, they are to man as points of exact and permanent reference; but he must have studied astronomy to little purpose who can suppose man to be the only object of his Creator’s care, or who does not see in the vast and wonderful apparatus around us provision for other races of animated beings. The planets, we have seen, derive their light from the sun, but that cannot be the case with the stars. These doubtless then are themselves suns, and may perhaps, each in its sphere, be the presiding centre round which other planets or bodies, of which we can form no conception from any analogy offered by our own system, may be circulating.”

Another circumstance shows how probable it is that dark bodies are revolving among the stars. The proper motion of Sirius is very irregular—sometimes it is rapid, and at other times slow; the cause is ascribed by MM. Bessel and Peters to a dark companion which revolves with Sirius about their common centre of gravity, and by its attraction disturbs the equable motion of the star.

Sometimes stars have all at once appeared, shone with a bright light, and vanished. Several instances of these temporary stars are on record. A remarkable one occurred in the year 125, which is said to have induced Hipparchus to form the first catalogue of stars. Another star appeared suddenly near α Aquilæ in the year 389, which vanished after remaining for three weeks as bright as Venus. On the 10th of October, 1604, a brilliant star burst forth in the constellation of Serpentarius, which continued visible for a year; and on the 11th of November, 1572, a star all at once shone forth in Cassiopeia, which rapidly increased in brightness till it surpassed that of Jupiter so much as to be visible at midday. It began to decrease in December of the same year, and, in March, 1574, it had entirely disappeared, having exhibited a variety of tints. It is suspected, however, that this star is periodically variable and identical with stars which appeared in the years 945 and 1264. A more recent case occurred in the year 1670, when a new star was discovered in the head of the Swan, which, after becoming invisible, reappeared, and, having undergone many variations in light, vanished after two years, and has never since been seen. On the 28th of April, 1848, Mr. Hind discovered a star of the 5th magnitude in the constellation Ophiuchus, which was very conspicuous to the naked eye, and where he was certain no star even so bright as the 9th magnitude had ever existed, nor was there any record of such a star. From the time of its discovery it continued to diminish till it became extinct. Its colour was ruddy, and was thought to undergo remarkable changes, probably an effect of its low position, as its polar distance was 102° 39ʹ 14ʺ.

Sir John Herschel discovered very singular variations in the star η of the constellation Argo. It is surrounded by a wonderful nebula, and between the years 1677 and 1826 it varied twice from the 4th to the 2nd magnitude; but in the beginning of 1838 it suddenly increased in lustre, so as to be nearly as bright as α Centauri. Thence it diminished, but not below the first magnitude till April 1843, when it had again increased, so as to surpass Canopus, and nearly equal Sirius in splendour. With regard to this singular phenomenon, Sir John Herschel observes, that “Temporary stars heretofore recorded have all become totally extinct. Variable stars, as far as they have been carefully attended to, have exhibited periodical and regular alternations (in some degree at least) of splendour and comparative obscurity; but here we have a star fitfully variable to an astonishing extent, and whose fluctuations are spread over centuries, apparently in no settled period, and in no regular progression. What origin can we ascribe to these sudden flashes and relapses? What conclusions are we to draw as to the comfort or habitability of a system depending for its supply of light and heat on so variable a source? Its future career will be a subject of high physical interest. To this account I will only add, that in the beginning of 1838 the brightness of this star was so great as materially to interfere with the observations of that part of the nebula surrounding it.” Sir John has also discovered that α Orionis is variable, a circumstance the more remarkable as it is one of the conspicuous stars of our hemisphere, and yet its changes had never been remarked. The inferences Sir John draws from the phenomena of variable stars are too interesting not to be given in his own words. “A periodic change existing to so great an extent in so large and brilliant a star as α Orionis cannot fail to awaken attention to the subject, and to revive the consideration of those speculations respecting the possibility of a change in the lustre of our sun itself, which were first put forth by my father. If there be really a community of nature between the sun and the fixed stars, every proof that we obtain of the extensive prevalence of such periodical changes in those remote bodies adds to the probability of finding something of the kind nearer home. If our sun were ever intrinsically much brighter than at present, the mean temperature of the surface of our globe would of course be proportionally greater. I speak now not of periodical, but secular changes. But the argument is complicated with the consideration of the possible imperfect transparency of space, which may be due to material non-luminous particles, diffused irregularly in patches analogous to nebulæ, but of great extent—to cosmical clouds, in short, of whose existence we have, I think, some indication in the singular and apparently capricious phenomena of temporary stars, and perhaps in the recent extraordinary increase, and hardly less sudden diminution, of η Argûs.” Mr. Hind has come to the same conclusion with Goodricke and Sir John Herschel, that the changes in the variable stars are owing to opaque bodies revolving round them; indeed there are strong reasons to believe that there are solar systems analogous to our own in the remote regions of space. Our sun requires nine times the period of Algol to perform a revolution on its axis, while, on the other hand, the periodic time of an opaque revolving body, sufficiently large to produce a similar temporary obscuration of the sun seen from a fixed star, would be less than fourteen hours.

It is possible that the decrease of light in some of the variable stars may arise from large spots on their surface, like those occasionally seen in the radiant fluid masses on the surface of the sun. One of these spots which was measured by Sir John Herschel on the 20th of March, 1836, with its penumbra, occupied an area of 3780 millions of square miles; and the black central part of a spot that appeared on the 25th of May following would have allowed the globe of the earth to drop through it, leaving a thousand miles clear of contact all around this tremendous abyss.

All the variable stars on record of which the places are distinctly indicated have occurred without exception in, or close upon, the borders of the Milky Way, and that only within the following semicircle, the preceding having offered no example of the kind.

Many stars have actually disappeared from the heavens. 42 Virginis seems to be of the number, having been missed by Sir John Herschel on the 9th of May, 1828, and not again found, though he frequently had occasion to observe that part of the sky. Mr. Cooper, of the Markree Observatory, has given a list of fifty stars that are missing since the publication of his list of stars in 1847. Comparing the present state of the heavens with more ancient catalogues, a much greater number have disappeared.

Thousands of stars that seem to be only brilliant points of light, when carefully examined are found to be in reality systems of two or more suns, many of which are known to revolve about one another. These binary and multiple systems are very remote, requiring powerful telescopes to show the stars separately. They are divided into eight classes, according to the proximity of the two stars. The first class comprises only such as are less than 1ʺ of space apart; those of the second class are more apart than 1ʺ and less than 2ʺ, &c. &c. Sometimes the two stars are of equal magnitude, but more frequently a conspicuous star is accompanied by a smaller companion. In some cases the conspicuous star itself is double, as in ζ Cancri, ξ Scorpio, 11 Monocerotis, and 12 Lyncis, which are triple stars. Each of the two stars of ε Lyræ is a beautiful and close double star; so that which in a common telescope appears merely to be a double star, is found to be quadruple with a very excellent instrument. The multiple system of θ Orionis is one of the most remarkable objects in our hemisphere. To the naked eye and with an ordinary telescope it seems to be a single star, but it really consists of four brilliant stars forming a trapezium, and accompanied by two excessively minute and very close companions, to perceive both of which is the severest test of a telescope.

The first catalogue of double stars in which their places and relative positions are given was accomplished by the talent and industry of Sir William Herschel, who made so many great discoveries, and with whom the idea of their combination in binary and multiple systems originated; and that important fact he established by the discovery of a revolving motion in 50 or 60, and by the determination of the revolution of one star about the other of Castor or α Geminorum, the largest and finest double star in the northern hemisphere. He even assigned the approximate periodic times of this and of several other binary systems. More than 100 stars are now known to be stellar systems. The positions of many hundreds were measured by Sir John Herschel and Sir James South; and the catalogue of the double stars in the northern hemisphere, which have been micrometrically measured, has been increased to more than 6000 by MM. Bessel, Struve, and British astronomers.

Extensive catalogues of double stars in the southern hemisphere have been published by the astronomers in our colonial establishments. To these Sir John Herschel added 1081 during his residence at the Cape of Good Hope: the angles of position and distances of the stars from one another he measured, and found that many of them have very rapid orbital motions. The elliptical elements of the orbits and periodic times of fifteen have been determined by the most eminent astronomers with wonderful accuracy, considering the enormous distances and the extreme delicacy and difficulty of the subject. M. Savary has the merit of having first determined the elements of the orbit of a double star from observation. The difficulty of doing so is great, because the nearest fixed star is 211,000 times farther from the sun than the earth is, and the orbit itself is only visible with the best telescopes; consequently a very small error in observation occasions an enormous error in the determination of quantities at that distance.

In observing the relative position of the stars of a binary system, the distance between them, and also the angle of position, that is, the angle which the meridian, or a parallel to the equator, makes with the line joining the two stars, are measured. The different values of the angle of position show whether the revolving star moves from east to west, or the contrary; whether the motion be uniform or variable, and at what points it is greatest or least. The measures of the distances show whether the two stars approach or recede from one another. From these the form and nature of the orbit are determined. Were observations perfectly accurate, four values of the angle of position, and of the corresponding distances at given epochs, would be sufficient to assign the form and position of the curve described by the revolving star; this, however, scarcely ever happens. The accuracy of each result depends upon taking the mean of a great number of the best observations, and eliminating error by mutual comparison. The distances between the stars are so minute that they cannot be measured with the same accuracy as the angles of position; therefore, in order to determine the orbit of a star independently of the distance, it is necessary to assume, as the most probable hypothesis, that the stars are subject to the law of gravitation, and consequently that one of the two stars revolves in an ellipse about the other, supposed to be at rest, though not necessarily in the focus. A curve is thus constructed graphically by means of the angles of position and the corresponding times of observation. The angular velocities of the stars are obtained by drawing tangents to this curve at stated intervals, whence the apparent distances, or radii vectores of the revolving star, become known for each angle of position, because, by the laws of elliptical motion, they are equal to the square roots of the apparent angular velocities. Now that the angles of position estimated from a given line, and the corresponding distances of the two stars, are known, another curve may be drawn, which will represent on paper the actual orbit of the star projected on the visible surface of the heavens; so that the elliptical elements of the true orbit, and its position in space, may be determined by a combined system of measurements and computation. But, as this orbit has been obtained on the hypothesis that gravitation prevails in these distant regions, which could not be known à priori, it must be compared with as many observations as can be obtained, to ascertain how far the computed ellipse agrees with the curve actually described by the star.

γ Virginis consists of two stars of nearly the same magnitude; they were so far apart in the beginning and middle of last century, that they were mentioned by Bradley, and marked in Mayer’s catalogue, as two distinct stars. Since that time they have been continually approaching each other, till in January, 1836, one star was seen to eclipse the other, by Admiral Smyth at his Observatory at Bedford, and by Sir John Herschel at the Cape of Good Hope. A series of observations since the beginning of the present century has enabled Sir John to determine the form and position of the elliptical orbit of the revolving star with extraordinary truth by the preceding method. According to his calculation, it came to its perihelion on the 18th of August of the year 1834. Its previous velocity was so great that the revolving star described an angle of 68° in one year. By the laws of elliptical motion its angular velocity must diminish till it arrives at its aphelion. The accuracy with which the motions of the binary systems are measured, and the skill employed in the deduction of the elliptical elements, are now so great, that the periodic time of γ Virginis, determined by Sir John Herschel and Admiral Smyth from their respective observatories, combined with those of Sir William Herschel, only differ by two years, Sir John having obtained a period of 182 years, Admiral Smyth that of 180. By the aid of more numerous observations Mr. Fletcher has found that the true period is 184·53 years, and that the revolving star passed its perihelion in 1837. It is by such successive steps that astronomy is brought to perfection (N. 232).

Some of the double stars have very long periods, such as ς Coronæ, where the revolving star takes 737 years nearly to accomplish a circuit. Others again have very short periods, as η Coronæ, ζ Cancri, and ξ Ursæ Majoris, whose periodic times are 42·500, 58·91, and 58·26 years respectively: therefore each of these has performed more than one entire revolution since their motions were observed. ζ Herculis, whose periodic time is only about 30-1/4 years, has accomplished two complete circuits, the lesser star having been eclipsed by the greater each time. The first of these two truly wonderful events, of one sun eclipsing another sun, was seen by Sir William Herschel in 1782.

The orbits and periodic times of so many of these binary systems having been determined proves beyond a doubt that sun revolves about sun in the starry firmament by the same law of gravitation that makes the earth and planets revolve about the sun (N. 232).

Since the parallax of 61 Cygni and that of α Centauri have been determined, Sir John Herschel has made the following approximation to the dimensions of their orbits and masses. The distance between the two stars of 61 Cygni, that is the radius vector of the revolving star, has hardly varied from 15ʺ·5 ever since the earliest observations; while in that time the star has moved through 50°; it is evident therefore that the orbit must be nearly circular. It is at right angles to the visual ray, and the periodic time is 514 years. The parallax or radius of the earth’s orbit as seen from the star is 0ʺ·348, while the radius of the star’s orbit as seen from the earth is 15ʺ·5; hence the radius of the star’s orbit is to that of the earth’s orbit as 15ʺ·5 to 0ʺ·348, or nearly as 45 to 1. So the orbit described by the two stars of 61 Cygni about one another greatly exceeds that which Neptune describes about the sun. Since the mean distance of the stars and their periodic time are given, the sum of the masses of the two stars is computed to be 0·3529, that of the sun being 1. Thus our sun is not vastly greater nor vastly less than the stars composing 61 Cygni, which is a small inconspicuous star to the naked eye, not exceeding the 6th magnitude.

Of all the double stars α Centauri is the most beautiful: it is the brightest star in the southern hemisphere, equal, if not superior, to Arcturus in lustre. The distance between the two stars has been decreasing at the rate of half a second annually since the year 1822, while the angular motion has undergone very little change, which shows that the plane of the orbit passes through the earth like the orbits of 44 Boötes, and π Serpentarii; that is to say, the edge of the orbit in these three stellar systems is presented to the earth, so that the revolving star seems to move in a straight line, and to oscillate on each side of its primary. Were this libration owing to parallax, it would be annual from the revolution of the earth about the sun; but as years elapse before it amounts to a sensible quantity, it can only arise from a real orbital motion seen obliquely. In this case five observations are sufficient for the determination of the orbit, provided they be exact; but the quantities to be measured are so minute, that it is only by a very long series of observations that accuracy can be attained. In 1834 Captain Jacob determined the periodic time of the revolving star of α Centauri to be 77 years, and the distance between the two to be 17ʺ·5; and since the decrease is half a second annually, the distance or radius vector of the revolving star was 12ʺ·5 in the year 1822; and as Mr. Henderson had determined the parallax or radius of the earth’s orbit as seen from the star to be ·913, it follows that the real semi-axis of the revolving star’s orbit is 13-1/2 times greater than the semi-axis of the earth’s orbit as a minimum. The real dimensions of the ellipse therefore cannot be so small as the orbit of Saturn, and may possibly exceed that of Uranus. It is very probable that an occultation of one of the suns by the other will take place in 1867, or a very close appulse of the two stars.

Singular anomalies have appeared in the motions of 70 Ophiuchi, which was discovered to be a binary system by Sir William Herschel in 1779, and which has since nearly accomplished a revolution. Various orbits have been computed: those which best represent the angles of position fail with regard to the distances of the stars from one another, and vice versâ. But it is a very remarkable fact that the errors are periodical, being for considerable periods of time alternately in excess and defect. Captain W. S. Jacob, who determined the periodic time of the revolving star to be 93 years, attributes this anomaly to the disturbing action of an opaque body revolving round the lesser star. Assuming that to be the case, and computing, he found that the errors were considerably diminished both in the angle of position and distance. It is a subject of the highest interest, and well worthy of the attention of such astronomers as have the means of making the necessary observations. Among the triple systems, as ζ Cancri, two of the stars revolve about one another in 58·9 years; but the motion of the third and most distant is so slow, that it has only accomplished a tenth part of its revolution about the other two since the system was discovered.

It appears from the calculations of Mr. Dunlop that ς Eridani accomplishes a revolution in little more than 30 years. The motion of Mercury is more rapid than that of any of the planets, being at the rate of 107,000 miles an hour. The perihelion velocity of the comet of 1680 was 880,000 miles an hour; but, if the two stars of ς Eridani, or of ξ Ursæ Majoris, be as remote from one another as the nearest fixed star is from the sun, the velocity of the revolving star must exceed the power of imagination to conceive. The elliptical motion of the double stars shows that gravitation is not confined to the planetary motions, but that systems of suns in the far distant regions of the universe are also obedient to its laws. The stellar systems present a kind of sidereal chronometer, by which the chronology of the heavens will be marked out to future ages by epochs of their own, liable to no fluctuations from such disturbances as take place in our system. Some stars are apparently double, though altogether unconnected, one being far behind the other in space, as α Lyræ, which apparently consists of two stars, one of the first, the other of the eleventh magnitude. Aldebaran, α Aquilæ, and Pollux are remarkable instances of these optically double stars. It has been shown how favourable that circumstance is for ascertaining the parallax of the nearest of the two. (N. 232.)

The double stars are of various hues: sometimes both stars are of the same colour, as in α Centauri and 61 Cygni, where the larger stars are of a bright orange and the smaller ones a deeper tint of the same, but they most frequently exhibit the contrasted colours. The large star is generally yellow, orange, or red; and the small star blue, purple, or green. Sometimes a white star is combined with a blue or a purple, and more rarely a red and white are united. In many cases these appearances are due to the influence of contrast on our judgment of colours. For example, in observing a double star, where the large one is a full ruby red, or almost blood colour, and the small one a fine green, the latter loses its colour when the former is hid by the cross wires of the telescope. That is the case with γ Andromedæ, which is a triple star, the small one, which appears green, being closely double. ι Cancri is an instance of a large yellow star and a small one which appears blue by contrast. Still there are a vast number where the colours are decidedly different, and suggest the curious idea of two suns, a red and a green, or a yellow and a blue, so that a planet circulating round one of them may have the variety of a red day and a green day, a yellow day and a blue day. Sir John Herschel observes, in one of his papers in the Philosophical Transactions, as a very remarkable fact, that, although red stars are common enough, no example of a solitary blue, green, or purple star has yet been produced.

Sirius is the only star on record whose colour has changed. In the time of Ptolemy it was red; now it is one of the whitest stars in the heavens.

M. Struve has found that, out of 596 bright double stars, 375 pairs have the same intensity of light and colour; 101 pairs have different intensity, but the same colour; and 120 pairs have the colours of the two stars decidedly different.

Certain rays, which exist in the sun’s light, are wanting in the spectra of every coloured star, and probably never existed in the light of these stars, as there is no reason to believe that they are absorbed by the stars’ atmosphere, though they may be by the earth’s. There are no defective rays in the white light of Sirius, Procyon, and others; but Sir David Brewster found in the spectrum of the orange-coloured light of ζ Herculis a defective band in the red space, and two or more in the blue; consequently, the orange colour of the star is owing to a want of blue rays; for flames in which certain rays are wanting take the colour of the predominating rays. If the black rays in the solar spectrum were owing to the absorption of the sun’s atmosphere, the light from the margin of his disc, having to pass through a greater thickness of it, would exhibit deeper lines than that which comes from his centre; but, as no difference is perceptible, it may be inferred that the analogous bands in the light of the coloured stars are not due to the absorption of their atmospheres, but that they arise from the different kinds of combustion by which these bodies are lighted up.

All the ordinary methods fail for finding the parallax when the distances of the stars are very great. An angle even of one or two seconds, viewed in the focus of our largest telescopes, does not equal the thickness of a spider’s thread, which makes it impossible to measure such minute quantities with any degree of accuracy. In some cases, however, the binary systems of stars furnish a method of estimating an angle of even the tenth of a second, which is thirty times more accurate than by any other means. From them the actual distances of some of the more remote stars will ultimately be known.

Suppose that one star revolves round another in an orbit which is so obliquely seen from the earth as to look like an ellipse in a horizontal position, then it is clear that one-half of the orbit will be nearer to us than the other half. Now, in consequence of the time which light takes to travel, we always see the satellite star in a place which it has already left. Hence, when that star sets out from the point of its orbit which is nearest to us, its light will take more and more time to come to us in proportion as the star moves round to the most distant point in its orbit. On that account the star will appear to us to take more time in moving through that half of its orbit than it really does. Exactly the contrary takes place on the other half; for the light will take less and less time to arrive at the earth in proportion as the star approaches nearer to us; and therefore it will seem to move through this half of its orbit in less time than it really does. This circumstance furnishes the means of finding the absolute breadth of the orbit in miles, and from that the true distance of the star from the earth. For, since the greatest and least distances of the satellite star from the earth differ by the breadth of its orbit, the time which the star takes to move from the nearest to the remotest point of its orbit is greater than it ought to be by the whole time its light takes to cross the orbit, and the period of moving through the other half is exactly as much less. Hence the difference between the observed times of these two semi-revolutions of the star is equal to twice the time that its light employs to cross its orbit; and, as we know the velocity of light, the diameter of the orbit may be found in miles, and from that its whole dimensions; for the position of the orbit with regard to us is known by observation, as well as the place, inclination, and apparent magnitude of its major axis, or, which is the same thing, the angle under which it is seen from the earth. Since, then, three things are known in this great triangle, namely, the base or major axis of the orbit in miles, the angle opposite to it at the earth, and the angle it makes with the visual ray, the distance of the satellite star from the earth may be found by the most simple of calculations. The merit of having first proposed this very ingenious method of finding the distance of the stars is due to M. Savary; but, unfortunately, it is not of general application, as it depends upon the position of the orbit, and a long time must elapse before observation can furnish data, since the shortest period of any revolving star that we know of is 30 years. Still the distances of a vast number of stars may ultimately be made out in this way; and, as one important discovery almost always leads to another, their masses may thus be weighed against that of the earth or sun.

The only data employed for finding the mass of the earth, as compared with that of the sun, are, the angular motion of our globe round the sun in a second of time, and the distance of the earth from the sun in miles (N. 233). Now, by observations of the binary systems, we know the angular velocity of the small star round the great one; and, when we know the distance between the two stars in miles, it will be easy to compute how many miles the small star would fall through by the attraction of the great one in a second of time. A comparison of this space with the space through which the earth would descend towards the sun in a second will give the ratio of the mass of the great star to that of the sun or earth. According to M. Bessel, the weight of the two stars of 61 Cygni is equal to half the weight of the sun. Little as we know of the absolute magnitude of the fixed stars, the quantity of light emitted by many of them shows that they must be much larger than the sun. Dr. Wollaston determined the approximate ratio which the light of a wax candle bears to that of the sun, moon, and stars, by comparing their respective images reflected from small glass globes filled with mercury, whence a comparison was established between the quantities of light emitted by the celestial bodies themselves. By this method he found that the light of α Lyræ is five and a half times greater than that of the sun. Sir John Herschel reflected the moon’s light totally by a prism, which, concentrated by a lens, was compared directly with that of α Centauri. After making allowance for the quantity of the moon’s light lost in passing through the lens and prism, he found that the mean quantity of light sent to the earth by a full moon exceeds that sent by α Centauri in the proportion of 27,408 to 1. Now, Dr. Wollaston found the proportion of the sun’s light to that of the full moon to be that of 801,072 to 1. Hence, the light sent to us by the sun is to that sent by α Centauri as about twenty-two thousand millions to one. But, as the parallax of α Centauri is 1ʺ, it really is two and a half times brighter than the sun. The light of Sirius is four times that of α Centauri, but its parallax is only 0ʺ·230: hence it has an intrinsic splendour 63·02 times that of our luminary. It is therefore estimated to be a hundred times as large; so that, were Sirius in the earth’s place, its surface would extend 150 times as far as the orbit of the moon. The light of Sirius, according to the observations of Sir John Herschel, is 324 times greater than that of a star of the sixth magnitude; if we suppose the two to be really of the same size, their distances from us must be in the ratio of 57·3 to 1, because light diminishes as the square of the distance of the luminous body increases.

So many of the stars have proper motions altogether independent of the annual rotation of the earth in its orbit, that it may be doubted whether there be such a thing as a fixed star. Groombridge is the most rapid known: it has a proper motion of 7ʺ of arc annually; α Centauri moves at the rate of 3ʺ·58 annually, and 61 Cygni describes a line in space of 5ʺ·12 in the same time. These motions are probably in curves, but at the distance of the earth they will appear to be rectilineal for ages to come. The motion of little more than five seconds of space, which 61 Cygni describes annually, seems to us to be extremely small; but at the distance of that star an angle of one second corresponds to twenty-four millions of millions of miles; consequently the annual motion of 61 Cygni is 120 millions of millions of miles, and yet, as M. Arago observes, we call it a fixed star. From the same cause it is evident that the crowding of the stars in the Milky Way may be apparent only, and that the stars may be at vast distances from one another, and no doubt are.

Were the solar system and the whole of the stars visible to us carried forward in space by a motion common to all, like ships drifting in a current, it would be impossible for us, moving with the rest, to ascertain its direction. Sir William Herschel perceived that a great part of the motions of the stars is only apparent, arising from a real motion of the sun in a contrary direction. Among many discrepancies he found that the stars in the northern hemisphere have a general tendency to move towards a point diametrically opposite to λ Herculis, which he attributed to a motion of the solar system in a contrary direction. For it was evident to him, that the stars, from the effects of perspective alone, would seem to diverge in the direction to which the solar system was going, and would converge towards the space it had left, and that there would be a regularity in these apparent motions which would hereafter be detected. Since Sir William Herschel’s time the proper motions of the stars have been determined with much greater accuracy, and many have been added to the list by comparing the ancient and modern tables of their places; his views have been established by four of the greatest astronomers of the age, MM. Lundahles, Argelander, Otto Struve, and Peters, who have clearly proved the motion of the sun from that of the stars in the northern hemisphere, and Mr. Galloway has come to the same conclusion from the motions of the stars in the southern hemisphere (N. 234). The result is, that the sun, accompanied by all his attendant planets, is moving at the rate of 422,424 miles—or over a space nearly equal to his own diameter—in the course of a day, and that the motion is directed towards a point in a line joining the two stars μ and π Herculis at a quarter of the apparent distance of these two stars, reckoning from π Herculis. This investigation was founded upon no law assumed or observed, such as the circulation of all the stars of our firmament about a common centre, though philosophers have speculated as to the probability of such a motion in the sun and stars in the plane of the Milky Way. Should the sun and his stellar companions be moving in a nearly circular orbit, the centre of motion would be in the plane passing through the sun perpendicular to the direction of his motion. The constellations through which that great circle would pass are Pisces, Australis, Pegasus, Andromeda, Perseus, &c. M. Argelander is of opinion that the sun’s orbit is nearly in the plane of the Milky Way, and, therefore, that its centre must probably be in Perseus, while M. Mädler places it in the Pleiades, which seems to be inadmissible; but the data are too uncertain at present to admit of any absolute conclusion as to the sun’s orbit and the general motion of the stellar firmament: for though the stars in every region of the sky tend towards a point in Hercules, it is not yet known whether their motions are uniform or variable, whether the sun’s motion be gradually changing, and whether the stars form different independent systems, each having its own centre of attraction, or if all obey one powerful controlling force which pervades the whole universe. Accurate observations of the places of a select number of stars of all dimensions in the Milky Way continued for a series of years would no doubt decide this point.

The proper motion of a star combined with the progressive velocity of light alters the apparent periodic time of the revolving star of a binary system. If the orbit of a double star be at right angles to the visual ray, and both the sun and the star at rest, the periodic time of the revolving star, say of 10,000 days, would always be the same. But if the centre of gravity of the star were to recede in a direct line from the sun with the velocity of one tenth of the radius of the earth’s orbit in a day, then at the end of 10,000 days it would be more remote from us by 1000 of such radii—a space light would take 57 days to traverse: hence, although the periodic time of the star would really be the same, the completion of its period would only be known to us 57 days after it had taken place, so that the periodic time would appear to us to be 10,057 days instead of 10,000. Were the star to approach to the sun by the same quantity instead of receding, the apparent periodic time would be diminished by 57 days.

As the sun is only a unit in the stellar system, so the Milky Way, and all the stars that adorn the firmament of both hemispheres, constitute a group which is but a unit among the infinite numbers of starry clusters and nebulæ that are profusely scattered throughout the universe.

By the aid of a good telescope there may be seen on the clear vault of heaven, between the stars of our own stellar system, and far in the depths of space, an immense multitude of objects like comets or clouds of white vapour of all forms and sizes. Some are mixed with stars, others are entirely formed of them. Many appear as if they were stellar, but required a telescope of higher power to resolve them, and vast numbers appear to be matter rarefied in the highest possible degree, giving no indication of a stellar nature; and these are in every state of condensation, from a vague film hardly to be discerned to such as have actually arrived at a solid nucleus of stars. The cloudy appearance is merely the blending of the rays of innumerable stars which are themselves invisible from their extreme distance, like parts of the Milky Way. Sir William Herschel was at first of that opinion, and the nebulæ that have been resolved by Lord Rosse’s telescope have led astronomers to believe that such is the case. Yet the tails of comets, the zodiacal light, and the extensive luminous atmospheres which encompass many of the stars, show that, in all probability, a self-luminous phosphorescent material substance in a highly diluted or gaseous form exists in vast abundance.

The number of the nebulæ, like that of the stars, is only limited by the imperfection of our instruments, for each improvement in the telescope only enables us to penetrate a little farther into the infinity of space—to see a few more of these shadowy existences in the far distance, and to resolve a few more of those that are comparatively near. Sir William Herschel examined the nature and determined the position of 2500 nebulæ in the northern hemisphere whose places were computed from his observations, reduced to a common epoch, and arranged into a catalogue, in order of right ascension, by his sister, Miss Caroline Herschel, who added lustre to the name she bore by her eminence in astronomical knowledge and discovery. Sir John Herschel revised his father’s observations, and added 800 nebulæ to the catalogue before he went to the Cape of Good Hope, in order to complete the survey of the heavens. On his return he published a catalogue of 2049 nebulæ of the southern hemisphere, of which 500 were previously unknown, with their position in the heavens. In a work unparalleled for elegance of style, depth of knowledge, and originality of views, he has given engravings from his drawings of the most remarkable objects, so that whatever changes may take place in their form, place, or condensation, will be known by astronomers of future ages.

Though infinite in variety, the nebulæ are of two distinct classes; one consists of patches of great dimensions, capriciously irregular, assuming all the fantastic forms of clouds, now bright, now obscure; sometimes like vapour flying before the wind; sometimes stretching long arms into space. Many present an ill-defined surface, in which it is difficult to say where the centre of the greatest brightness is. Large portions are resolvable into stars; many have a granulated appearance, as if they were resolvable; and others probably are not so merely from the smallness and closeness of the stars, and possibly from their remoteness, indicating the complex and irregular form the Milky Way would present if seen from a distance. A wonderful nebula of this kind is visible to the naked eye in the constellation of Orion; it is of vast extent, sending branches even into the southern hemisphere; and, although Lord Rosse’s telescope has resolved much that had hitherto resisted others, there are parts that still maintain their nebulous appearance from extreme remoteness, presenting a kind of mottled aspect, like flocks or wisps of wool, or mackerel sky. There can be no doubt of its being an unfathomable congeries of stars, which there is reason to believe has changed its form in some parts within the last fifty years. Vast multitudes of nebulæ of this kind are so faint as to be with difficulty discerned at all till they have been for some time in the field of the telescope, or are just about to quit it. Occasionally they are so vague, that the eye is conscious of something being present, without being able to define what it is; but the unchangeableness of its position convinces the mind that it is a real object—“an image was before mine eyes, but I could not discern the form thereof.”

No drawing can give an idea of the boundaries of such nebulæ as that of Orion; even with Lord Rosse’s telescope the edges either fade into a luminous mist, which becomes more rare till it is imperceptible, or end in a tissue of faintish flocculi, or in filaments which become finer and more scattered till they cease to be visible, showing that the real boundaries have not been seen.

The other class of nebulæ, vastly inferior in size, of definite forms and great variety of character, are scattered through the remote heavens, or congregated in a great nebulous district far from the Milky Way. Many cling to stars like wisps of clouds, others are exactly like comets with comæ and tails; but the most definite forms are annular and lenticular nebulæ, nebulous stars, planetary and elliptical nebulæ, and starry clusters. However, there are two in the northern hemisphere differing from all of these, which are described by Sir John Herschel as amazing objects. One in Vulpecula is like an hourglass or dumb bell of bright matter, surrounded by a thin hazy atmosphere so as to give the whole an oval form, or the appearance of an oblate spheroid; with a higher optical power its form is much the same, but the brighter part is resolved into stars, and the hazy part, though still nebulous, assumes that mottled appearance which shows that the whole is a stellar system of the most peculiar structure: it is a phenomenon that bears no resemblance to any known object. (Fig. 3, plate 8, and fig. 3, plate 9). The other is indeed most wonderful, and its history shows the gradual increase in the space-penetrating power of telescopes. To Messier it appeared merely to be a double nebula with stars; with Sir William Herschel’s telescope it presented the appearance of a bright round nebula encompassed at a little distance by a halo or glory, and accompanied by a companion; while in Sir John Herschel’s 20 feet reflector it appeared to “consist of a bright round nucleus, surrounded at a distance by a nebulous ring split through half its circumference, and having the split portions separated at an angle of 45 degrees each to the plane of the other.” (Fig. 1, plate 10.) This nebula appeared to Sir John to “bear a strong similitude to the Milky Way, suggesting the idea of a brother system bearing a real physical resemblance and strong analogy of structure to our own.”

This object, which disclosed to Lord Rosse the astonishing phenomenon of spiral nebulæ seen in his telescope, presents the appearance of the fig. 1 in plate 10, in which the partial division of the limb of the ring into two branches is at once recognised in the bright convolutions of the spiral. The outlying nebula is connected by a narrow curved band of light with the ring; the whole is either resolved into stars, or evidently might be with a still higher optical power. With regard to the marvellous nebula in question Lord Rosse observes, that “with each increase of optical power the structure has become more complicated, and more unlike anything that could result from any form of a dynamical law of which we find a counterpart in our system. The connection of the companion with this great nebula, of which there is not the least doubt, adds to the difficulty of forming any hypothesis. It is impossible that such a system could exist without internal movement, to which may be added a resisting medium; but it cannot be regarded as a case of mere static equilibrium.” This is by no means the only instance of a spiral nebula; Lord Rosse has discovered several others: some are easily seen—others require the highest powers of his telescope. From the numerous offsets that branch from the Milky Way and run far into space, it may possibly partake also of the spiral form.

There are seven annular nebulæ in the northern hemisphere, since Lord Rosse has discovered that five of the planetary nebulæ belong to this class. One of the finest examples of an annular nebula is to be seen midway between β and γ Lyræ (fig. 2, plate 9). According to Sir John Herschel, it is elliptical in the ratio of 4 to 5, and is sharply defined—the internal opening occupying about half the diameter. This opening is not entirely dark, but filled with a faint hazy light like fine gauze stretched over a hoop. Its diameter, if it is as far from us as 61 Cygni, must be 1300 times greater than the diameter of the earth’s orbit—dimensions that are most astounding. Lord Rosse’s telescope resolves this object into stars of extreme minuteness, with filaments of stars adhering to its edges and a pretty bright star in its interior. These rings are like hollow shells whose borders seem brighter because the nebulous substance, whatever it may be, is more condensed to appearance than the central part. The other annular nebula in the northern hemisphere described by Sir John Herschel is a small faint object, and more easily resolvable into stars. One of the annular nebulæ seen by Lord Rosse is surrounded by a faint external flat ring; another has ansæ, as if an annular nebulous ring encompassed it and was foreshortened. Two annular nebulæ have perforations as if the black sky was seen through openings in the interior haze, for in no instance is the central opening quite dark.

Some nebulæ are like very elliptical annular systems seen obliquely. If they be elliptical flat rings, the dark centre may be a real opening; but should the systems be a series of very long elliptical concentric shells surrounding a hollow, the dark axis may be merely a line of comparative darkness.

The connection of the elliptical nebulæ with double stars is mentioned as very remarkable. In one elliptical nebula whose longer axis is 50ʺ there are two individuals of a double star each of the 10th magnitude symmetrically placed rather nearer the vertex of the ellipse than the foci; in another the stars are unequal, but placed exactly at the extremities of the major axis, as in plate 8: besides these there are several other instances.

Double nebulæ are not unfrequent in both hemispheres, exhibiting all the varieties of distance, position, and relative brightness, with their counterparts the double stars. The rarity of single nebulæ as large, faint, and as little condensed in the centre as these, makes it extremely improbable that two such bodies should be accidentally so near as to touch, and often in part to overlap each other, as these do. It is much more likely that they constitute systems; and, if so, it will form an interesting object of future inquiry to discover whether they possess orbital motion.

Nebulous stars are beautiful objects, quite different from all the preceding. They are round or oval, increasing in density towards the centre. Sometimes the central matter is so vividly and sharply condensed and defined that the nebula might be taken for a bright star surrounded by a thin atmosphere. One is a star of the 8th magnitude exactly in the centre of a round bright atmosphere 25ʺ in diameter; the star is quite stellar, and not a nucleus: it has not the smallest appearance of being resolvable. Another nebulous star is ι Orionis, which has a broad atmosphere in which is a dark cavity not symmetrical with the star, and a small double star with a similar opening on the edge of the atmosphere. Lord Rosse observes that these openings appear to be of the same nature with that within the bright stars in the trapezium of Orion, the stars being at its edge; and he is convinced that the stars are not only connected with the nebula, but that they are equidistant with it; hence, if their parallax can be found, the distance of this nebula would be determined. The zodiacal light or lenticular shaped luminous haze surrounding the sun which may be seen extending beyond the orbits of Mercury and Venus soon after sunset in the months of April and May, or before dawn in November and December, seems to place our luminary in the class of nebulous stars. The extensive and delicate atmosphere of these nebulous stars assumes all degrees of ellipticity, from the circular to the spindle-shaped ray, or almost the right line.

Planetary nebulæ have exactly the appearance of planets with round or oval discs, sometimes sharply terminated, at other times hazy and ill-defined. Their surface, which is blue or blueish white, is equable or slightly mottled, and their light occasionally rivals that of the planets in vividness. They are generally attended by minute stars, which give the idea of accompanying satellites. These nebulæ are of enormous dimensions. One near γ Aquarii has a sensible diameter of about twenty seconds, and another presents a diameter of twelve. Sir John Herschel has computed that, if these objects be as far from us as the stars, their real magnitude, on the lowest estimation, must be such as would fill the orbit of Uranus. He concludes that, if they be solid bodies of a solar nature, their intrinsic splendour must be far inferior to that of the sun, because a circular portion of the sun’s disc subtending an angle of twenty seconds would give a light equal to that of a hundred full moons; while, on the contrary, the objects in question are hardly, if at all, visible to the naked eye. From the uniformity of the discs of these planetary nebulæ, and their apparent want of condensation, he presumes that they may be hollow shells emitting light from their surface only. The southern hemisphere is very rich in them, where twenty-eight or twenty-nine have been discovered, some in the midst of a cluster of stars, with which they form a beautiful contrast. Three are of a decided blue colour, one Prussian blue, or verditer green, the other two of a bright sky blue, of great beauty and delicacy. One seems to belong to the class of double nebulæ or double stellar nebulæ of the utmost remoteness. Since Lord Rosse’s telescope has shown that five of the planetary nebulæ are annular, some of those in the southern hemisphere may ultimately be found to belong to the same class.

Probably nine tenths at least of the nebulous contents of the heavens consist of spherical or elliptical forms presenting every variety of elongation and central condensation. Of these a great number have been resolved into stars, and a great many present that mottled appearance which renders it certain that an increase of optical power would decompose them. Those which resist do so on account of the smallness and closeness of the stars of which they consist.

Elliptical nebulæ are very common; by much the finest may be seen near the star υ in the girdle of Andromeda. It is visible to the naked eye, and has frequently been taken for a comet. With a low optical power it has the spindle-shaped form of fig. 6, plate 5, the brightness being at first gradually and then rapidly condensed towards the centre, so that it has been compared to a star shining through horn, but had never appeared resolvable even with high optical powers till Mr. Bond examined it at the observatory of Cambridge in the United States. He found that its brightness extends over 2-1/2 degrees in length, and more than a degree in breadth, including two small adjacent nebulæ, so that it is oval. It is strongly and rapidly condensed into a nucleus on its northern side; and although it was not all resolved, it was seen to be strewed over with star dust, or extremely minute visible stars, which leaves not a doubt of its being a starry system. The most remarkable part of Mr. Bond’s discovery are two very narrow dark lines which extend along one side of the oval parallel to its major axis. These black streaks, difficult to distinguish, indicate a stratified structure, and are not the only instance of that arrangement in nebulæ. Fig. 1, in plate 9, is from Mr. Bond’s drawing of this nebula.

Multitudes of nebulæ appear to the unassisted eye, or are seen with ordinary telescopes, like round comets without tails; but when viewed with powerful instruments they convey the idea of a globular space, insulated in the heavens and full of stars, constituting a family or society apart from the rest, subject only to its own internal laws. To attempt to count the stars in one of these globular clusters, Sir John Herschel says, would be a vain task; they are not to be reckoned by hundreds. On a rough computation, it appears that many clusters of this description must contain ten or twenty thousand stars compacted and wedged together in a round space, whose apparent area is not more than a tenth part of that covered by the moon; so that its centre, where the stars are seen projected on each other, is one blaze of light. If each of these stars be a sun, and if they be separated by intervals equal to that which separates our sun from the nearest fixed star, the distance which renders the whole cluster barely visible to the naked eye must be so great, that the existence of such a splendid assemblage can only be known to us by light which must have left it at least a thousand years ago. These magnificent globular or spheroidal aggregates of stars are so arranged that the interior strata are more crowded and become more nearly spherical as they approach the centre. A most splendid object of this nature may be seen in the constellation Hercules (N. 235).

Of 131 of these magnificent objects in the southern hemisphere, two of them are pre-eminently splendid. The globular cluster of α Centauri is beyond comparison the finest of its kind: it is perfectly spherical, and occupies a quarter of a square degree; the stars in it are literally innumerable, crowding and densely aggregated towards the centre; and, as its light is not more to the naked eye than that of a star of the 4th or 5th magnitude, their minuteness is extreme. It has a dark hole in its centre, with a bridge of stars across,—a circumstance peculiar to this cluster.

Lacaille’s globular cluster, or 47 Toucani, is completely insulated in a very dark part of the sky not far from the lesser of the Magellanic clouds. The stars, which are of the 14th magnitude, immensely numerous, compressed and white, form three distinct stages round a centre, where they suddenly change in hue, and form a blaze of rose-coloured light. One cluster consists of large ruddy stars and small white ones; another of greater beauty consists of shells or coats of stars of the 11th and 15th magnitude. There are thirty globular clusters of extreme beauty collected within a circular space of not more than eighteen degrees radius, which lies in the part of the sky occupied by the constellations Corona Australis, the body and head of Sagittarius, the tail of Scorpio, part of Telescopium and Ara. The Milky Way passes diametrically across the circular area in question, which gives prodigious brilliancy to this part of the sky. For besides these globular clusters, which all lie in the starry part, and not in the dark spaces, there are the only two annular nebulæ known to exist in the southern hemisphere. No part of the heavens is fuller of objects beautiful and remarkable in themselves, and rendered still more so by their mode of association, and by the peculiar features assumed by the Milky Way, which are without a parallel for richness and magnificence in any other part of the sky. Some of the globular clusters are so remote that the stars are scarcely discernible—mere star dust. There is a double globular cluster in the southern hemisphere of very small dimensions, separated by a minute interval,—a combination which suggests the idea of a globular cluster revolving about a very oblate spheroidal one in the plane of the equator, and in an orbit which is circular, and seen obliquely like the central nebula itself, with a diameter somewhat more than four times the latter,—a stupendous system doubtless, but of which the reality can hardly be supposed improbable.

There appears to be some connexion between ellipticity of form and difficulty of resolution, for spherical clusters are in general easily resolved into their component stars, while there is scarcely an instance of an elliptical cluster yielding except to a very high optical power. Vast masses of the nebulæ have never been resolved. Lord Rosse’s great telescope has resolved parts of the nebula of Orion, and various others which had not yielded to instruments of less power; it enables the astronomer to penetrate farther into space, and shows objects with greater clearness, than any other. But, excellent as this instrument is, thousands of nebulæ are not to be resolved even by it. Those who imagine that any work of man can resolve all the nebulous matter in the heavens must have a very limited idea of the extent and sublimity of creation.

Innumerable nebulæ in both hemispheres take the form of clusters of stars, but are totally different from the globular clusters, inasmuch as they are of irregular form and follow no uniform law of condensation. The Pleiades is an instance in our own stellar system; for although only 7 or 8 stars are visible to the naked eye, telescopes show that more than 200 belong to the group. In the constellation Cancer there is a luminous spot called the Præsepe or Beehive, which a very low power resolves into stars; and the constellation Coma Berenices is another stellar group. Many are of exquisite beauty, as that round α Crucis, which, though consisting of only a hundred and ten stars, is like a piece of fancy jewellery, from the colours of the stars, which are greenish white, green, blueish green, and red. Many of these clusters contain thousands of stars, and are frequently in the poorer parts of the sky, as if in the course of ages the stars had been attracted towards a centre.

The existence of every degree of ellipticity in the nebulæ—from long lenticular rays to the exact circular form—and of every shade of central condensation, from the slightest increase of density to apparently a solid nucleus—may be accounted for by supposing the general constitutions of those nebulæ to be that of oblate spheroidal masses of every degree of flatness from the sphere to the disc, and of every variety in their density and ellipticity towards the centre. It would be erroneous, however, to imagine that the forms of these systems are maintained by forces identical with those already described, which determine the form of a fluid mass in rotation; because, if the nebulæ be only clusters of separate stars, as in the greater number of cases there is every reason to believe them to be, no pressure can be propagated through them. Consequently, since no general rotation of such a system as one mass can be supposed, it may be conceived to be a quiescent form, comprising within its limits an indefinite number of stars, each of which may be moving in an orbit about the common centre of the whole, in virtue of a law of internal gravitation resulting from the compound gravitation of all its parts. Sir John Herschel has proved that the existence of such a system is not inconsistent with the law of gravitation under certain conditions.

The distribution of the nebulæ over the heavens is even more irregular than that of the stars. In some places they are so crowded together as scarcely to allow one to pass through the field of the telescope before another appears, while in other parts hours elapse without a single nebula occurring. They are in general only to be seen with the best telescopes, and are most abundant in a zone whose general direction is not far from the hour circles 0^h and 12^h, and which crosses the Milky Way nearly at right angles. Where that nebulous zone passes over the constellations Virgo, Coma Berenices, and the Great Bear, they are to be found in multitudes.

The nebulous system is nearly divided into two parts by the Milky Way. One-third of the whole visible nebulous contents of the heavens forms a broad irregular mass, interspersed with vacant intervals, which fills about an eighth of the surface of the northern hemisphere. It occupies the constellations Leo, Leo Minor, the body, tail, and hind legs of Ursa Major, the nose of Camelopard, the point of the tail of Draco, Canis Venatica, Coma Berenices, the preceding leg of Boötes, and the head, wings, and shoulder of Virgo, which is the richest part. There is a lesser nebulous region in this hemisphere, but entirely separated from the preceding, which occupies the chest and wing of Pegasus, the constellations Pisces and Andromeda. If we could imagine the ring or zone of the Milky Way to encircle or coincide with the horizon, the great nebulous mass would form a canopy over head, descending down to a considerable distance on all sides, chiefly towards the north pole; and the richest part, which is in Virgo, would then be directly over head in the north pole of the Milky Way, that is in 12^h 47^m right ascension, and 64° north polar distance.

With the exception of the Magellanic clouds, there is a much greater uniformity in the distribution of the nebulæ in the southern hemisphere than in the northern. They are separated by spaces of vacuity of greater or less dimensions. One of these barren regions extends for nearly fifteen degrees all around the south pole, and close on its border; the lesser of the Magellanic clouds occurs completely insulated; while the greater Magellanic cloud is in connexion with something approaching to a zone of connected nebulous patches which extends along the back of Doradus, through a portion of Horologium and Eridanus, part of Fornix, and over the paws of Cetus to the equator, where it unites with the nebulous regions of Pisces.

The Magellanic clouds form two of the most striking features in the southern hemisphere; both of these nebulæ are visible to the unassisted eye, being nearly of the same intensity as the brighter portions of the Milky Way; but the smaller is entirely effaced by moonlight, and the larger nearly so. They are altogether unconnected with the Milky Way and with one another. The Nubecula Major is far superior to the Nubecula Minor in every respect, though they are similar in internal structure. The former consists of large tracts and ill-defined patches of irresolvable nebulæ, and nebulosity in every stage of resolution, up to perfectly resolved stars like the Milky Way; and also of regular and irregular nebulæ, properly so called; of globular clusters in every stage of resolvability; and of clustering groups sufficiently insulated and condensed to come under the designation of clusters of stars. Of these the nebula known as Lacaille’s 30 Doradus is too remarkable to be passed over. It is very large, situate within the Nubecula Major, and consists of an assemblage of nearly circular loops uniting in a centre, in or near which there is a circular black hole. In short, for the number and variety of the objects, there is nothing like this cloud. Within an area of only forty-two square degrees, Sir John Herschel has determined the places, and registered 278 nebulæ and clusters of stars, with fifty or sixty in outlying members immediately adjacent. Even the most crowded parts of the stratum of Virgo, in the wing of that constellation, or in Coma Berenices, offer nothing approaching to it. It is evident, from the intermixture of stars and unresolved nebulosity, which probably might be resolved with a higher optical power, that the nubeculæ are to be regarded as systems sui generis, to which there is nothing analogous in our hemisphere.

Next to the Magellanic clouds the great nebula round η Argûs is one of the most wonderful objects of the southern sky. It is situate in that part of the Milky Way which lies between the Centaur and the body of Argus, in the midst of one of those rich and brilliant masses, a succession of which is so curiously contrasted with the profoundly dark adjacent spaces, and surrounded by one of the most beautiful parts of the southern heavens. Sir John Herschel says: “It would be impossible, by verbal description, to give any just idea of the capricious forms and irregular gradations of light affected by the different branches and appendages of this nebula. Nor is it easy for language to convey a full impression of the beauty and sublimity of the spectacle it offers when viewed in a sweep, ushered in as it is by so glorious and innumerable a procession of stars, to which it forms a sort of climax, justifying expressions which, though I find them written in my journal in the excitement of the moment, would be thought extravagant if transferred to these pages. In fact, it is impossible for any one, with the least spark of astronomical enthusiasm about him, to pass soberly in review with a powerful telescope, and on a fine night, that portion of the southern sky which is comprised between the 6th and 13th degrees of right ascension, and from 146° to 149° of north polar distance; such are the variety and interest of the objects he will encounter, and such the dazzling richness of the starry ground on which they are represented to his gaze.” In that portion of the sky there are many fine double stars—rich starry clusters; the elegant cluster of variously coloured stars round κ Crucis; a large planetary nebula with a satellite star; another of a bright blue colour, exquisitely beautiful and unique; and, lastly, η Argûs itself, the most extraordinary instance of a variable star in astronomical history.

It frequently occurred, during Sir John Herschel’s survey of the southern heavens, that some parts of the sky were noted for deeper blackness than others, and no stars could be seen; it frequently happened that far from the Milky Way, or any large nebula or cluster of stars, there were some indications of very remote branches of the Milky Way, or of an independent sidereal system or systems, bearing a resemblance to such branches. These were indicated by an exceedingly delicate and uniform dotting or stippling of the sky by points of light too small to admit of any one of them being steadily and fixedly viewed, and too numerous to be counted even if possible to view them. The truth of this existence was felt at the moment of observation; but the conviction, though often renewed, was not permanent. The places where these appearances occurred are given, in order that those who wish to verify them may have it in their power.

Such is a brief account of a very few of the discoveries contained in Sir John Herschel’s great work on the Nebulæ and other Phenomena of the Southern Hemisphere,—a work which will rise in estimation with the lapse of years. No doubt the form and internal structure of many of these nebulæ will be changed by telescopes of higher power; but as the places of the leading phenomena have been determined, the date of that great work may be regarded as the epoch of nebular time whence the relative changes that take place in the most distant regions of the universe will be estimated for ages to come; and in the inimitable writings of the highly gifted father and son the reader will find these subjects treated of in a style worthy of it and of them. Of late years the excellence of the instruments, and still more of the astronomers, in the foreign observatories, have aided the progress of sidereal astronomy immensely. Nor has it been cultivated with less success in our home and colonial establishments: certainly one of the most remarkable features of the times is the number of private observatories, built and furnished with the best instruments by private gentlemen, whose zeal has been rewarded by eminent success in all departments of the science. (N. 236.)

So numerous are the objects which meet our view in the heavens, that we cannot imagine a point of space where some light would not strike the eye;—innumerable stars, thousands of double and multiple systems, clusters in one blaze with their tens of thousands of stars, and the nebulæ amazing us by the strangeness of their forms and the incomprehensibility of their nature, till at last, from the limit of our senses, even these thin and airy phantoms vanish in the distance. If such remote bodies shone by reflected light, we should be unconscious of their existence. Each star must then be a sun, and may be presumed to have its system of planets, satellites, and comets, like our own; and, for aught we know, myriads of bodies may be wandering in space unseen by us, of whose nature we can form no idea, and still less of the part they perform in the economy of the universe. Even in our own system, or at its farthest limits, minute bodies may be revolving like the telescopic planets, which are so small that their masses have hitherto been inappreciable, and there may be many still smaller. Nor is this an unwarranted presumption; many such do come within the sphere of the earth’s attraction, are ignited by the velocity with which they pass through the atmosphere, but leave no residuum. These, which are known as falling stars and meteors, are periodical; but that is by no means the case with aërolites, which are also ignited by the sudden condensation of the air on entering our atmosphere, and are precipitated in solid masses with such violence on the earth’s surface that they are often deeply buried in the ground.

The fall of meteoric stones is much more frequent than is generally believed. Hardly a year passes without some instances occurring; and, if it be considered that only a small part of the earth is inhabited, it may be presumed that numbers fall in the ocean, or on the uninhabited part of the land, unseen by man. They are sometimes of great magnitude; the volume of several has exceeded that of the planet Ceres, which is about 70 miles in diameter. One which passed within 25 miles of us was estimated to weigh about 600,000 tons, and to move with a velocity of about 20 miles in a second; a fragment of it alone reached the earth. The obliquity of the descent of meteorites, the peculiar substances they are composed of, and the explosion accompanying their fall, show that they are foreign to our system; but whence derived is still a mystery.

Shooting stars and meteors burst from the clear azure sky, and, darting along the heavens, are extinguished without leaving any residuum except a vapour-like smoke, and generally without noise. Their parallax shows them to be very high in the atmosphere, sometimes even beyond its supposed limit, and the direction of their motion is for the most part diametrically opposite to the motion of the earth in its orbit. The astonishing multitudes of shooting stars and fire-balls that have appeared at stated periods over different parts of the globe, warrant the conclusion that there is either a nebula or that there are myriads of bodies revolving in groups round the sun which only become visible when inflamed by entering our atmosphere.

One of these nebulæ or groups seems to meet the earth in its annual revolution on the 12th and 13th of November.

On the morning of the 12th of November, 1799, thousands of shooting stars, mixed with large meteors, illuminated the heavens for many hours over the whole continent of America, from Brazil to Labrador: it extended to Greenland, and even Germany. Meteoric showers were seen off the coast of Spain, and in the Ohio country, on the morning of the 13th of November, 1831; and during many hours on the morning of the 13th November, 1832, prodigious multitudes of shooting stars and meteors fell at Mocha on the Red Sea, in the Atlantic, in Switzerland, and at many places in England. But by much the most splendid meteoric shower on record began at nine o’clock in the evening of the 12th of November, 1833, and lasted till sunrise next morning. It extended from Niagara and the northern lakes of America to the south of Jamaica, and from 61° of longitude in the Atlantic to 100° of longitude in central Mexico. Shooting stars and meteors, of the apparent size of Jupiter, Venus, and even the full moon, darted in myriads towards the horizon, as if every star in the heavens had started from their spheres. They are described as having been frequent as flakes of snow in a snow-storm, and to have been seen with equal brilliancy over the greater part of the continent of North America.

Those who witnessed this grand spectacle were surprised to see that every one of the luminous bodies, without exception, moved in lines which converged in one point in the heavens: none of them started from that point; but their paths, when traced backwards, met in it like rays in a focus, and the manner of their fall showed that they descended from it in nearly parallel straight lines towards the earth.

By far the most extraordinary part of the whole phenomenon is, that this radiant point was observed to remain stationary near the star γ Leonis for more than two hours and a half, which proved the source of the meteoric shower to be altogether independent of the earth’s rotation, and its parallax showed it to be far above the atmosphere.

As a body could not be actually at rest in that position, the group or nebula must either have been moving round the earth or the sun. Had it been moving about the earth, the course of the meteors would have been tangential to its surface; whereas they fell almost perpendicularly, so that the earth in its annual revolution must have met with the group. The bodies or the parts of the nebula that were nearest must have been attracted towards the earth by its gravity, and, as they were estimated to move at the rate of fourteen miles in a second, they must have taken fire on entering our atmosphere, and been consumed in their passage through it.

As all the circumstances of the phenomena were similar on the same day and during the same hours in 1832, and as extraordinary flights of shooting stars were seen at many places both in Europe and America on the 13th of November, 1834, 1835, and 1836, tending also from a fixed point in the constellation Leo, it has been conjectured, with much apparent probability, that this nebula or group of bodies performs its revolution round the sun in a period of about 182 days, in an elliptical orbit, whose major axis is 119 millions of miles; and that its aphelion distance, where it comes in contact with the earth’s atmosphere, is about 95 millions of miles, or nearly the same with the mean distance of the earth from the sun. This body must have met with disturbances after 1799, which prevented it from encountering the earth for 32 years, and it may again deviate from its path from the same cause.

It is now well ascertained that great showers of shooting stars occur also on the 12th of August, whose point of divergence is β Camelopardali, so that the earth’s atmosphere comes into contact with a zone of these small bodies twice in the year. By a systematic series of observations, MM. Benzenberg and Brand have clearly made out that the heights at which the falling stars appear and vanish vary from 16 miles to 140, and their velocities from 18 to 36 miles in a second, velocities so great as certainly to indicate a planetary revolution round the sun. As shooting stars are seen almost every night when the sky is clear, Sir John Lubbock has thought it probable that some of these bodies may have come so near, that the attraction of the earth has overcome that of the sun, and caused them to revolve as satellites round it. Should that be the case, they might shine by the reflected light of the sun, and suddenly cease to be visible on entering the earth’s shadow. The splitting of the falling stars like a rocket, and the trains of light, may be accounted for by supposing the stars to graze the surface of the shadow before being eclipsed; and the disappearance would be more or less rapid according to the breadth of the penumbra traversed. The calculations of M. Petit, Director of the Observatory of Toulouse, not only render probable the existence of small satellites, but tend to establish the identity of a body revolving round the earth in three hours and twenty minutes, at a distance of 5000 miles above its surface. It is evident that in this case the same satellite would be seen very often, and a very few would be sufficient to account for their nightly appearance. It is possible, however, that some shooting stars may belong to one class, and some to the other, since one group may be revolving about the sun, and another round the earth. In the case of a satellite shooting star, geometry furnishes the means of ascertaining its exact distance from the spectator, or from the centre of the earth, if the time and place of its disappearance be known with regard to the neighbouring stars. Since the falling stars are consumed in the atmosphere, their masses must be small, but it is possible that occasionally one may be large enough to arrive at the surface of the earth as an aërolite.

SECTION XXXVII.

Diffusion of Matter through Space—Gravitation—Its Velocity—Simplicity of its Laws—Gravitation independent of the Magnitude and Distances of the Bodies—Not impeded by the intervention of any Substance—Its Intensity invariable—General Laws—Recapitulation and Conclusion.

THE known quantity of matter bears a very small proportion to the immensity of space. Large as the bodies are, the distances which separate them are immeasurably greater; but, as design is manifest in every part of creation, it is probable that, if the various systems in the universe had been nearer to one another, their mutual disturbances would have been inconsistent with the harmony and stability of the whole. It is clear that space is not pervaded by atmospheric air of such density as that we breathe, since its resistance would long ere this have arrested the motion of the planets: it certainly is not a void, but replete with a medium possibly in itself electric or magnetic, but at all events capable of transmitting light, heat, magnetism, gravity, and probably influences of which we can form no idea.

Whatever the laws may be that obtain in the more distant regions of creation, we are assured that one alone regulates the motions, not only of our own system, but also of the binary systems of the fixed stars; and, as general laws form the ultimate object of philosophical research, we cannot conclude these remarks without considering the nature of gravitation—that extraordinary power whose effects we have been endeavouring to trace through some of their mazes. It was at one time imagined that the acceleration in the moon’s mean motion was occasioned by the successive transmission of the gravitating force. It has been proved that, in order to produce this effect, its velocity must be about fifty millions of times greater than that of light, which flies at the rate of 192,000 miles in a second. Its action, even at the distance of the sun, may therefore be regarded as instantaneous; yet, remote as the fixed stars are, the solar gravitation must have some influence on the nearest of them, as, for example, α Centauri, which is only 20,602 times the radius of the earth’s orbit from the sun, while La Place has computed that the solar gravitation extends a hundred millions of times farther than the semidiameter of the terrestrial orbit. Possibly the star dust in the Milky Way may be beyond, or on the verge of, that enormous limit; yet it is very unlikely that either the sun, or any of the stars which form the great cluster to which we belong, should be unconnected bodies.

The curves in which the celestial bodies move by the force of gravitation are only lines of the second order. The attraction of spheroids, according to any other law of force than that of gravitation, would be much more complicated; and, as it is easy to prove that matter might have been moved according to an infinite variety of laws, it may be concluded that gravitation must have been selected by Divine Wisdom out of an infinity of others, as being the most simple, and that which gives the greatest stability to the celestial motions.

It is a singular result of the simplicity of the laws of nature, which admit only of the observation and comparison of ratios, that the gravitation and theory of the motions of the celestial bodies are independent of their absolute magnitudes and distances. Consequently, if all the bodies of the solar system, their mutual distances, and their velocities, were to diminish proportionally, they would describe curves in all respects similar to those in which they now move; and the system might be successively reduced to the smallest sensible dimensions, and still exhibit the same appearances.

The action of the gravitating force is not impeded by the intervention even of the densest substances. If the attraction of the sun for the centre of the earth, and of the hemisphere diametrically opposite to him, were diminished by a difficulty in penetrating the interposed matter, the tides would be more obviously affected. Its attraction is the same also, whatever the substances of the celestial bodies may be; for, if the action of the sun upon the earth differed by a millionth part from his action upon the moon, the difference would occasion a periodical variation in the moon’s parallax, whose maximum would be the 1/15 of a second, and also a variation in her longitude amounting to several seconds—a supposition proved to be impossible by the agreement of theory with observation. Thus all matter is pervious to gravitation, and is equally attracted by it.

Gravitation is a feeble force, vastly inferior to electric action, chemical affinity, and cohesion; yet, as far as human knowledge extends, the intensity of gravitation has never varied within the limits of the solar system; nor does even analogy lead us to expect that it should: on the contrary, there is every reason to be assured that the great laws of the universe are immutable, like their Author. Nor can we suppose the structure of the globe alone to be exempt from the universal fiat of general laws, though ages may pass before the changes it has undergone, or that are now in progress, can be referred to existing causes with the same certainty with which the motions of the planets, and all their periodic and secular variations, are referable to the law of gravitation. The traces of extreme antiquity perpetually occurring to the geologist give that information, as to the origin of things, in vain looked for in the other parts of the universe. They date the beginning of time with regard to our system, since there is ground to believe that the formation of the earth was contemporaneous with that of the rest of the planets; but they show that creation is the work of Him with whom “a thousand years are as one day, and one day as a thousand years.”

In the work now brought to a conclusion, it has been necessary to select from the whole circle of the sciences a few of the most obvious of those proximate links which connect them together, and to pass over innumerable cases both of evident and occult alliance. Any one branch traced through its ramifications would alone have occupied a volume; it is hoped, nevertheless, that the view here given will suffice to show the extent to which a consideration of the reciprocal influence of even a few of these subjects may ultimately lead. It thus appears that the theory of dynamics, founded upon terrestrial phenomena, is indispensable for acquiring a knowledge of the revolutions of the celestial bodies and their reciprocal influences. The motions of the satellites are affected by the forms of their primaries, and the figures of the planets themselves depend upon their rotations. The symmetry of their internal structure proves the stability of these rotatory motions, and the immutability of the length of the day, which furnishes an invariable standard of time; and the actual size of the terrestrial spheroid affords the means of ascertaining the dimensions of the solar system, and provides an invariable foundation for a system of weights and measures. The mutual attraction of the celestial bodies disturbs the fluids at their surfaces, whence the theory of the tides and of the oscillations of the atmosphere. The density and elasticity of the air, varying with every alternation of temperature, lead to the consideration of barometrical changes, the measurement of heights, and capillary attraction; and the doctrine of sound, including the theory of music, is to be referred to the small undulations of the aërial medium. A knowledge of the action of matter upon light is requisite for tracing the curved path of its rays through the atmosphere, by which the true places of distant objects are determined, whether in the heavens or on the earth. By this we learn the nature and properties of the sunbeam, the mode of its propagation through the ethereal medium, or in the interior of material bodies, and the origin of colour. By the eclipses of Jupiter’s satellites the velocity of light is ascertained; and that velocity, in the aberration of the fixed stars, furnishes a direct proof of the real motion of the earth (N. 237). The effects of the invisible rays of the spectrum are immediately connected with chemical action; and heat, forming a part of the solar ray, so essential to animated and inanimated existence, is too important an agent in the economy of creation not to hold a principal place in the connexion of physical sciences; whence follows its distribution in the interior and over the surface of the globe, its power on the geological convulsions of our planet, its influence on the atmosphere and on climate, and its effects on vegetable and animal life, evinced in the localities of organized beings on the earth, in the waters, and in the air. The correlation between molecular and chemical action, light, heat, electricity, and magnetism, is continually becoming more perfect, and there is every reason to believe that these different modes of force, as well as gravity itself, will ultimately be found to merge in one great and universal power. Many more instances might be given in illustration of the immediate connexion of the physical sciences, most of which are united still more closely by the common bond of analysis, which is daily extending its empire, and will ultimately embrace almost every subject in nature in its formulæ.

These formulæ, emblematic of Omniscience, condense into a few symbols the immutable laws of the universe. This mighty instrument of human power itself originates in the primitive constitution of the human mind, and rests upon a few fundamental axioms, which have eternally existed in Him who implanted them in the breast of man when He created him after His own image.

NOTES.

NOTE 1, page 2. Diameter. A straight line passing through the centre, and terminated both ways by the sides or surface of a figure, such as of a circle or sphere. In fig. 1, q Q, N S, are diameters.

NOTE 2, p. 2. Mathematical and mechanical sciences. Mathematics teach the laws of number and quantity; mechanics treat of the equilibrium and motion of bodies.

NOTE 3, p. 2. Analysis is a series of reasoning conducted by signs or symbols of the quantities whose relations form the subject of inquiry.

NOTE 4, p. 3. Oscillations are movements to and fro, like the swinging of the pendulum of a clock, or waves in water. The tides are oscillations of the sea.

NOTE 5, p. 3. Gravitation. Gravity is the reciprocal attraction of matter on matter; gravitation is the difference between gravity and the centrifugal force induced by the velocity of rotation or revolution. Sensible gravity, or weight, is a particular instance of gravitation. It is the force which causes substances to fall to the surface of the earth, and which retains the celestial bodies in their orbits. Its intensity increases as the squares of the distance decrease.

NOTE 6, p. 4. Particles of matter are the indefinitely small or ultimate atoms into which matter is believed to be divisible. Their form is unknown; but, though too small to be visible, they must have magnitude.

NOTE 7, p. 4. A hollow sphere. A hollow ball, like a bomb-shell. A sphere is a ball or solid body, such, that all lines drawn from its centre to its surface are equal. They are called radii, and every line passing through the centre and terminated both ways by the surface is a diameter, which is consequently equal to twice the radius. In fig. 3, Q q or N S is a diameter, and C Q, C N are radii. A great circle of the sphere has the same centre with the sphere as the circles Q E q d and Q N q S. The circle A B is a lesser circle of the sphere.

NOTE 8, p. 4. Concentric hollow spheres. Shells, or hollow spheres, having the same centre, like the coats of an onion.

NOTE 9, p. 4. Spheroid. A solid body, which sometimes has the shape of an orange, as in fig. 1; it is then called an oblate spheroid, because it is flattened at the poles N and S. Such is the form of the earth and planets. When, on the contrary, it is drawn out at the poles like an egg, as in fig. 2, it is called a prolate spheroid. It is evident that in both these solids the radii C q, C a, C N, &c., are generally unequal; whereas in the sphere they are all equal.

NOTE 10, p. 4. Centre of gravity. A point in every body, which if supported, the body will remain at rest in whatever position it may be placed. About that point all the parts exactly balance one another. The celestial bodies attract each other as if each were condensed into a single particle situate in the centre of gravity, or the particle situate in the centre of gravity of each may be regarded as possessing the resultant power of the innumerable oblique forces which constitute the whole attraction of the body.

NOTE 11, pp. 4, 6. Poles and equator. Let fig. 1 or 3 represent the earth, C its centre, N C S the axis of rotation, or the imaginary line about which it performs its daily revolution. Then N and S are the north and south poles, and the great circle q E Q, which divides the earth into two equal parts, is the equator. The earth is flattened at the poles, fig. 1, the equatorial diameter, q Q, exceeding the polar diameter, N S, by about 26-1/2 miles. Lesser circles, A B G, which are parallel to the equator, are circles or parallels of latitude, which is estimated in degrees, minutes, and seconds, north and south of the equator, every place in the same parallel having the same latitude. Greenwich is in the parallel of 51° 28ʹ 40ʺ. Thus terrestrial latitude is the angular distance between the direction of a plumb-line at any place and the plane of the equator. Lines such as N Q S, N G E S, fig. 3, are called meridians; all the places in any one of these lines have noon at the same instant. The meridian of Greenwich has been chosen by the British as the origin of terrestrial longitude, which is estimated in degrees, minutes, and seconds, east and west of that line. If N G E S be the meridian of Greenwich, the position of any place, B, is determined, when its latitude, Q C B, and its longitude, E C Q, are known.

NOTE 12, p. 4. Mean quantities are such as are intermediate between others that are greater and less. The mean of any number of unequal quantities is equal to their sum divided by their number. For instance, the mean between two unequal quantities is equal to half their sum.

NOTE 13, p. 4. A certain mean latitude. The attraction of a sphere on an external body is the same as if its mass were collected into one heavy particle in its centre of gravity, and the intensity of its attraction diminishes as the square of its distance from the external body increases. But the attraction of a spheroid, fig. 1, on an external body at m in the plane of its equator, E Q, is greater, and its attraction on the same body when at mʹ in the axis N S less, than if it were a sphere. Therefore, in both cases, the force deviates from the exact law of gravity. This deviation arises from the protuberant matter at the equator; and, as it diminishes towards the poles, so does the attractive force of the spheroid. But there is one mean latitude, where the attraction of a spheroid is the same as if it were a sphere. It is a part of the spheroid intermediate between the equator and the pole. In that latitude the square of the sine is equal to 1/3 of the equatorial radius.

NOTE 14, p. 4. Mean distance. The mean distance of a planet from the centre of the sun, or of a satellite from the centre of its planet, is equal to half the sum of its greatest and least distances, and, consequently, is equal to half the major axis of its orbit. For example, let P Q A D, fig. 6, be the orbit or path of the moon or of a planet; then P A is the major axis, C the centre, and C S is equal to C F. Now, since the earth or the sun is supposed to be in the point S according as P D A Q is regarded as the orbit of the moon or that of a planet, S A, S P are the greatest and least distances. But half the sum of S A and S P is equal to half of A P, the major axis of the orbit. When the body is at Q or D, it is at its mean distance from S, for S Q, S D, are each equal to C P, half the major axis by the nature of the curve.

NOTE 15, p. 4. Mean radius of the earth. The distance from the centre to the surface of the earth, regarded as a sphere. It is intermediate between the distances of the centre of the earth from the pole and from the equator.

NOTE 16, p. 5. Ratio. The relation which one quantity bears to another.

NOTE 17, p. 5. Square of moon’s distance. In order to avoid large numbers, the mean radius of the earth is taken for unity: then the mean distance of the moon is expressed by 60; and the square of that number is 3600, or 60 times 60.

NOTE 18, p. 5. Centrifugal force. The force with which a revolving body tends to fly from the centre of motion: a sling tends to fly from the hand in consequence of the centrifugal force. A tangent is a straight line touching a curved line in one point without cutting it, as m T, fig. 4. The direction of the centrifugal force is in the tangent to the curved line or path in which the body revolves, and its intensity increases with the angular swing of the body, and with its distance from the centre of motion. As the orbit of the moon does not differ much from a circle, let it be represented by m d g h, fig. 4, the earth being in C. The centrifugal force arising from the velocity of the moon in her orbit balances the attraction of the earth. By their joint action, the moon moves through the arc m n during the time that she would fly off in the tangent m T by the action of the centrifugal force alone, or fall through m p by the earth’s attraction alone. T n, the deflection from the tangent, is parallel and equal to m p, the versed sine of the arc m n, supposed to be moved over by the moon in a second, and therefore so very small that it may be regarded as a straight line. T n, or m p, is the space the moon would fall through in the first second of her descent to the earth, were she not retained in her orbit by her centrifugal force.

NOTE 19, p. 5. Action and reaction. When motion is communicated by collision or pressure, the action of the body which strikes is returned with equal force by the body which receives the blow. The pressure of a hand on a table is resisted with an equal and contrary force. This necessarily follows from the impenetrability of matter, a property by which no two particles of matter can occupy the same identical portion of space at the same time. When motion is communicated without apparent contact, as in gravitation, attraction, and repulsion, the quantity of motion gained by the one body is exactly equal to that lost by the other, but in a contrary direction; a circumstance known by experience only.

NOTE 20, p. 5. Projected. A body is projected when it is thrown: a ball fired from a gun is projected; it is therefore called a projectile. But the word has also another meaning. A line, surface, or solid body, is said to be projected upon a plane, when parallel straight lines are drawn from every point of it to the plane. The figure so traced upon a plane is a projection. The projection of a terrestrial object is therefore its daylight shadow, since the sun’s rays are sensibly parallel.

NOTE 21, p. 5. Space. The boundless region which contains all creation.

NOTE 22, pp. 5, 11. Conic sections. Lines formed by any plane cutting a cone. A cone is a solid figure, like a sugar-loaf, fig. 5, of which A is the apex, A D the axis, and the plane B E C F the base. The axis may or may not be perpendicular to the base, and the base may be a circle, or any other curved line. When the axis is perpendicular to the base, the solid is a right cone. If a right cone with a circular base be cut at right angles to the base by a plane passing through the apex, the section will be a triangle. If the cone be cut through both sides by a plane parallel to the base, the section will be a circle. If the cone be cut slanting quite through both sides, the section will be an ellipse, fig. 6. If the cone be cut parallel to one of the sloping sides as A B, the section will be a parabola, fig. 7. And if the plane cut only one side of the cone, and be not parallel to the other, the section will be a hyperbola, fig. 8. Thus there are five conic sections.

NOTE 23, p. 5. Inverse square of distance. The attraction of one body for another at the distance of two miles is four times less than at the distance of one mile; at three miles, it is nine times less than at one; at four miles, it is sixteen times less, and so on. That is, the gravitating force decreases in intensity as the squares of the distance increase.

NOTE 24, p. 5. Ellipse. One of the conic sections, fig. 6. An ellipse may be drawn by fixing the ends of a string to two points, S and F, in a sheet of paper, and then carrying the point of a pencil round in the loop of the string kept stretched, the length of the string being greater than the distance between the two points. The points S and F are called the foci, C the centre, S C or C F the excentricity, A P the major axis, Q D the minor axis, and P S the focal distance. It is evident that, the less the excentricity C S, the nearer does the ellipse approach to a circle; and from the construction it is clear that the length of the string S m F is equal to the major axis P A. If T t be a tangent to the ellipse at m, then the angle T m S is equal to the angle t m F; and, as this is true for every point in the ellipse, it follows that, in an elliptical reflecting surface, rays of light or sound coming from one focus S will be reflected by the surface to the other focus F, since the angle of incidence is equal to the angle of reflection by the theories of light and sound.

NOTE 25, p. 5. Periodic time. The time in which a planet or comet performs a revolution round the sun, or a satellite about its planet.

NOTE 26, p. 5. Kepler discovered three laws in the planetary motions by which the principle of gravitation is established:—1st law, That the radii vectores of the planets and comets describe areas proportional to the time.—Let fig. 9 be the orbit of a planet; then, supposing the spaces or areas P S p, p S a, a S b, &c., equal to one another, the radius vector S P, which is the line joining the centres of the sun and planet, passes over these equal spaces in equal times; that is, if the line S P passes to S p in one day, it will come to S a in two days, to S b in three days, and so on. 2nd law, That the orbits or paths of the planets and comets are conic sections, having the sun in one of their foci. The orbits of the planets and satellites are curves like fig. 6 or 9, called ellipses, having the sun in the focus S. Several comets are known to move in ellipses; but the greater part seem to move in parabolas, fig. 7, having the sun in S, though it is probable that they really move in very long flat ellipses; others appear to move in hyperbolas, like fig. 8. The third law is, that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. The square of a number is that number multiplied by itself, and the cube of a number is that number twice multiplied by itself. For example, the squares of the numbers 2, 3, 4, &c., are 4, 9, 16, &c., but their cubes are 8, 27, 64, &c. Then the squares of the numbers representing the periodic times of two planets are to one another as the cubes of the numbers representing their mean distances from the sun. So that, three of these quantities being known, the other may be found by the rule of three. The mean distances are measured in miles or terrestrial radii, and the periodic times are estimated in years, days, and parts of a day. Kepler’s laws extend to the satellites.

NOTE 27, p. 5. Mass. The quantity of matter in a given bulk. It is proportional to the density and volume or bulk conjointly.

NOTE 28, p. 5. Gravitation proportional to mass. But for the resistance of the air, all bodies would fall to the ground in equal times. In fact, a hundred equal particles of matter at equal distances from the surface of the earth would fall to the ground in parallel straight lines with equal rapidity, and no change whatever would take place in the circumstances of their descent, if 99 of them were united in one solid mass; for the solid mass and the single particle would touch the ground at the same instant, were it not for the resistance of the air.

NOTE 29, p. 5. Primary signifies, in astronomy, the planet about which a satellite revolves. The earth is primary to the moon.

NOTE 30, p. 6. Rotation. Motion round an axis, real or imaginary.

NOTE 31, p. 7. Compression of a spheroid. The flattening at the poles. It is equal to the difference between the greatest and least diameters, divided by the greatest, these quantities being expressed in some standard measure, as miles.

NOTE 32, p. 7. SATELLITES. Small bodies revolving about some of the planets. The moon is a satellite to the earth.

NOTE 33, p. 7. Nutation. A nodding motion in the earth’s axis while in rotation, similar to that observed in the spinning of a top. It is produced by the attraction of the sun and moon on the protuberant matter at the terrestrial equator.

NOTE 34, p. 7. Axis of rotation. The line, real or imaginary, about which a body revolves. The axis of the earth’s rotation is that diameter, or imaginary line, passing through the centre and both poles. Fig. 1 being the earth, N S is the axis of rotation.

NOTE 35, p. 7. Nutation of lunar orbit. The action of the bulging matter at the earth’s equator on the moon occasions a variation in the inclination of the lunar orbit to the plane of the ecliptic. Suppose the plane N p n, fig. 13, to be the orbit of the moon, and N m n the plane of the ecliptic, the earth’s action on the moon causes the angle p N m to become less or greater than its mean state. The nutation in the lunar orbit is the reaction of the nutation in the earth’s axis.

NOTE 36, p. 7. Translated. Carried forward in space.

NOTE 37, p. 7. Force proportional to velocity. Since a force is measured by its effect, the motions of the bodies of the solar system among themselves would be the same whether the system be at rest or not. The real motion of a person walking the deck of a ship at sea is compounded of his own motion and that of the ship, yet each takes place independently of the other. We walk about as if the earth were at rest, though it has the double motion of rotation on its axis and revolution round the sun.

NOTE 38, p. 8. Tangent. A straight line which touches a curved line in one point without cutting it. In fig. 4, m T is tangent to the curve in the point m. In a circle the tangent is at right angles to the radius, C m.

NOTE 39, p. 8. Motion in an elliptical orbit. A planet m, fig. 6, moves round the sun at S in an ellipse P D A Q, in consequence of two forces, one urging it in the direction of the tangent m T, and another pulling it towards the sun in the direction m S. Its velocity, which is greatest at P, decreases throughout the arc to P D A to A, where it is least, and increases continually as it moves along the arc A Q P till it comes to P again. The whole force producing the elliptical motion varies inversely as the square of the distance. See note 23.

NOTE 40, p. 8. Radii vectores. Imaginary lines adjoining the centre of the sun and the centre of a planet or comet, or the centres of a planet and its satellite. In the circle, the radii are all equal; but in an ellipse, fig. 6, the radius vector S A is greater, and S P less than all the others. The radii vectores S Q, S D, are equal to C A or C P, half the major axis P A, and consequently equal to the mean distance. A planet is at its mean distance from the sun when in the points Q and D.

NOTE 41, p. 8. Equal areas in equal times. See Kepler’s 1st law, in note 26, p. 5.

NOTE 42, p. 8. Major axis. The line P A, fig. 6 or 10.

NOTE 43, p. 8. If the planet described a circle, &c. The motion of a planet about the sun, in a circle A B P, fig. 10, whose radius C A is equal to the planet’s mean distance from him, would be equable, that is, its velocity, or speed, would always be the same. Whereas, if it moved in the ellipse A Q P, its speed would be continually varying, by note 39; but its motion is such, that the time elapsing between its departure from P and its return to that point again would be the same whether it moved in the circle or in the ellipse; for these curves coincide in the points P and A.

NOTE 44, p. 8. True motion. The motion of a body in its real orbit P D A Q, fig. 10.

NOTE 45, p. 9. Mean motion. Equable motion in a circle P E A B, fig. 10, at the mean distance C P or C m, in the time that the body would accomplish a revolution in its elliptical orbit P D A Q.

NOTE 46, p. 9. The equinox. Fig. 11 represents the celestial sphere, and C its centre, where the earth is supposed to be. q ♈ Q ♎ is the equinoctial or great circle, traced in the starry heavens by an imaginary extension of the plane of the terrestrial equator, and E ♈ e ♎ is the ecliptic, or apparent path of the sun round the earth. ♈ ♎, the intersection of these two planes, is the line of the equinoxes; ♈ is the vernal equinox, and ♎ the autumnal. When the sun is in these points, the days and nights are equal. They are distant from one another by a semicircle, or two right angles. The points E and e are the solstices, where the sun is at his greatest distance from the equinoctial. The equinoctial is everywhere ninety degrees distant from its poles N and S, which are two points diametrically opposite to one another, where the axis of the earth’s rotation, if prolonged, would meet the heavens. The northern celestial pole N is within 1° 24ʹ of the pole star. As the latitude of any place on the surface of the earth is equal to the height of the pole above the horizon, it is easily determined by observation. The ecliptic E ♈ e ♎ is also everywhere ninety degrees distant from its poles P and p. The angle P C N, between the poles P and N of the equinoctial and ecliptic, is equal to the angle e C Q, called the obliquity of the ecliptic.

NOTE 47, p. 9. Longitude. The vernal equinox, ♈, fig. 11, is the zero point in the heavens whence celestial longitudes, or the angular motions of the celestial bodies, are estimated from west to east, the direction in which they all revolve. The vernal equinox is generally called the first point of Aries, though these two points have not coincided since the early ages of astronomy, about 2233 years ago, on account of a motion in the equinoctial points, to be explained hereafter. If S ♈, fig. 10, be the line of the equinoxes, and ♈ the vernal equinox, the true longitude of a planet p is the angle ♈ S p, and its mean longitude is the angle ♈ C m, the sun being in S. Celestial longitude is the angular distance of a heavenly body from the vernal equinox; whereas terrestrial longitude is the angular distance of a place on the surface of the earth from a meridian arbitrarily chosen, as that of Greenwich.

NOTE 48, pp. 9, 58. Equation of the centre. The difference between ♈ C m and ♈ S p, fig. 10; that is, the difference between the true and mean longitudes of a planet or satellite. The true and mean places only coincide in the points P and A; in every other point of the orbit, the true place is either before or behind the mean place. In moving from A through the arc A Q P, the true place p is behind the mean place m; and through the arc P D A the true place is before the mean place. At its maximum, the equation of the centre measures C S, the excentricity of the orbit, since it is the difference between the motion of a body in an ellipse and in a circle whose diameter A P is the major axis of the ellipse.

NOTE 49, p. 9. Apsides. The points P and A, fig. 10, at the extremities of the major axis of an orbit. P is commonly called the perihelion, a Greek term signifying round the sun; and the point A is called the aphelion, a Greek term signifying at a distance from the sun.

NOTE 50, p. 9. Ninety degrees. A circle is divided into 360 equal parts, or degrees; each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds. It is usual to write these quantities thus, 15° 16ʹ 10ʺ, which means fifteen degrees, sixteen minutes, and ten seconds. It is clear that an arc m n, fig. 4, measures the angle m C n; hence we may say, an arc of so many degrees, or an angle of so many degrees; for, if there be ten degrees in the angle m C n, there will be ten degrees in the arc m n. It is evident that there are 90° in a right angle, m C d, or quadrant, since it is the fourth part of 360°.

NOTE 51, p. 9. Quadratures. A celestial body is said to be in quadrature when it is 90 degrees distant from the sun. For example, in fig. 14, if d be the sun, S the earth, and p the moon, then the moon is said to be in quadrature when she is in either of the points Q or D, because the angles Q S d and D S d, which measure her apparent distance from the sun, are right angles.

NOTE 52, p. 9. Excentricity. Deviation from circular form. In fig. 6, C S is the excentricity of the orbit P Q A D. The less C S, the more nearly does the orbit or ellipse approach the circular form; and, when C S is zero, the ellipse becomes a circle.

NOTE 53, p. 9. Inclination of an orbit. Let S, fig. 12, be the centre of the sun, P N A n the orbit of a planet moving from west to east in the direction N p. Let E N m e n be the shadow or projection of the orbit on the plane of the ecliptic, then N S n is the intersection of these two planes, for the orbit rises above the plane of the ecliptic towards N p, and sinks below it at N P. The angle p N m, which these two planes make with one another, is the inclination of the orbit P N p A to the plane of the ecliptic.

NOTE 54, p. 9. Latitude of a planet. The angle p S m, fig. 12, or the height of the planet p above the ecliptic E N m. In this case the latitude is north. Thus, celestial latitude is the angular distance of a celestial body from the plane of the ecliptic, whereas terrestrial latitude is the angular distance of a place on the surface of the earth from the equator.

NOTE 55, p. 9. Nodes. The two points N and n, fig. 12, in which the orbit N A n P of a planet or comet intersects the plane of the ecliptic e N E n. The part N A n of the orbit lies above the plane of the ecliptic, and the part n P N below it. The ascending node N is the point through which the body passes in rising above the plane of the ecliptic, and the descending node n is the point in which the body sinks below it. The nodes of a satellite’s orbit are the points in which it intersects the plane of the orbit of the planet.

NOTE 56, p. 10. Distance from the sun. S p in fig. 12. If ♈ be the vernal equinox, then ♈ S p is the longitude of the planet p, m S p is its latitude, and S p its distance from the sun. When these three quantities are known, the place of the planet p is determined in space.

NOTE 57, pp. 10, 59. Elements of an orbit. Of these there are seven. Let P N A n, fig. 12, be the elliptical orbit of a planet, C its centre, S the sun in one of the foci, ♈ the point of Aries, and E N e n the plane of the ecliptic. The elements are—the major axis A P; the excentricity C S; the periodic time, that is, the time of a complete revolution of the body in its orbit; and the fourth is the longitude of the body at any given instant—for example, that at which it passes through the perihelion P, the point of its orbit nearest to the sun. That instant is assumed as the origin of time, whence all preceding and succeeding periods are estimated. These four quantities are sufficient to determine the form of the orbit, and the motion of the body in it. Three other elements are requisite for determining the position of the orbit in space. These are, the angle ♈ S P, the longitude of the perihelion; the angle A N e, which is the inclination of the orbit to the plane of the ecliptic; and, lastly, the angle ♈ S N, the longitude of N the ascending node.

NOTE 58, p. 10. Whose planes, &c. The planes of the orbits, as P N A n, fig. 12, in which the planets move, are inclined or make small angles e N A with the plane of the ecliptic E N e n, and cut it in straight lines, N S n passing through S, the centre of the sun.

NOTE 59, p. 11. Momentum. Force measured by the weight of a body and its speed, or simple velocity, conjointly. The primitive momentum of the planets is, therefore, the quantity of motion which was impressed upon them when they were first thrown into space.

NOTE 60, p. 11. Unstable equilibrium. A body is said to be in equilibrium when it is so balanced as to remain at rest. But there are two kinds of equilibrium, stable and unstable. If a body balanced in stable equilibrium be slightly disturbed, it will endeavour to return to rest by a number of movements to and fro, which will continually decrease till they cease altogether, and then the body will be restored to its original state of repose. But, if the equilibrium be unstable, these movements to and fro, or oscillations, will become greater and greater till the equilibrium is destroyed.

NOTE 61, p. 14. Retrograde. Going backwards, as from east to west, contrary to the motion of the planets.

NOTE 62, p. 14. Parallel directions. Such as never meet, though prolonged ever so far.

NOTE 63, pp. 14, 16. The whole force, &c. Let S, fig. 13, be the sun, N m n the plane of the ecliptic, p the disturbed planet moving in its orbit n p N, and d the disturbing planet. Now, d attracts the sun and the planet p with different intensities in the directions d S, d p: the difference only of these forces disturbs the motion of p; it is therefore called the disturbing force. But this whole disturbing force may be regarded as equivalent to three forces, acting in the directions p S, p T, and p m. The force acting in the radius vector p S, joining the centres of the sun and planet, is called the radial force. It sometimes draws the disturbed planet p from the sun, and sometimes brings it nearer to him. The force which acts in the direction of the tangent p T is called the tangential force. It disturbs the motion of p in longitude, that is, it accelerates its motion in some parts of its orbit and retards it in others, so that the radius vector S p does not move over equal areas in equal times. (See note 26.) For example, in the position of the bodies in fig. 14, it is evident that, in consequence of the attraction of d, the planet p will have its motion accelerated from Q to C, retarded from C to D, again accelerated from D to O, and lastly retarded from O to Q. The disturbing body is here supposed to be at rest, and the orbit circular; but, as both bodies are perpetually moving with different velocities in ellipses, the perturbations or changes in the motions of p are very numerous. Lastly, that part of the disturbing force which acts in the direction of a line p m, fig. 13, at right angles to the plane of the orbit N p n, may be called the perpendicular force. It sometimes causes the body to approach nearer, and sometimes to recede farther from, the plane of the ecliptic N m n, than it would otherwise do. The action of the disturbing forces is admirably explained in a work on gravitation, by Mr. Airy, the Astronomer Royal.

NOTE 64, pp. 16, 74. Perihelion. Fig. 10, P, the point of an orbit nearest the sun.

NOTE 65, p. 16. Aphelion. Fig. 10, A, the point of an orbit farthest from the sun.

NOTE 66, pp. 16, 17. In fig. 15 the central force is greater than the exact law of gravity; therefore the curvature P p a is greater than P p A the real ellipse; hence the planet p comes to the point a, called the aphelion, sooner than if it moved in the orbit P p A, which makes the line P S A advance to a. In fig. 16, on the contrary, the curvature P p a is less than in the true ellipse, so that the planet p must move through more than the arc P p A, or 180°, before it comes to the aphelion a, which causes the greater axis P S A to recede to a.

NOTE 67, pp. 16, 17. Motion of apsides. Let P S A, fig. 17, be the position of the elliptical orbit of a planet, at any time; then, by the action of the disturbing forces, it successively takes the position Pʹ S Aʹ, Pʺ S Aʺ, &c., till by this direct motion it has accomplished a revolution, and then it begins again; so that the motion is perpetual.

NOTE 68, p. 17. Sidereal revolution. The consecutive return of an object to the same star.

NOTE 69, p. 17. Tropical revolution. The consecutive return of an object to the same tropic or equinox.

NOTE 70, p. 17. The orbit only bulges, &c. In fig. 18 the effect of the variation in the excentricity is shown where P p A is the elliptical orbit at any given instant; after a time it will take the form P pʹ A, in consequence of the decrease in the excentricity C S; then the forms P pʺ A, P pʹʹʹ A, &c., consecutively from the same cause; and, as the major axis P A always retains the same length, the orbit approaches more and more nearly to the circular form. But, after this has gone on for some thousands of years, the orbit contracts again, and becomes more and more elliptical.

NOTE 71, pp. 18, 19. The ecliptic is the apparent path of the sun in the heavens. See note 46.

NOTE 72, p. 18. This force tends to pull, &c. The force in question, acting in the direction p m, fig. 13, pulls the planet p towards the plane N m n, or pushes it farther above it, giving the planet a tendency to move in an orbit above or below its undisturbed orbit N p n, which alters the angle p N m, and makes the node N and the line of nodes N n change their positions.

NOTE 73, p. 18. Motion of the nodes. Let S, fig. 19, be the sun; S N n the plane of the ecliptic; P the disturbing body; and p a planet moving in its orbit p n, of which p n is so small a part that it is represented as a straight line. The plane S n p of this orbit cuts the plane of the ecliptic in the straight line S n. Suppose the disturbing force begins to act on p, so as to draw the planet into the arc p pʹ; then, instead of moving in the orbit p n, it will tend to move in the orbit p pʹ nʹ, whose plane cuts the ecliptic in the straight line S nʹ. If the disturbing force acts again upon the body when at pʹ, so as to draw it into the arc pʹ pʺ, the planet will now tend to move in the orbit pʹ pʺ nʺ, whose plane cuts the ecliptic in the straight line S nʺ. The action of the disturbing force on the planet when at pʺ will bring the node to nʹʹʹ, and so on. In this manner the node goes backwards through the successive points n, nʹ, nʺ, nʹʹʹ, &c., and the line of nodes S n has a perpetual retrograde motion about S, the centre of the sun. The disturbing force has been represented as acting at intervals for the sake of illustration: in nature it is continuous, so that the motion of the node is continuous also; though it is sometimes rapid and sometimes slow, now retrograde and now direct; but, on the whole, the motion is slowly retrograde.

NOTE 74, p. 18. When the disturbing planet is anywhere in the line S N, fig. 19, or in its prolongation, it is in the same plane with the disturbed planet; and, however much it may affect its motions in that plane, it can have no tendency to draw it out of it. But when the disturbing planet is in P, at right angles to the line S N, and not in the plane of the orbit, it has a powerful effect on the motion of the nodes: between these two positions there is great variety of action.

NOTE 75, p. 19. The changes in the inclination are extremely minute when compared with the motion of the node, as evidently appears from fig. 19, where the angles n p nʹ, nʹ pʹ nʺ, &c., are much smaller than the corresponding angles n S nʹ, S nʺ, &c.

NOTE 76, p. 20. Sines and cosines. Figure 4 is a circle; n p is the sine, and C p is the cosine of an arc m n. Suppose the radius C m to begin to revolve at m, in the direction m n a; then at the point m the sine is zero, and the cosine is equal to the radius C m. As the line C m revolves and takes the successive positions C n, C a, C b, &c., the sines n p, a q, b r, &c., of the arcs m n, m a, m h, &c., increase, while the corresponding cosines C p, C q, C r, &c., decrease; and when the revolving radius takes the position C d, at right angles to the diameter g m, the sine becomes equal to the radius C d, and the cosine is zero. After passing the point d, the contrary happens; for the sines e K, l V, &c., diminish, and the cosines C K, C V, &c., go on increasing, till at g the sine is zero, and the cosine is equal to the radius C g. The same alternation takes place through the remaining parts g h, h m, of the circle, so that a sine or cosine never can exceed the radius. As the rotation of the earth is invariable, each point of its surface passes through a complete circle, or 360 degrees, in twenty-four hours, at a rate of 15 degrees in an hour. Time, therefore, becomes a measure of angular motion, and vice versâ, the arcs of a circle a measure of time, since these two quantities vary simultaneously and equably; and, as the sines and cosines of the arcs are expressed in terms of the time, they vary with it. Therefore, however long the time may be, and how often soever the radius may revolve round the circle, the sines and cosines never can exceed the radius; and, as the radius is assumed to be equal to unity, their values oscillate between unity and zero.

NOTE 77, p. 20. The small excentricities and inclinations of the planetary orbits, and the revolutions of all the bodies in the same direction, were proved by Euler, La Grange, and La Place, to be conditions necessary for the stability of the solar system. Subsequently, however, the periodicity of the terms of the series expressing the perturbations was supposed to be sufficient alone, but M. Poisson has shown that to be a mistake; that these three conditions are requisite for the necessary convergence of the series, and that therefore the stability of the system depends on them conjointly with the periodicity of the sines and cosines of each term. The author is aware that this note can only be intelligible to the analyst, but she is desirous of correcting an error, and the more so as the conditions of stability afford one of the most striking instances of design in the original construction of our system, and of the foresight and supreme wisdom of the Divine Architect.

NOTE 78, p. 22. Resisting medium. A fluid which resists the motions of bodies, such as atmospheric air, or the highly elastic fluid called ether, with which space is filled.

NOTE 79, p. 23. Obliquity of the ecliptic. The angle e ♈ q, fig. 11, between the plane of the terrestrial equator q ♈ Q, and the plane of the ecliptic E ♈ e. The obliquity is variable.

NOTE 80, p. 23. Invariable plane. In the earth the equator is the invariable plane which nearly maintains a parallel position with regard to itself while revolving about the sun, as in fig. 20, where E Q represents it. The two hemispheres balance one another on each side of this plane, and would still do so if all the particles of which they consist were moveable among themselves, provided the earth were not disturbed by the action of the sun and moon, which alters the parallelism of the equator by the small variation called nutation, to be explained hereafter.

NOTE 81, p. 24. If each particle, &c. Let P, Pʹ, Pʺ, &c., fig. 21, be planets moving in their orbits about the centre of gravity of the system. Let P S M, Pʹ S Mʹ, &c., be portions of these orbits moved over by the radii vectores S P, S Pʹ, &c., in a given time, and let p S m, pʹ S mʹ, &c., be their shadows or projections on the invariable plane. Then, if the numbers which represent the masses of the planets P, Pʹ, &c., be respectively multiplied by the numbers representing the areas or spaces p S m, pʹ S mʹ, &c., the sum of the whole will be greater for the invariable plane than it would be for any plane that could pass through S, the centre of gravity of the system.

NOTE 82, p. 24. The centre of gravity of the solar system lies within the body of the sun, because his mass is much greater than the masses of all the planets and satellites added together.

NOTE 83, pp. 25, 36. Conjunction. A planet is said to be in conjunction when it has the same longitude with the sun, and in opposition when its longitude differs from that of the sun by 180 degrees. Thus two bodies are said to be in conjunction when they are seen exactly in the same part of the heavens, and in opposition when diametrically opposite to one another. Mercury and Venus, which are nearer to the sun than the earth, are called inferior planets; while all the others, being farther from the sun than the earth, are said to be superior planets. Suppose the earth to be at E, fig. 24; then a superior planet will be in conjunction with the sun at C, and in opposition to him when at O. Again, suppose the earth to be in O, then an inferior planet will be in conjunction when at E, and in opposition when at F.

NOTE 84, p. 26. The periodic inequalities are computed for a given time; and consequently for a given form and position of the orbits of the disturbed and disturbing bodies. Although the elements of the orbits vary so slowly that no sensible effect is produced on inequalities of a short period, yet, in the course of time, the secular variations of the elements change the forms and relative positions of the orbits so much, that Jupiter and Saturn, which would have come to the same relative positions with regard to the sun and to one another after 850 years, do not arrive at the same relative positions till after 918 years.

NOTE 85, p. 26. Configuration. The relative position of the planets with regard to one another, to the sun, and to the plane of the ecliptic.

NOTE 86, p. 27. In the same manner that the excentricity of an elliptical orbit may be increased or diminished by the action of the disturbing forces, so a circular orbit may acquire less or more ellipticity from the same cause. It is thus that the forms of the orbits of the first and second satellites of Jupiter oscillate between circles and ellipses differing very little from circles.

NOTE 87, p. 28. The plane of Jupiter’s equator is the imaginary plane passing through his centre at right angles to his axis of rotation, and corresponds to the plane q E Q e, in fig. 1. The satellites move very nearly in the plane of Jupiter’s equator; for, if J be Jupiter, fig. 22, P p his axis of rotation, e Q his equatorial diameter, which is 6000 miles longer than P p, and if J O and J E be the planes of his orbit and equator seen edgewise, then the orbits of his four satellites seen edgewise will have the positions J1, J2, J3, J4. These are extremely near to one another, for the angle E J O is only 3° 5ʹ 30ʺ.

NOTE 88, p. 28. In consequence of the satellites moving so nearly in the plane of Jupiter’s equator, when seen from the earth, they appear to be always very nearly in a straight line, however much they may change their positions with regard to one another and to their primary. For example, on the evenings of the 3rd, 4th, 5th, and 6th of January, 1835, the satellites had the configurations given in fig. 23, where O is Jupiter, and 1, 2, 3, 4, are the first, second, third, and fourth satellites. The satellite is supposed to be moving in a direction from the figure towards the point. On the sixth evening the second satellite was seen on the disc of the planet.

NOTE 89, p. 28. Angular motion or velocity is the swiftness with which a body revolves—a sling, for example; or the speed with which the surface of the earth performs its daily rotation about its axis.

NOTE 90, p. 29. Displacement of Jupiter’s orbit. The action of the planets occasions secular variations in the position of Jupiter’s orbit J O, fig. 22, without affecting the plane of his equator J E. Again, the sun and satellites themselves, by attracting the protuberant matter at Jupiter’s equator, change the position of the plane J E without affecting J O. Both of these cause perturbations in the motions of the satellites.

NOTE 91, p. 29. Precession, with regard to Jupiter, is a retrograde motion of the point where the lines J O, J E, intersect fig. 22.

NOTE 92, p. 30. Synodic motion of a satellite. Its motion during the interval between two of its consecutive eclipses.

NOTE 93, p. 30. Opposition. A body is said to be in opposition when its longitude differs from that of the sun by 180°. If S, fig. 24, be the sun, and E the earth, then Jupiter is in opposition when at O, and in conjunction when at C. In these positions the three bodies are in the same straight line.

NOTE 94, p. 30. Eclipses of the satellites. Let S, fig. 25, be the sun, J Jupiter, and a B b his shadow. Let the earth be moving in its orbit, in the direction E A R T H, and the third satellite in the direction a b m n. When the earth is at E, the satellite, in moving through the arc a b, will vanish at a, and reappear at b, on the same side of Jupiter. If the earth be in R, Jupiter will be in opposition; and then the satellite, in moving through the arc a b, will vanish close to the disc of the planet, and will reappear on the other side of it. But, if the satellite be moving through the arc m n, it will appear to pass over the disc, and eclipse the planet.

NOTE 95, pp. 30, 43. Meridian. A terrestrial meridian is a line passing round the earth and through both poles. In every part of it noon happens at the same instant. In figures 1 and 3, the lines N Q S and N G S are meridians, C being the centre of the earth, and N S its axis of rotation. The meridian passing through the Observatory at Greenwich is assumed by the British as a fixed origin from whence terrestrial longitudes are measured. And as each point on the surface of the earth passes through 360°, or a complete circle, in twenty-four hours, at the rate of 15° in an hour, time becomes a representative of angular motion. Hence, if the eclipse of a satellite happens at any place at eight o’clock in the evening, and the Nautical Almanac shows that the same phenomenon will take place at Greenwich at nine, the place of observation will be in the 15° of west longitude.

NOTE 96, p. 31. Conjunction. Let S be the sun, fig. 24, E the earth, and J O Jʹ Cʹ the orbit of Jupiter. Then the eclipses which happen when Jupiter is in O are seen 16^m 26^s sooner than those which take place when the planet is in C. Jupiter is in conjunction when at C, and in opposition when in O.

NOTE 97, p. 31. In the diagonal, &c. Were the line A S, fig. 26, 100,000 times longer than A B, Jupiter’s true place would be in the direction A Sʹ, the diagonal of the figure A B Sʹ S, which is, of course, out of proportion.

NOTE 98, p. 31. Aberration of light. The celestial bodies are so distant that the rays of light coming from them may be reckoned parallel. Therefore, let S A, Sʹ B, fig. 26, be two rays of light coming from the sun, or a planet, to the earth moving in its orbit in the direction A B. If a telescope be held in the direction A S, the ray S A, instead of going down the tube, will impinge on its side, and be lost in consequence of the telescope being carried with the earth in the direction A B. But, if the tube be held in the position A E, so that A B is to A S as the velocity of the earth to the velocity of light, the ray will pass through Sʹ E A. The star appears to be in the direction A Sʹ, when it really is in the direction A S; hence the angle S A Sʹ is the angle of aberration.

NOTE 99, p. 32. Density proportional to elasticity. The more a fluid, such as atmospheric air, is reduced in dimensions by pressure, the more it resists the pressure.

NOTE 100, p. 32. Oscillations of pendulum retarded. If a clock be carried from the pole to the equator, its rate will be gradually diminished, that is, it will go slower and slower: because the centrifugal force, which increases from the pole to the equator, diminishes the force of gravity.

NOTE 101, p. 34. Disturbing action. The disturbing force acts here in the very same manner as in note 63; only that the disturbing body d, fig. 14, is the sun, S the earth, and p the moon.

NOTE 102, pp. 35, 36, 86. Perigee. A Greek word, signifying round the earth. The perigee of the lunar orbit is the point P, fig. 6, where the moon is nearest to the earth. It corresponds to the perihelion of a planet. Sometimes the word is used to denote the point where the sun is nearest to the earth.

NOTE 103, p. 35. Evection. The evection is produced by the action of the radial force in the direction S p, fig. 14, which sometimes increases and sometimes diminishes the earth’s attraction to the moon. It produces a corresponding temporary change in the excentricity, which varies with the position of the major axis of the lunar orbit in respect of the line S d, joining the centres of the earth and sun.

NOTE 104, p. 35. Variation. The lunar perturbation called the variation is the alternate acceleration and retardation of the moon in longitude, from the action of the tangential force. She is accelerated in going from quadratures in Q and D, fig. 14, to the points C and O, called syzygies, and is retarded in going from the syzygies C and O to Q and D again.

NOTE 105, p. 36. Square of time. If the times increase at the rate of 1, 2, 3, 4, &c., years or hundreds of years, the squares of the times will be 1, 4, 9, 16, &c., years or hundreds of years.

NOTE 106, p. 37. In all investigations hitherto made with regard to the acceleration, it was tacitly assumed that the areas described by the radius vector of the moon were not permanently altered; that is to say, that the tangential disturbing force produced no permanent effect. But Mr. Adams has discovered that, in consequence of the constant decrease in the excentricity of the earth’s orbit, there is a gradual change in the central disturbing force which affects the aërial velocity, and consequently it alters the amount of the acceleration by a very small quantity, as well as the variation and other periodical inequalities of the moon. On the latter, however, it has no permanent effect, because it affects them in opposite directions in very moderate intervals of time, whereas a very small error in the amount of the acceleration goes on increasing as long as the excentricity of the earth’s orbit diminishes, so that it would ultimately vitiate calculations of the moon’s place for distant periods of time. This shows how complicated the moon’s motions are, and what rigorous accuracy is required in their determination.

To give an idea of the labour requisite merely to perfect or correct the lunar tables, the moon’s place was determined by observation at the Greenwich Observatory in 6000 different points of her orbit, each of which was compared with the same points calculated from Baron Plana’s formulæ, and to do that sixteen computers were constantly employed for eight years. Since the longitude is determined by the motions of the moon, the lunar tables are of the greatest importance.

NOTE 107, p. 37. Mean anomaly. The mean anomaly of a planet is its angular distance from the perihelion, supposing it to move in a circle. The true anomaly is its angular distance from the perihelion in its elliptical orbit. For example, in fig. 10, the mean anomaly is P C m, and the true anomaly is P S p.

NOTE 108, pp. 38, 68. Many circumferences. There are 360 degrees or 1,296,000 seconds in a circumference; and, as the acceleration of the moon only increases at the rate of eleven seconds in a century, it must be a prodigious number of ages before it accumulates to many circumferences.

NOTE 109, p. 39. Phases of the moon. The periodical changes in the enlightened part of her disc, from a crescent to a circle, depending upon her position with regard to the sun and earth.

NOTE 110, p. 39. Lunar eclipse. Let S, fig. 27, be the sun, E the earth, and m the moon. The space a A b is a section of the shadow, which has the form of a cone or sugar-loaf, and the spaces A a c, A b d, are the penumbra. The axis of the cone passes through A, and through E and S, the centres of the sun and earth, and n m nʹ is the path of the moon through the shadow.

NOTE 111, p. 39. Apparent diameter. The diameter of a celestial body as seen from the earth.

NOTE 112, p. 40. Penumbra. The shadow or imperfect darkness which precedes and follows an eclipse.

NOTE 113, p. 40. Synodic revolution of the moon. The time between two consecutive new or full moons.

NOTE 114, p. 40. Horizontal refraction. The light, in coming from a celestial object, is bent into a curve as soon as it enters our atmosphere; and that bending is greatest when the object is in the horizon.

NOTE 115, p. 40. Solar eclipse. Let S, fig. 28, be the sun, m the moon, and E the earth. Then a E b is the moon’s shadow, which sometimes eclipses a small portion of the earth’s surface at e, and sometimes falls short of it. To a person at e, in the centre of the shadow, the eclipse may be total or annular; to a person not in the centre of the shadow a part of the sun will be eclipsed; and to one at the edge of the shadow there will be no eclipse at all. The spaces P b E, Pʹ a E, are the penumbra.

NOTE 116, p. 43. From the extremities, &c. If the length of the line a b, fig. 29, be measured, in feet or fathoms, the angles S b a, S a b, can be measured, and then the angle a S b is known, whence the length of the line S C may be computed. a S b is the parallax of the object S; and it is clear that, the greater the distance of S, the less the base a b will appear, because the angle a Sʹ b is less than a S b.

NOTE 117, p. 44. Every particle will describe a circle, &c. If N S, fig. 3, be the axis about which the body revolves, then particles at B, Q, &c., will whirl in the circles B G A a, Q E q d, whose centres are in the axis N S, and their planes parallel to one another. They are, in fact, parallels of latitude, Q E q d being the equator.

NOTE 118, p. 44. The force of gravity, &c. Gravity at the equator acts in the direction Q C, fig. 30. Whereas the direction of the centrifugal force is exactly contrary, being in the direction C Q; hence the difference of the two is the force called gravitation, which makes bodies fall to the surface of the earth. At any point, m, not at the equator, the direction of gravity is m b, perpendicular to the surface, but the centrifugal force acts perpendicularly to N S, the axis of rotation. Now the effect of the centrifugal force is the same as if it were two forces, one of which acting in the direction b m, diminishes the force of gravity, and another which, acting in the direction m t, tangent to the surface at m, urges the particles towards Q, and tends to swell out the earth at the equator.

NOTE 119, p. 45. Homogeneous mass. A quantity of matter, everywhere of the same density.

NOTE 120, p. 45. Ellipsoid of revolution. A solid formed by the revolution of an ellipse about its axis. If the ellipse revolve about its minor axis Q D, fig. 6, the ellipsoid will be oblate, or flattened at the poles like an orange. If the revolution be about the greater axis A P, the ellipsoid will be prolate, like an egg.

NOTE 121, p. 45. Concentric elliptical strata. Strata, or layers, having an elliptical form and the same centre.

NOTE 122, p. 46. On the whole, &c. The line N Q S q, fig. 1, represents the ellipse in question, its major axis being Q q, its minor axis N S.

NOTE 123, p. 46. Increase in the length of the radii, &c. The radii gradually increase from the polar radius C N, fig. 30, which is least, to the equatorial radius C Q, which is greatest. There is also an increase in the lengths of the arcs corresponding to the same number of degrees from the equator to the poles; for, the angle N C r being equal to q C d, the elliptical arc N r is less than q d.

NOTE 124, p. 46. Cosine of latitude. The angles m C a, m C b, fig. 4, being the latitudes of the points a, b, &c., the cosines are C q, C r, &c.

NOTE 125, p. 47. An arc of the meridian. Let N Q S q, fig. 30, be the meridian, and m n the arc to be measured. Then, if Zʹ m, Z n, be verticals, or lines perpendicular to the surface of the earth, at the extremities of the arc m n they will meet in p. Q a n, Q b m, are the latitudes of the points m and n, and their difference is the angle m p n. Since the latitudes are equal to the height of the pole of the equinoctial above the horizon of the places m and n, the angle m p n may be found by observation. When the distance m n is measured in feet or fathoms, and divided by the number of degrees and parts of a degree contained in the angle m p n, the length of an arc of one degree is obtained.

NOTE 126, p. 47. A series of triangles. Let M Mʹ, fig. 31, be the meridian of any place. A line A B is measured with rods, on level ground, of any number of fathoms, C being some point seen from both ends of it. As two of the angles of the triangle A B C can be measured, the lengths of the sides A C, B C, can be computed; and if the angle m A B, which the base A B makes with the meridian, be measured, the length of the sides B m, A m, may be obtained by computation, so that A m, a small part of the meridian, is determined. Again, if D be a point visible from the extremities of the known line B C, two of the angles of the triangle B C D may be measured, and the length of the sides C D, B D, computed. Then, if the angle B m mʹ be measured, all the angles and the side B m of the triangle B m mʹ are known, whence the length of the line m mʹ may be computed, so that the portion A mʹ of the meridian is determined, and in the same manner it may be prolonged indefinitely.

NOTE 127, pp. 47, 49. The square of the sine of the latitude. Q b m, fig. 30, being the latitude of m, e m is the sine and b e the cosine. Then the number expressing the length of e m, multiplied by itself, is the square of the sine of the latitude; and the number expressing the length of b e, multiplied by itself, is the square of the cosine of the latitude.

NOTE 128, p. 48. The polar diameter of the earth determined by the survey of Great Britain is 7900 miles; the equatorial is 7926, which gives a compression of 1/299·33.

NOTE 129, p. 50. A pendulum is that part of a clock which swings to and fro.

NOTE 130, p. 52. Parallax. The angle a S b, fig. 29, under which we view an object a b: it therefore diminishes as the distance increases. The parallax of a celestial object is the angle which the radius of the earth would be seen under, if viewed from that object. Let E, fig. 32, be the centre of the earth, E H its radius, and m H O the horizon of an observer at H. Then H m E is the parallax of a body m, the moon for example. As m rises higher and higher in the heavens to the points mʹ, mʺ, &c., the parallax H mʹ E, H mʺ E, &c., decreases. At Z, the zenith, or point immediately above the head of the observer, it is zero; and at m, where the body is in the horizon, the angle H m E is the greatest possible, and is called the horizontal parallax. It is clear that with regard to celestial bodies the whole effect of parallax is in the vertical, or in the direction m mʹ Z; and as a person at H sees mʹ in the direction H mʹ A, when it really is in the direction E mʹ B, it makes celestial objects appear to be lower than they really are. The distance of the moon from the earth has been determined from her horizontal parallax. The angle E m H can be measured. E H m is a right angle, and E H, the radius of the earth, is known in miles; whence the distance of the moon E m is easily found. Annual parallax is the angle under which the diameter of the earth’s orbit would be seen if viewed from a star.

NOTE 131, p. 52. The radii n B, n G, &c., fig. 3, are equal in any one parallel of latitude, A a B G; therefore a change in the parallax observed in that parallel can only arise from a change in the moon’s distance from the earth; and when the moon is at her mean distance, which is a constant quantity equal to half the major axis of her orbit, a change in the parallax observed in different latitudes, G and E, must arise from the difference in the lengths of the radii n G and C E.

NOTE 132, p. 52. When Venus is in her nodes. She must be in the line N S n where her orbit P N A n cuts the plane of the ecliptic E N e n, fig. 12.

NOTE 133, p. 53. The line described, &c. Let E, fig. 33, be the earth, S the centre of the sun, and V the planet Venus. The real transit of the planet, seen from E the centre of the earth, would be in the direction A B. A person at W would see it pass over the sun in the line v a, and a person at O would see it move across him in the direction vʹ aʹ.

NOTE 134, p. 54. Kepler’s law. Suppose it were required to find the distance of Jupiter from the sun. The periodic times of Jupiter and Venus are given by observation, and the mean distance of Venus from the centre of the sun is known in miles or terrestrial radii; therefore, by the rule of three, the square root of the periodic time of Venus is to the square root of the periodic time of Jupiter as the cube root of the mean distance of Venus from the sun to the cube root of the mean distance of Jupiter from the sun, which is thus obtained in miles or terrestrial radii. The root of a number is that number which, once multiplied by itself, gives its square; twice multiplied by itself, gives its cube, &c. For example, twice 2 are 4, and twice 4 are 8; 2 is therefore the square root of 4, and the cube root of 8. In the same manner 3 times 3 are 9, and 3 times 9 are 27; 3 is therefore the square root of 9, and the cube root of 27.

NOTE 135, p. 55. Inversely, &c. The quantities of matter in any two primary planets are greater in proportion as the cubes of the numbers representing the mean distances of their satellites are greater, and also in proportion as the squares of their periodic times are less.

NOTE 136, p. 55. As hardly anything appears more impossible than that man should have been able to weigh the sun as it were in scales and the earth in a balance, the method of doing so may have some interest. The attraction of the sun is to the attraction of the earth as the quantity of matter in the sun to the quantity of matter in the earth; and, as the force of this reciprocal attraction is measured by its effects, the space the earth would fall through in a second by the sun’s attraction is to the space which the sun would fall through by the earth’s attraction as the mass of the sun to the mass of the earth. Hence, as many times as the fall of the earth to the sun in a second exceeds the fall of the sun to the earth in the same time, so many times does the mass of the sun exceed the mass of the earth. Thus the weight of the sun will be known if the length of these two spaces can be found in miles or parts of a mile. Nothing can be easier. A heavy body falls through 16·0697 feet in a second at the surface of the earth by the earth’s attraction; and, as the force of gravity is inversely as the square of the distance, it is clear that 16·0697 feet are to the space a body would fall through at the distance of the sun by the earth’s attraction, as the square of the distance of the sun from the earth to the square of the distance of the centre of the earth from its surface; that is, as the square of 95,000,000 miles to the square of 4000 miles. And thus, by a simple question in the rule of three, the space which the sun would fall through in a second by the attraction of the earth may be found in parts of a mile. The space the earth would fall through in a second, by the attraction of the sun, must now be found in miles also. Suppose m n, fig. 4, to be the arc which the earth describes round the sun in C, in a second of time, by the joint action of the sun and the centrifugal force. By the centrifugal force alone the earth would move from m to T in a second, and by the sun’s attraction alone it would fall through T n in the same time. Hence the length of T n, in miles, is the space the earth would fall through in a second by the sun’s attraction. Now, as the earth’s orbit is very nearly a circle, if 360 degrees be divided by the number of seconds in a sidereal year of 365-1/4 days, it will give m n, the arc which the earth moves through in a second, and then the tables will give the length of the line C T in numbers corresponding to that angle; but, as the radius C n is assumed to be unity in the tables, if 1 be subtracted from the number representing C T, the length of T n will be obtained; and, when multiplied by 95,000,000, to reduce it to miles, the space which the earth falls through, by the sun’s attraction, will be obtained in miles. By this simple process it is found that, if the sun were placed in one scale of a balance, it would require 354,936 earths to form a counterpoise.

NOTE 137, p. 59. The sum of the greatest and least distances S P, S A, fig. 12, is equal to P A, the major axis; and their difference is equal to twice the excentricity C S. The longitude ♈ S P of the planet, when in the point P, at its least distance from the sun, is the longitude of the perihelion. The greatest height of the planet above the plane of the ecliptic E N e n, is equal to the inclination of the orbit P N A n to that plane. The longitude of the planet, when in the plane of the ecliptic, can only be the longitude of one of the points N or n; and, when one of these points is known, the other is given, being 180° distant from it. Lastly, the time included between two consecutive passages of the planet through the same node N or n, is its periodic time, allowance being made for the recess of the node in the interval.

NOTE 138, p. 60. Suppose that it were required to find the position of a point in space, as of a planet, and that one observation places it in n, fig. 34, another observation places it in nʹ, another in nʺ, and so on; all the points n, nʹ, nʺ, nʹʹʹ, &c., being very near to one another. The true place of the planet P will not differ much from any of these positions. It is evident, from this view of the subject, that P n, P nʹ, P nʺ, &c., are the errors of observation. The true position of the planet P is found by this property, that the squares of the numbers representing the lines P n, P nʹ, &c., when added together, is the least possible. Each line P n, P nʹ, &c., being the whole error in the place of the planet, is made up of the errors of all the elements; and, when compared with the errors obtained from theory, it affords the means of finding each. The principle of least squares is of very general application; its demonstration cannot find a place here; but the reader is referred to Biot’s Astronomy, vol. ii. p. 203.

NOTE 139, p. 61. The true longitude of Uranus was in advance of the tables previous to 1795, and continued to advance till 1822, after which it diminished rapidly till 1830-1, when the observed and calculated longitudes agreed, but then the planet fell behind the calculated place so rapidly that it was clear the tables could no longer represent its motion.

NOTE 140, p. 65. An axis that, &c. Fig. 20 represents the earth revolving in its orbit about the sun in S, the axis of rotation P p being everywhere parallel to itself.

NOTE 141, p. 65. Angular velocities that are sensibly uniform. The earth and planets revolve about their axis with an equable motion, which is never either faster or slower. For example, the length of the day is never more nor less than twenty-four hours.

NOTE 142, p. 68. If fig. 1 be the moon, her polar diameter N S is the shortest; and of those in the plane of the equator, Q E q, that which points to the earth is greater than all the others.

NOTE 143, p. 73. Inversely proportional, &c. That is, the total amount of solar radiation becomes less as the minor axis C Cʹ, fig. 20, of the earth’s orbit becomes greater.

NOTE 144, p. 75. Fig. 35 represents the position of the apparent orbit of the sun as it is at present, the earth being in E. The sun is nearer to the earth in moving through ♎ P ♈ than in moving through ♈ A ♎, but its motion through ♎ P ♈ is more rapid than its motion through ♈ A ♎; and, as the swiftness of the motion and the quantity of heat received vary in the same proportion, a compensation takes place.

NOTE 145, p. 76. In an ellipsoid of revolution, fig. 1, the polar diameter N S, and every diameter in the equator q E Q e, are permanent axes of rotation, but the rotation would be unstable about any other. Were the earth to begin to rotate about C a, the angular distance from a to the equator at q would no longer be ninety degrees, which would be immediately detected by the change it would occasion in the latitudes.

NOTE 146, pp. 50, 80. Let q ♈ Q, and E ♎ e, fig. 11, be the planes of the equator and ecliptic. The angle e ♈ Q, which separates them, called the obliquity of the ecliptic, varies in consequence of the action of the sun and moon upon the protuberant matter at the earth’s equator. That action brings the point Q towards e, and tends to make the plane q ♈ Q coincide with the ecliptic E ♈ e, which causes the equinoctial points ♈ and ♎ to move slowly backwards on the plane e ♈ E, at the rate of 50ʺ·41 annually. This part of the motion, which depends upon the form of the earth, is called luni-solar precession. Another part, totally independent of the form of the earth, arises from the mutual action of the earth, planets, and sun, which, altering the position of the plane of the ecliptic e ♈ E, causes the equinoctial points ♈ and ♎ to advance at the rate of Oʺ·31 annually; but, as this motion is much less than the former, the equinoctial points recede on the plane of the ecliptic at the rate of 50ʺ·1 annually. This motion is called the precession of the equinoxes.

NOTE 147, p. 81. Let q ♈ Q, e ♈ E, fig. 36, be the planes of the equinoctial or celestial equator and ecliptic, and p, P, their poles. Then suppose p, the pole of the equator, to revolve with a tremulous or wavy motion in the little ellipse p c d b in about 19 years, both motions being very small, while the point a is carried round in the circle a A B in 25,868 years. The tremulous motion may represent the half-yearly variation, the motion in the ellipse gives an idea of the nutation discovered by Bradley, and the motion in the circle a A B arises from the precession of the equinoxes. The greater axis p d of the small ellipse is 18ʺ·5, its minor axis b c is 13ʺ·74. These motions are so small that they have very little effect on the parallelism of the axis of the earth’s rotation during its revolution round the sun, as represented in fig. 20. As the stars are fixed, this real motion in the pole of the earth must cause an apparent change in their places.

NOTE 148, p. 83. By means of a transit instrument, which is a telescope mounted so as to revolve only in the plane of the meridian, the instant of the transit or passage of a celestial body across the meridian can be determined. The transits of the principal stars are used to ascertain the time, or, which is the same thing, the amount of the error of clocks. A system of equidistant wires, as represented in the figure, is placed in the focus of the eye-piece, so that the middle wire is perpendicular and at right angles to the axis of the telescope. It consequently represents a portion of the celestial meridian; and when a star is seen to cross that wire it then crosses the celestial meridian of the place of observation. A clock beating seconds being close at hand, the duty of an observer is to note the exact second and part of a second at which a star crosses each wire successively in consequence of the rotation of the earth. Then the mean of all these observations will give the time at which the star crosses the celestial meridian of the place of observation to the tenth of a second, provided the observations are accurate. Now it happens that the simultaneous impression on the eye and ear is estimated differently by different observers, so that one person will note the transit of a star, for example, as happening the fraction of a second sooner or later than another person; and as that is the case in every observation he makes, it is called his personal equation, that is to say, it is a correction that must be applied to all the observations of the individual, and a curious instance of individuality it is. For instance, M. Otto Struve notes every observation Oʺ·11 too soon, M. Peters Oʺ·13 too late; M. Struve noted every observation one second later than M. Bessel, and M. Argelander estimated the transit of a star 1ʺ·2 later than M. Bessel. All these gentlemen were or are first-rate observers; and when the personal equation is known it is easy to correct the observations. However, to avoid that inconvenience Mr. Bond has introduced a method in the Observatory at Cambridge in the United States in which touch is combined with sight instead of hearing, which is now used also at Greenwich. The observer at the moment of the observation presses his fingers on a machine which by means of a galvanic battery conveys the impression to where time is measured and marked, so that the observation is at once recorded and the personal equation avoided.

NOTE 149, p. 84. Let N be the pole, fig. 11, e E the ecliptic, and Q q the equator. Then, N n m S being a meridian, and at right angles to the equator, the arc ♈ m is less than the arc ♈ n.

NOTE 150, p. 85. Heliacal rising of Sirius. When the star appears in the morning, in the horizon, a little before the rising of the sun.

NOTE 151, p. 87. Let P ♈ A ♎, fig. 35, be the apparent orbit or path of the sun, the earth being in E. Its major axis, A P, is at present situate as in the figure, where the solar perigee P is between the solstice of winter and the equinox of spring. So that the time of the sun’s passage through the arc ♈ A ♎ is greater than the time he takes to go through the arc ♎ P ♈. The major axis A P coincided with ♎ ♈, the line of the equinoxes, 4000 years before the Christian era; at that time P was in the point ♈. In 6468 of the Christian era the perigee P will coincide with ♎. In 1234 A.D. the major axis was perpendicular to ♈ ♎, and then P was in the winter solstice.

NOTE 152, p. 88. At the solstices, &c. Since the declination of a celestial object is its angular distance from the equinoctial, the declination of the sun at the solstice is equal to the arc Q e, fig. 11, which measures the obliquity of the ecliptic, or angular distance of the plane ♈ e ♎ from the plane ♈ Q ♎.

NOTE 153, p. 88. Zenith distance is the angular distance of a celestial object from the point immediately over the head of an observer.

NOTE 154, p. 89. Reduced to the level of the sea. The force of gravitation decreases as the square of the height above the surface of the earth increases, so that a pendulum vibrates slower on high ground; and, in order to have a standard independent of local circumstances, it is necessary to reduce it to the length that would exactly make 86,400 vibrations in a mean solar day at the level of the sea.

NOTE 155, p. 90. A quadrant of the meridian is a fourth part of a meridian, or an arc of a meridian containing 90°, as N Q, fig. 11.

NOTE 156, p. 93. Moon’s southing. The time when the moon is on the meridian of any place, which happens about forty-eight minutes later every day.

NOTE 157, p. 96. The angular velocity of the earth’s rotation is at the rate of 180° in twelve hours, which is the time included between the passages of the moon at the upper and under meridian.

NOTE 158, p. 96. If S be the earth, fig. 14, d the sun, and C Q O D the orbit of the moon, then C and O are the syzygies. When the moon is new, she is at C, and when full she is at O; and, as both sun and moon are then on the same meridian, it occasions the spring-tides, it being high water at places under C and O, while it is low water at those under Q and D. The neap-tides happen when the moon is in quadrature at Q or D, for then she is distant from the sun by the angle d S Q, or d S D, each of which is 90°.

NOTE 159, p. 97. Declination. If the earth be in C, fig. 11, and if q ♈ Q be the equinoctial, and N m S a meridian, then m C n is the declination of a body at n. Therefore the cosine of that angle is the cosine of the declination.

NOTE 160, pp. 99, 131. Fig 37 shows the propagation of waves from two points C and Cʹ, where stones are supposed to have fallen. Those points in which the waves cross each other are the places where they counteract each other’s effects, so that the water is smooth there, while it is agitated in the intermediate spaces.

NOTE 161, p. 100. The centrifugal force may, &c. The centrifugal force acts in a direction at right angles to N S, the axis of rotation, fig. 30. Its effects are equivalent to two forces, one of which is in the direction b m perpendicular to the surface Q m n of the earth, and diminishes the force of gravity at m. The other acts in the direction of the tangent m T, which makes the fluid particles tend towards the equator.

NOTE 162, p. 106. Analytical formula or expression. A combination of symbols or signs expressing or representing a series of calculation, and including every particular case that can arise from a general law.

NOTE 163, p. 106. Fig. 38 is a perfect octahedron. Sometimes its angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is cut off its edges A a, X a, a a, &c. Occasionally both these modifications take place.

NOTE 164, p. 107. Prismatic crystals of sulphate of nickel are somewhat like fig. 62, only that they are thin, like a hair.

NOTE 165, p. 108. Zinc, a metal either found as an ore or mixed with other metals. It is used in making brass.

NOTE 166, p. 108. A cube is a solid contained by six plane square surfaces, as fig. 39.

NOTE 167, p. 108. A tetrahedron is a solid contained by four triangular surfaces, as fig. 40: of this solid there are many varieties.

NOTE 168, p. 108. There are many varieties of the octahedron. In that mentioned in the text, the base a a a a, fig. 38, is a square, but the base may be a rhomb; this solid may also be elongated in the direction of its axis A X, or it may be depressed.

NOTE 169, pp. 109, 192, 273. A rhombohedron is a solid contained by six plane surfaces, as in fig. 63, the opposite planes being equal and similar rhombs parallel to one another; but all the planes are not necessarily equal or similar, nor are its angles right angles. In carbonate of lime the angle C A B is 105°·55, and the angle B or C is 75°·05.

NOTE 170, p. 109. Sublimation. Bodies raised into vapour which is again condensed into a solid state.

NOTE 171, p. 112. Platinum. The heaviest of metals; its colour is between that of silver and lead.

NOTE 172, p. 113. The surface of a column of water, or spirit of wine, in a capillary tube, is hollow; and that of a column of quicksilver is convex, or rounded, as in fig. 41.

NOTE 173, p. 113. Inverse ratio, &c. The elevation of the liquid is greater in proportion as the internal diameter of the tube is less.

NOTE 174, p. 114. In fig. 41 the line c d shows the direction of the resulting force in the two cases.

NOTE 175, p. 115. When two plates of glass are brought near to one another in water, the liquid rises between them; and, if the plates touch each other at one of their upright edges, the outline of the water will become an hyperbola.

NOTE 176, p. 115. Let A Aʹ, fig. 42, be two plates, both of which are wet, and B Bʹ two that are dry. When partly immersed in a liquid, its surface will be curved close to them, but will be of its usual level for the rest of the distance. At such a distance they will neither attract nor repel one another. But, as soon as they are brought near enough to have the whole of the liquid surface between them curved, as in a aʹ, b bʹ, they will rush together. If one be wet and another dry, as C Cʹ, they will repel one another at a certain distance; but, as soon as they are brought very near, they will rush together, as in the former cases.

NOTE 177, p. 123. In a paper on the atmospheric changes that produce rain and wind, by Thomas Hopkins, Esq., in the Geographical Journal, it is shown that, when vapour is condensed and falls in rain, a partial vacuum is formed, and that heavier air presses in as a current of wind. Thus the vacuum arising from the great precipitation at the tropics causes the polar winds to descend from the upper regions of the atmosphere and blow along the surface to the equator as trade winds to supply the place of the hot currents that are continually raising them into the higher regions. This circumstance removes the only difficulty in Lieutenant Maury’s theory of the winds.

NOTE 178, p. 134. Latent or absorbed heat. There is a certain quantity of heat in all bodies, which cannot be detected by the thermometer, but which may become sensible by compression.

NOTE 179, p. 137. Reflected waves. A series of waves of light, sound, or water, diverge in all directions from their origin I, fig. 43, as from a centre. When they meet with an obstacle S S, they strike against it, and are reflected or turned back by it in the same form as if they had proceeded from the centre C, at an equal distance on the other side of the surface S S.

NOTE 180, p. 138. Elliptical shell. If fig. 6 be a section of an elliptical shell, then all sounds coming from the focus S to different points on the surface, as m, are reflected back to F, because the angle T m S is equal to t m F. In a spherical hollow shell, a sound diverging from the centre is reflected back to the centre again.

NOTE 181, p. 142. Fig. 44 represents musical strings in vibration; the straight lines are the strings when at rest. The first figure of the four would give the fundamental note, as, for example, the low C. The second and third figures would give the first and second harmonics; that is, the octave and the 12th above C, n n n being the points at rest; the fourth figure shows the real motion when compounded of all three.

NOTE 182, p. 143. Fig. 45 represents sections of an open and of a shut pipe, and of a pipe open at one end. When sounded, the air spontaneously divides itself into segments. It remains at rest in the divisions or nodes n nʹ, &c., but vibrates between them in the direction of the arrow-heads. The undulations of the whole column of air give the fundamental note, while the vibrations of the divisions give the harmonics.

NOTE 183, p. 144. Fig. 1, plate 1, shows the vibrating surface when the sand divides it into squares, and fig. 2 represents the same when the nodal lines divide it into triangles. The portions marked a a are in different states of vibration from those marked b b.

NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni’s figures. The white lines are the forms assumed by the sand, from different modes of vibration, corresponding to musical notes of different degrees of pitch. Plate 3 contains six of Chladni’s circular figures.

NOTE 185, p. 145. Mr. Wheatstone’s principle is, that when vibrations producing the forms of figs. 1 and 2, plate 3, are united in the same surface, they make the sand assume the form of fig. 3. In the same manner, the vibrations which would separately cause the sand to take the forms of figs. 4 and 5, would make it assume the form in fig. 6 when united. The figure 9 results from the modes of vibration of 7 and 8 combined. The parts marked a a are in different states of vibration from those marked b b. Figs. 1, 2, and 3, plate 4, represent forms which the sand takes in consequence of simple modes of vibration; 4 and 5 are those arising from two combined modes of vibration; and the last six figures arise from four superimposed simple modes of vibration. These complicated figures are determined by computation independent of experiment.

NOTE 186, p. 146. The long cross-lines of fig. 46 show the two systems of nodal lines given by M. Savart’s laminæ.

NOTE 187, p. 146. The short lines on fig. 46 show the positions of the nodal lines on the other sides of the same laminæ.

NOTE 188, p. 146. Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.

NOTE 189, pp. 138, 153, 156. Reflection and Refraction. Let P C p, fig. 48, be perpendicular to a surface of glass or water A B. When a ray of light, passing through the air, falls on this surface in any direction I C, part of it is reflected in the direction C S, and the other part is bent at C, and passes through the glass or water in the direction C R. I C is called the incident ray, and I C P the angle of incidence; C S is the reflected ray, and P C S the angle of reflection; C R is the refracted ray, and p C R the angle of refraction. The plane passing through S C and I C is the plane of reflection, and the plane passing through I C and C R is the plane of refraction. In ordinary cases, C I, C S, C R, are all in the same plane. We see the surface by means of the reflected light, which would otherwise be invisible. Whatever the reflecting surface may be, and however obliquely the light may fall upon it, the angle of reflection is always equal to the angle of incidence. Thus I C, Iʹ C, being rays incident on the surface at C, they will be reflected into C S, C Sʹ, so that the angle S C P will be equal to the angle I C P, and Sʹ C P equal to Iʹ C P. That is by no means the case with the refracted rays. The incident rays I C, Iʹ C, are bent at C towards the perpendicular, in the direction C R, C Rʹ; and the law of refraction is such, that the sine of the angle of incidence has a constant ratio to the sine of the angle of refraction; that is to say, the number expressing the length of I m, the sine of I C P, divided by the number expressing the length of R n, the sine of R C p, is the same for all the rays of light that can fall upon the surface of any one substance, and is called its index of refraction. Though the index of refraction be the same for any one substance, it is not the same for all substances. For water it is 1·336; for crown-glass it is 1·535; for flint-glass, 1·6; for diamond, 2·487; and for chromate of lead it is 3, which substance has a higher refractive power than any other known. Light falling perpendicularly on a surface passes through it without being refracted. If the light be now supposed to pass from a dense into a rare medium, as from glass or water into air, then R C, Rʹ C, become the incident rays; and in this case the refracted rays, C I, C Iʹ, are bent from the perpendicular instead of towards it. When the incidence is very oblique, as r C, the light never passes into the air at all, but it is totally reflected in the direction C rʹ, so that the angle p C r is equal to p C rʹ; that frequently happens at the second surface of glass. When a ray I C falls from air upon a piece of glass A B, it is in general refracted at each surface. At C it is bent towards the perpendicular, and at R from it, and the ray emerges parallel to I C; but, when the ray is very oblique to the second surface, it is totally reflected. An object seen by total reflection is nearly as vivid as when seen by direct vision, because no part of the light is refracted. When light falls upon a plate of crown-glass, at an angle of 4° 32ʹ counted from the surface, the glass reflects 4 times more light than it transmits. At an angle of 7° 1ʹ the reflected light is double of the transmitted; at an angle of 11° 8ʹ the light reflected is equal to that transmitted; at 17° 17ʹ the reflected is equal to 1/2 the transmitted light; at 26° 38ʹ it is equal to 1/4, the variation, according to Arago, being as the square of the cosine.

NOTE 189, p. 154. Atmospheric refraction. Let a b, a b, &c., fig. 49, be strata, or extremely thin layers, of the atmosphere, which increase in density towards m n, the surface of the earth. A ray coming from a star meeting the surface of the atmosphere at S would be refracted at the surface of each layer, and would consequently move in the curved line S v v v A; and as an object is seen in the direction of the ray that meets the eye, the star, which really is in the direction A S, would seem to a person at A to be in s. So that refraction, which always acts in a vertical direction, raises objects above their true place. For that reason, a body at Sʹ, below the horizon H A O, would be raised, and would be seen in sʹ. The sun is frequently visible by refraction after he is set, or before he is risen. There is no refraction in the zenith at Z. It increases all the way to the horizon, where it is greatest, the variation being proportional to the tangent of the angles Z A S, Z A Sʹ, the distances of the bodies S Sʹ from the zenith. The more obliquely the rays fall, the greater the refraction.

NOTE 190, p. 154. Bradley’s method of ascertaining the amount of refraction. Let Z, fig. 50, be the zenith or point immediately above an observer at A; let H O be his horizon, and P the pole of the equinoctial A Q. Hence P A Q is a right angle. A star as near to the pole as s would appear to revolve about it, in consequence of the rotation of the earth. At noon, for example, it would be at s above the pole, and at midnight it would be in sʹ below it. The sum of the true zenith distances, Z A s, Z A sʹ, is equal to twice the angle Z A P. Again, S and Sʹ being the sun at his greatest distances from the equinoctial A Q when in the solstices, the sum of his true zenith distances, Z A S, Z A Sʹ, is equal to twice the angle Z A Q. Consequently, the four true zenith distances, when added together, are equal to twice the right angle Q A P; that is, they are equal to 180°. But the observed or apparent zenith distances are less than the true on account of refraction; therefore the sum of the four apparent zenith distances is less than 180° by the whole amount of the four refractions.

NOTE 191, p. 155. Terrestrial refraction. Let C, fig. 51, be the centre of the earth, A an observer at its surface, A H his horizon, and B some distant point, as the top of a hill. Let the arc B A be the path of a ray coming from B to A; E B, E A, tangents to its extremities; and A G, B F, perpendicular to C B. However high the hill B may be, it is nothing when compared with C A, the radius of the earth; consequently, A B differs so little from A D that the angles A E B and A C B are supplementary to one another; that is, the two taken together are equal to 180°. A C B is called the horizontal angle. Now B A H is the real height of B, and E A H its apparent height; hence refraction raises the object B, by the angle E A B, above its real place. Again, the real depression of A, when viewed from B, is F B A, whereas its apparent depression is F B E, so E B A is due to refraction. The angle F B A is equal to the sum of the angles B A H and A C B; that is, the true elevation is equal to the true depression and the horizontal angle. But the true elevation is equal to the apparent elevation diminished by the refraction; and the true depression is equal to the apparent depression increased by refraction. Hence twice the refraction is equal to the horizontal angle augmented by the difference between the apparent elevation and the apparent depression.

NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. S P is the real ship, with its inverted and direct images seen in the air. Were there no refraction, the rays would come from the ship S P to the eye E in the direction of the straight lines; but, on account of the variable density of the inferior strata of the atmosphere, the rays are bent in the curved lines P c E, P d E, S m E, S n E. Since an object is seen in the direction of the tangent to that point of the ray which meets the eye, the point P of the real ship is seen at p and pʹ, and the point S seems to be in s and sʹ; and, as all the other points are transferred in the same manner, direct and inverted images of the ship are formed in the air above it.

NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the refraction produced by the hot air surrounding it.

NOTE 194, p. 156. The solar spectrum. A ray from the sun at S, fig. 54, admitted into a dark room, through a small round hole H in a window-shutter, proceeds in a straight line to a screen D, on which it forms a bright circular spot of white light, of nearly the same diameter with the hole H. But when the refracting angle B A C of a glass prism is interposed, so that the sunbeam falls on A C the first surface of the prism, and emerges from the second surface A B at equal angles, it causes the rays to deviate from the straight path S D, and bends them to the screen M N, where they form a coloured image V R of the sun, of the same breadth with the diameter of the hole H, but much longer. The space V R consists of seven colours—violet, indigo, blue, green, yellow, orange, and red. The violet and red, being the most and least refrangible rays, are at the extremities, and the green occupy the middle part at G. The angle D g G is called the mean deviation, and the spreading of the coloured rays over the angle V g R the dispersion. The deviation and dispersion vary with the refracting angle B A C of the prism, and with the substance of which it is made.

NOTE 195, pp. 159, 164. Under the same circumstances, and where the refracting angles of the two prisms are equal, the angles D g G and V g R, fig. 54, are greater for flint-glass than for crown-glass. But, as they vary with the angle of the prism, it is only necessary to augment the refracting angle of the crown-glass prism by a certain quantity, to produce nearly the same deviation and dispersion with the flint-glass prism. Hence, when the two prisms are placed with their refracting angles in opposite directions, as in fig. 54, they nearly neutralize each other’s effects, and refract a beam of light without resolving it into its elementary coloured rays. Sir David Brewster has come to the conclusion that there may be refraction without colour by means of two prisms, or two lenses, when properly adjusted, even though they be made of the same kind of glass.

NOTE 196, p. 165. The object glass of the achromatic telescope consists of a convex lens A B, fig. 55, of crown-glass placed on the outside, towards the object, and of a concave-convex lens C D of flint-glass, placed towards the eye. The focal length of a lens is the distance of its centre from the point in which the rays converge, as F, fig. 60. If, then, the lenses A B and C D be so constructed that their focal lengths are in the same proportion as their dispersive powers, they will refract rays of light without colour.

NOTE 197, p. 165. If the mean refracting angle of the prism D g G, fig. 54, were the same for all substances, then the difference D g V - D g R would be the dispersion. But the angle of the prism being the same, all these angles are different in each substance, so that in order to obtain the dispersion of any substance the angle D g V - D g R must be divided by the angle D g G or its excess above unity, to which the mean refraction is always proportional. According to Mr. Fraunhofer the refraction of the extreme violet and red rays in crown-glass is 1·5466 and 1·5258; so D g V - D g R = 1·5466 - 1·5258 = ·0208, and half the sum of the excess of each above unity is = ·5362; consequently

(D g V - D g R)/D g G = ·0208/·5362 = 0·03879; for diamond

(D g V - D g R)/D g G = (2·467 - 2·411)/1·439 = 0·0389;

so that the dispersive power of diamond is a little less than that of crown-glass; hence the splendid refracted colours which distinguish diamond from every other precious stone are not owing to its high dispersive power, but to its great mean refraction.—SIR DAVID BREWSTER.

NOTE 198, p. 168. When a sunbeam, after having passed through a coloured glass V Vʹ, fig. 56, enters a dark room by two small slits O Oʹ in a card, or piece of tin, they produce alternate bright and black bands on a screen S Sʹ at a little distance. When either one or other of the slits O or Oʹ is stopped, the dark bands vanish, and the screen is illuminated by a uniform light, proving that the dark bands are produced by the interference of the two sets of rays. Again, let H m, fig. 57, be a beam of white light passing through a hole at H, made with a fine needle in a piece of lead or a card, and received on a screen S Sʹ. When a hair, or a small slip of card h hʹ, about the 30th of an inch in breadth, is held in the beam, the rays bend round on each side of it, and, arriving at the screen in different states of vibration, interfere and form a series of coloured fringes on each side of a central white band m. When a piece of card is interposed at C, so as to intercept the light which passes on one side of the hair, the coloured fringes vanish. When homogeneous light is used, the fringes are broadest in red, and become narrower for each colour of the spectrum progressively to the violet, which gives the narrowest and most crowded fringes. These very elegant experiments are due to Dr. Thomas Young.

NOTE 199, pp. 171, 200. Fig. 58 shows Newton’s rings, of which there are seven, formed by screwing two lenses of glass together. Provided the incident light be white, they always succeed each other in the following order:—

1st ring, or 1st order of colours: Black, very faint blue, brilliant white, yellow, orange, red.

2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow green, vivid yellow, crimson red.

3rd ring: Purple, blue, rich grass green, fine yellow, pink, crimson.

4th ring: Dull blueish green, pale yellowish pink, red.

5th ring: Pale blueish green, white, pink.

6th ring: Pale blue green, pale pink.

7th ring: Very pale blueish green, very pale pink.

After the seventh order the colours become too faint to be distinguished. The rings decrease in breadth, and the colours become more crowded together, as they recede from the centre. When the light is homogeneous, the rings are broadest in the red, and decrease in breadth with every successive colour of the spectrum to the violet.

NOTE 200, p. 172. The absolute thickness of the film of air between the glasses is found as follows:—Let A F B C, fig. 59, be the section of a lens lying on a plane surface or plate of glass P Pʹ, seen edgewise, and let E C be the diameter of the sphere of which the lens is a segment. If A B be the diameter of any one of Newton’s rings, and B D parallel to C E, then B D or C F is the thickness of the air producing it. E C is a known quantity; and when A B, the diameter, is measured with compasses, B D or F C can be computed. Newton found that the length of B D, corresponding to the darkest part of the first ring, is the 98,000th part of an inch when the rays fall perpendicularly on the lens, and from this he deduced the thickness corresponding to each colour in the system of rings. By passing each colour of the solar spectrum in succession over the lenses, Newton also determined the thickness of the film of air corresponding to each colour, from the breadth of the rings, which are always of the same colour with the homogeneous light.

NOTE 201, p. 174. The focal length or distance of a lens is the distance from its centre to the point F, fig. 60, in which the refracted rays meet. Let L Lʹ be a lens of very short focal distance fixed in the window-shutter of a dark room. A sunbeam S L Lʹ passing through the lens will be brought to a focus in F, whence it will diverge in lines F C, F D, and will form a circular image of light on the opposite wall. Suppose a sheet of lead, having a small pin-hole pierced through it, to be placed in this beam; when the pin-hole is viewed from behind with a lens at E, it is surrounded with a series of coloured rings, which vary in appearance with the relative positions of the pin-hole and eye with regard to the point F. When the hole is the 30th of an inch in diameter and at the distance of 6-1/2 feet from F, when viewed at the distance of 24 inches, there are seven rings of the following colours:—

1st order: White, pale yellow, yellow, orange, dull red.

2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange red.

3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow green, red.

4th order: Blueish green, blueish white, red.

5th order: Dull green, faint blueish white, faint red.

6th order: Very faint green, very faint red.

7th order: A trace of green and red.

NOTE 202, p. 175. Let L Lʹ, fig. 61, be the section of a lens placed in a window-shutter, through which a very small beam of light S L Lʹ passes into a dark room, and comes to a focus in F. If the edge of a knife K N be held in the beam, the rays bend away from it in hyperbolic curves K r, K rʹ, &c., instead of coming directly to the screen in the straight line K E, which is the boundary of the shadow. As these bending rays arrive at the screen in different states of undulation, they interfere, and form a series of coloured fringes, r rʹ, &c., along the edge of the shadow K E S N of the knife. The fringes vary in breadth with the relative distances of the knife-edge and screen from F.

NOTE 203, p. 177. Fig. 43 represents the phenomena in question, where S S is the surface, and I the centre of incident waves. The reflected waves are the dark lines returning towards I, which are the same as if they had originated in C on the other side of the surface.

NOTE 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline, whose axis is A X. The slices that are used for polarising light are cut parallel to A X.

NOTE 205, p. 181. Double refraction. If a pencil of light R r, fig. 63, falls upon a rhombohedron of Iceland spar A B X C, it is separated into two equal pencils of light at r, which are refracted in the directions r O, r E: when these arrive at O and E they are again refracted, and pass into the air in the directions O o, E o, parallel to one another and to the incident ray R r. The ray r O is refracted according to the ordinary law, which is, that the sines of the angles of incidence and refraction bear a constant ratio to one another (see Note 184), and the rays R r, r O, O o, are all in the same plane. The pencil r E, on the contrary, is bent aside out of that plane, and its refraction does not follow the constant ratio of the sines; r E is therefore called the extraordinary ray, and r O the ordinary ray. In consequence of this bisection of the light, a spot of ink at O is seen double at O and E, when viewed from r I; and when the crystal is turned round, the image E revolves about O, which remains stationary.

NOTE 206, p. 182. Both of the parallel rays O o and E o, fig. 63, are polarised on leaving the doubly refracting crystal, and in both the particles of light make their vibrations at right angles to the lines O o, E o. In the one, however, these vibrations lie, for example, in the plane of the horizon, while the vibrations of the other lie in the vertical plane perpendicular to the horizon.

NOTE 207, p. 183. If light be made to fall in various directions on the natural faces of a crystal of Iceland spar, or on faces cut and polished artificially, one direction A X, fig. 63, will be found, along which the light passes without being separated into two pencils. A X is the optic axis. In some substances there are two optic axes forming an angle with each other. The optic axis is not a fixed line, it only has a fixed direction; for if a crystal of Iceland spar be divided into smaller crystals, each will have its optic axis; but if all these pieces be put together again, their optic axes will be parallel to A X. Every line, therefore, within the crystal parallel to A X is an optic axis; but as these lines have all the same direction, the crystal is still said to have but one optic axis.

NOTE 208, p. 184. If I C, fig. 48, be the incident and C S the reflected rays, then the particles of polarised light make their vibrations at right angles to the plane of the paper.

NOTE 209, p. 184. Let A A, fig. 48, be the surface of the reflector, I C the incident and C S the reflected rays; then, when the angle S C B is 57°, and consequently the angle P C S equal to 33°, the black spot will be seen at C by an eye at S.

NOTE 210, p. 185. Let A B, fig. 48, be a reflecting surface, I C the incident and C S the reflected rays; then, if the surface be plate-glass, the angle S C B must be 57°, in order that C S may be polarised. If the surface be crown-glass or water, the angle S C B must be 56° 55ʹ for the first, and 53° 11ʹ for the second, in order to give a polarised ray.

NOTE 211, p. 186. A polarising apparatus is represented in fig. 64, where R r is a ray of light falling on a piece of glass r at an angle of 57°: the reflected ray r s is then polarised, and may be viewed through a piece of tourmaline in s, or it may be received on another plate of glass, B, whose surface is at right angles to the surface of r. The ray r s is again reflected in s, and comes to the eye in the direction s E. The plate of mica, M I, or of any substance that is to be examined, is placed between the points r and s.

NOTE 212, p. 187. In order to see these figures, the polarised ray r s, fig. 64, must pass through the optic axis of the crystal, which must be held as near as possible to s on one side, and the eye placed as near as possible to s on the other. Fig. 65 shows the image formed by a crystal of Iceland spar which has one optic axis. The colours in the rings are exactly the same with those of Newton’s rings given in Note 199, and the cross is black. If the spar be turned round its axis, the rings suffer no change; but if the tourmaline through which it is viewed, or the plate of glass, B, be turned round, this figure will be seen at the angles 0°, 90°, 180°, and 270° of its revolution. But in the intermediate points, that is, at the angles 45°, 135°, 225°, and 315°, another system will appear, such as represented in fig. 66, where all the colours of the rings are complementary to those of fig. 65, and the cross is white. The two systems of rings, if superposed, would produce white light.

NOTE 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms having two optic axes inclined to one another at an angle of 5°. A slice of this substance about the 6th or 8th of an inch thick, cut perpendicularly to the axis of the prism, and placed very near to s, fig. 64, so that the polarised ray r s may pass through it, exhibits the system of rings represented in fig. 67, where the points C and C mark the position of the optic axes. When the plate B, fig. 64, is turned round, the image changes successively to those given in figs. 68, 69, and 70. The colours of the rings are the same with those of thin plates, but they vary with the thickness of the nitre. Their breadth enlarges or diminishes also with the colour, when homogeneous light is used.

NOTE 214, p. 189. Fig. 71 represents the appearance produced by placing a slice of rock crystal in the polarised ray r s, fig. 64. The uniform colour in the interior of the image depends upon the thickness of the slice; but whatever that colour may be, it will alternately attain a maximum brightness and vanish with the revolution of the glass B. It may be observed, that the two kinds of quartz, or rock crystal, mentioned in the text, are combined in the amethyst, which consists of alternate layers of right-handed and left-handed quartz, whose planes are parallel to the axis of the crystal.

NOTE 215, p. 193. Suppose the major axis A P of an ellipse, fig. 18, to be invariable, but the excentricity C S continually to diminish, the ellipse would bulge more and more; and when C S vanished, it would become a circle whose diameter is A P. Again, if the excentricity were continually to increase, the ellipse would be more and more flattened till C S was equal to C P, when it would become a straight line A P. The circle and straight line are therefore the limits of the ellipse.

NOTE 216, p. 194. The coloured rings are produced by the interference of two polarised rays in different states of undulation, on the principle explained for common light.

NOTE 217, p. 225. According to Mr. Joule, that heat is produced by motion, and that it is equivalent to it, Mr. Thompson of Glasgow investigates from whence the sun derives his heat, since he shows that neither combustion nor his primitive heat could have supplied the waste during 6000 years. He concludes that the solar heat is maintained by myriads of minute bodies that are revolving at the edge of his dense nebulosity or atmosphere, some of which are often seen by us as falling stars. These, vaporized by his heat, and drawn by his attraction, meet with intense resistance on entering the solar atmosphere as a shower of meteoric rain; through it they descend in spiral lines to the sun’s surface, producing enormous heat by friction during their fall, and serving for fuel on their arrival.

NOTE 218, p. 252. The class Cryptogamia contains the ferns, mosses, funguses, and sea-weeds; in all of which the parts of the flowers are in general too minute to be evident.

NOTE 219, p. 254. Zoophytes are the animals which form madrepores, corals, sponges, &c.

NOTE 220, p. 254. The Saurian tribe are creatures of the crocodile and lizard kind.

NOTE 221, p. 266. If heat from a non-luminous source be polarised by reflection or refraction at r, fig. 64, the polarised ray r s will be stopped or transmitted by a plate of mica M I, under the same circumstances that it would stop or transmit light; and if heat were visible, images analogous to those of figs. 65, 67, &c., would be seen at the point s.

NOTE 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force established by Mr. Joule, is the force that would raise one pound weight of matter to the height of one foot; or it is the impetus or force generated by a body of one pound weight falling by its gravitation through the height of one foot.

Impetus, vis viva, or living force, is equal to the mass of a body multiplied by the square of the velocity with which it is moving, and is the true measure of work or labour. For if a weight be raised 10 feet, it will require four times the labour to raise an equal weight 40 feet. If both these weights be allowed to descend freely by their gravitation, at the end of their fall their velocities will be as 1 to 2; that is, as the square roots of their heights; but the effect produced will be as their masses multiplied by 1 and 4; but these are the squares of their velocities: hence the impetus or vis viva is as the mass into the square of the velocity.

Thus impetus is the true measure of the labour employed to raise the weights, and of the effect of their descent, and is entirely independent of time. Now heat is proportional to impetus, and impetus is the true measure of labour. In percussion the heat evolved is in proportion to the force of the impetus, and is thus measured by labour.

Travail is a word used in mechanics, to express that work done is equal to the labouring force employed. The work done may be resistance overcome or any other effect produced, while the labouring force may be a horse, a steam-engine, wind, falling water, &c.

NOTE 223, p. 313. When a stream of positive electricity descends from P to n, fig. 72, in a vertical wire at right angles to the plane of the horizontal circle A B, the negative electricity ascends from n to P, and the force exerted by the current makes the north pole of a magnet revolve about the wire in the direction of the arrow-heads in the circumference, and it makes the south pole revolve in the opposite direction. When the current of positive electricity flows upwards from n to P, these effects are reversed.

NOTE 224, p. 314. Fig. 73 represents a helix or coil of copper wire, terminated by two cups containing a little quicksilver. When the positive wire of a Voltaic battery is immersed in the cup p, and the negative wire in the cup n, the circuit is completed. The quicksilver ensures the connection between the battery and the helix, by conveying the electricity from the one to the other. While the electricity flows through the helix, the magnet S N remains suspended within it, but falls down the moment it ceases. The magnet always turns its south pole S towards P, the positive wire of the battery, and its north pole towards the negative wire.

NOTE 225, p. 316. A copper wire coiled in the form represented in fig. 73 was the first and most simple form of the electro-dynamic cylinder. When its extremities P and n are connected with the positive and negative poles of a Voltaic battery, it becomes a perfect magnet during the time that a current of electricity is flowing through it, P and n being its north and south poles.

NOTE 226, p. 344. It is to Halley we are indebted for the first declination chart and the theory of 4 poles of maximum magnetic intensity, since confirmed by observation, as well as the earliest authentic values of the magnetic elements in London and St. Helena, where he went on purpose to make observations on terrestrial magnetism. Since that time M. Gauss has formed charts of the magnetic lines, and published a theory which very nearly represents the magnetic state of the globe. The mass of observations daily making by our cruizers and our Government surveys in every part of the earth is enormous.

NOTE 227, p. 360. In fig. 74 the hyperbola H P Y, the parabola p P R, and the ellipse A E P L, have the focal distance S P, and coincide through a small space on each side of the perihelion P; and, as a comet is only visible when near P, it is difficult to ascertain which of the three curves it moves in.

NOTE 228, p. 363. In fig. 75, E A represents the orbit of Halley’s comet, E T the orbit of the earth, and S the sun. The proportions are very nearly exact.

NOTE 229, p. 382. Fig. 74 represents the curves in question. It is evident that, for the same focal distance S P, there can be but one circle and one parabola p P R, but that there may be an infinity of ellipses between the circle and the parabola, and an infinity of hyperbolas H P Y exterior to the parabola p P R.

NOTE 230, p. 387. Let A B, fig. 26, be the diameter of the earth’s orbit, and suppose a star to be seen in the direction A Sʹ from the earth when at A. Six months afterwards, the earth, having moved through half of its orbit, would arrive at B, and then the star would appear in the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any sensible magnitude. But A B, which is 190,000,000 of miles, does not appear to be greater than the thickness of a spider’s thread, as seen from 61 Cygni, supposed to be the nearest of the fixed stars.

NOTE 231, p. 389. Stars whose parallax and proper motions are known.

Name of Star. Proper Motion. Parallax. Observers and Computers.

α Centauri 3ʺ·764 0ʺ·92 Maclear. „ .. 1ʺ Henderson. 61 Cygni 5ʺ·123 0ʺ·374 Bessel. α Lyræ 0ʺ·364 0ʺ·207 Peters. Sirius 1ʺ·234 0ʺ·230 Henderson. Arcturus 2ʺ·269 0ʺ·127 Peters. Pole Star 0ʺ·035 0ʺ·106 Peters. Capella .. 0ʺ·046 Peters. La Chevre 0ʺ·461 0ʺ·046 Peters. ι Great Bear 0ʺ·746 0ʺ·133 Peters.

The space run through in one second by these stars is therefore—

α Centauri 5 leagues Henderson and Maclear. 61 Cygni 10 leagues Bessel. α Lyræ 2 leagues Struve and Peters. Sirius 6 leagues Henderson and Maclear. Arcturus 22 leagues Peters. Pole Star ½ league Lindenau and Struve. La Chevre 12 leagues Peters. ι Great Bear 7 leagues Peters.

There are three great discrepancies in the parallax of the star Argelander or 1830 Groombridge. M. Otto Struve makes it 0ʺ·034, which gives it a velocity of 251 leagues per second, while M. Faye finds the parallax to be between 0ʺ·03 and 0ʺ·01, which makes its velocity from 30 to 85 leagues per second.

These are all minimum velocities, because we can only determine on the celestial vault a projection perhaps much foreshortened of the real motions of the stars.

NOTE 232, pp. 398, 401. The following are the binary systems whose orbits have been accurately determined:—

Name of Star. Period in Perihelion By whom Computed. Years. Passage.

ζ Herculis 30·216 1831·41 Madler.

η Coronæ 42·500 1807·21 Madler.

ζ Cancri 58·910 1853·37 Madler.

ξ Ursæ Majoris 58·262 1817·25 Savary.

ω Leonis 82·533 1849·76 Villarceaux.

ρ Ophiuchi 73·862 1806·83 Encke.

3062 in Dorpat 94·765 1837·41 Madler. Catalogue

ξ Bootis 117·140 1779·88 Sir J. Herschel.

δ Cygni 178·700 1862·87 Hind.

γ Virginis 182·120 1836·43 Sir J. Herschel.

Castor 252·660 1855·83 Sir J. Herschel.

ς Coronæ 736·880 1826·48 Hind.

γ Virginis 632·270 1699 Hind.

α Centauri 77·000 1851·50 Jacob.

Orbit of γ Virginis.

Perihelion passage 1836·40

Inclination 27° 36ʹ

Position of ascending Node 19 7

Angle between line of Nodes and 295° 13 Apsides

Excentricity 0·8794

Period in years 184·53

Orbit of ζ Herculis.

Perihelion passage 1830·56 Inclination 140° 39ʹ Position of ascending Node 217° 14ʹ Angle between line of Nodes and Apsides 266·53 Eccentricity 0·4381 Period in years 37·21

Computed by J. Fletcher, Esq., 1853.

NOTE 233, p. 403. The mass is found in the manner explained in the text; but the method of computing the distance of the star may be made more clear by what follows. Though the orbit of the satellite star is really and apparently elliptical, let it be represented by C D O, fig. 14, for the sake of illustration, the earth being in d. It is clear that, when the star moves through C D O, its light will take longer in coming to the earth from O than from C, by the whole time it employs in passing through O C, the breadth of its orbit. When that time is known by observation, reduced to seconds, and multiplied by 190,000, which is the number of miles light darts through in a second, the product will be the breadth of the orbit in miles. From this the dimensions of the ellipse will be obtained by the aid of observation; the length and position of any diameter as S p may be found; and as all the angles of the triangle d S p can be determined by observation, the distance of the star from the earth may be computed.

NOTE 234, p. 405. The mean results of MM. Argelander, Otto Struve, and Luhndahl for stars in the northern hemisphere and the epoch 1790, places the point to which the sun is tending in 259° 5ʹ of right ascension and 55° 23ʹ of north polar distance. Mr. Gallaway computed from stars in the southern hemisphere, at the same epoch, the point to have been in 260° 1ʹ right ascension and 55° 37ʹ north polar distance, results nearly identical, though from very different data.

NOTE 235, p. 414. One of the globular clusters mentioned in the text is represented in fig. 1, plate 8. The stars are gradually condensed towards the centre, where they run together in a blaze. The more condensed part is projected on a ground of irregularly scattered stars, which fills the whole field of the telescope. There are few stars near this cluster.

NOTE 236, p. 420. Plate 8 shows five nebulæ as seen in Sir John Herschel’s 20-feet telescope.

1. An enormous ring seen obliquely with a dark centre and a small star at each extremity.

2. The ring in the constellation Lyra.

3. The dumb-bell nebula in Vulpicula.

4. The spiral nebula or brother system in the 20-feet telescope.

5. A spindle-shaped nebula.

Plate 9 represents some of the same objects as seen by Lord Rosse.

1. Nebula in the girdle of Andromeda.

2. The circular nebula of Lyra.

3. The dumb-bell nebula in Vulpicula.

The spiral nebulæ of 51 Messier, as seen by Lord Rosse, 1 in plate 10, represents fig. 4 of plate 8; and fig. 2 in the same plate is part of the great nebula in Orion, for the whole has never been seen, on account of extreme remoteness.

NOTE 237, pp. 32, 427. The motion of the earth is visibly proved by M. Foucault’s experiments. If a pendulum be left to oscillate quite freely, the forces producing the oscillations being in the vertical plane, there is no cause that can produce an absolute change in its position with regard to space; but the motion of the earth changes the position of a spectator with respect to the vertical plane, and he refers his own motion to it, which seems gradually to turn away from its position, precisely as a person in a boat refers his own motion to that of the land, and thus the motion of the earth is truly and visibly proved.

INDEX.

Aberdeen, high water at, 94.

Absorption, influence of, on temperature, 239; difference of sea and land in power of, 242; gradually decreasing, in transmission of radiant heat, 259; of radiant heat, varying with substances, 268; a transfer of force, 275, 276.

Acceleration of the moon’s mean motion, 37, 38.

Adams, Mr., perturbation in Uranus’s motion computed by, 22; discovery of Neptune, 62.

Aërolites, theory of, 420, 423.

Africa, tidal wave passing, 94; mean annual equatorial temperature in, 245; indigenous productions of, 249, 250.

Air, comparative velocity of light in water and, 202. See Atmosphere.

Airy, Professor, periodic inequality in the solar system worked out by, 26; phenomenon observed by, during an eclipse, 41; mass of Jupiter ascertained by, 55; experiments ascertaining its density, 57; astronomical tables improved by, 63; discoveries in polarization of light, 192, 193.

Aldebaran, an optically double star, 401.

Aleutian Islands, the, vegetation of, 252.

Alexandria, arc of the meridian measured between Syene and, 49.

Algæ, districts of distinct species of, 252; banks of, in the Atlantic, 253.

Algol, fluctuations in lustre of, 390, 391.

Alhazen, effects of refraction observed by, 155.

Alkalies, resolved into metallic oxides, 307.

Alpha Antaris, “Coal Sacks” between α Centauri and, 386.

Alpha Aquilæ, an optically double star, 401.

—— Centauri, the parallax of, 54; its rank, 384; the Milky Way near, 386; parallax, as determined by Henderson and Maclear, 387; distance from the sun, 388; orbit and mass of, 399, 400; colour, 401; amount of light emitted by, 404; rate of its proper motion, 404, 405; globular nebulous cluster, 414.

—— Crucis, zone of stars passing through, 385; zone between η Argûs and, 390; nebulous cluster round, 415.

—— Lyræ, the polar star of the northern hemisphere, 82; parallax of, 388; distance from the sun, 389; an optically double star, 400; amount of light emitted by, 404.

—— Orionis, a variable star, 393, 394.

Alum, experiments on the crystallization of, 106, 107; heat transmitted through, 261, 262.

Amazons, the river of, distance from its mouth where tides are perceptible, 98; area occupied by forests on, 243.

America, course of the tidal wave along its coasts, 93, 94; mean annual equatorial temperature in, 245; separation of isothermal lines in high latitudes, ib.; number of known species of plants indigenous in, 249; number of species of trees, 252; shooting stars over the continent of, 421.

——, South, area of country raised by an earthquake in, 234.

Ampère, M., his discovery in electricity, 316; theory of magnetism, 317, 318; experiment testing his theory, 319, 320.

Analysis, boundless dominion of, 427, 428.

Andes, the, proportion of, to the earth’s mass, 6; increasing rarity of the air experienced in ascending, 118.

Andromeda, nebula in, 413; nebulous region of, 417.

Angström, the electric spark defined by, 303.

Animals, specific diversity of, laws regulating their distribution, 254, 255.

Annual equation, the, of the moon, 35, 36.

—— variations in mean values of the magnetic elements, 343.

Annular nebulæ, 409; in the northern hemisphere, 410, 411.

Antarctic Ocean, tidal wave rising in 93; period of its passage to the Thames, 94; depth of the stratum of constant temperature in, 101; depression of the barometer observed in, 120.

Antilles Islands, hurricanes beginning at, 126.

Antinori, Cav., experiments of, in electricity, 333.

Antinous, comet observed in the constellation of, 372; the Milky Way between Orion and, 386.

Antithesis, the general character of magnetism, 339.

Aphelion of a planet’s path defined, 16.

Apogee, solar, its coincidence with the solstices, 86, 87.

April, 1833, disappearance of Saturn’s rings, 67; apparent and mean time coinciding in, 84.

Apsides of an axis defined, 9; direct, variable motion of, 14; cause of their advance, or recession, 16.

Apures, the mission of the, Humboldt’s observations on sound at, 135.

Aqueous vapour, proportion of, in the atmosphere, 117.

Ara, nebula in, 414.

Arabian Gulf, the, monsoons blowing over, 124.

Arabs, the, their observations on planetary irregularities, 26; lunar eclipses observed by, 38; their division of time, 85; the pendulum used as a measure of time by, 90.

Arago, François, experiment by, in proof of the undulatory theory of light, 200; decisive experiment suggested by, 202; observations in photography, 213; observations on the moon’s atmosphere, 226; increase of temperature below the earth’s surface calculated by, 230; slow communication of temperature from the earth, observed, 244; source of magnetism discovered, 330; theory of his magnetic experiments, 332; divergent flames of a comet described by, 364; his treatise on comets, 368; nature of comet’s light determined by, 380, 381; numbers of comets computed, 381, 382; remark of, on fixed stars, 405.

Arc, the Voltaic, 303-305.

Arcet, M. d’, vibration of fibres of the retina according to, 178.

Archer, Scott, stimulus given to photography by, 207.

Arcs of the meridian, mode of measuring, 47.

Arctic Sea, depth of the zone of constant temperature, 101.

—— regions, vegetation found in, 249.

Arcturus, comet bearing comparison with, 379; rank of, 384.

Areas, described by the radii vectores of planets, a test of disturbing forces, 10; unequable description of, 15.

Argelander, M., period of a comet calculated by, 370; his mode of estimating distance of fixed stars, 389; periods of fluctuation in stars computed by, 390, 391; sun’s motion proved, 405.

Argentine preparations in photography, chemical energy varying with, 207, 208; changes effected by washing with alkalies, 210, 211.

Argo, variable star in, 393.

Aries, season of the sun’s entrance into, in Hipparchus’ age, 80.

Arseniate of soda, its crystals, 109.

Artesian wells, mode of sinking, origin of the name, 230.

Asia, indigenous productions of, 249.

Assyrians, the, division of time by, 85.

Astronomers, fruits of their labours, 3; question still to be resolved by, 24; terrestrial orbit differently measured by, 36.

Astronomical distances, method of measuring, 43; tables, method of forming, 58-64.

Astronomy, its rank in the physical sciences, an important office of, 1; studies necessary to the study of, 2; the key to divers problems in physical science, 3; the two greatest discoveries in, 23; the three departments of, 58; standards for measurement afforded by, 83; application of, to chronology, 87-89; furnishing standards of weights and measures, 89, 90; atmospheric effects connecting the laws of molecular attraction with, 102; progress lately made by, 419, 420.

Atalanta, diameter of, 56.

Atlantic Ocean, direction of tidal waves in, 93; conditions modifying tides, 94; depth of, 96; currents, 100; origin of hurricanes, 126; superficial temperature of, 244; distinct vegetation of the polar basin, 252; beds of algæ in, 253; meteors falling in, 421.

—— telegraph, 325, 326; terrestrial magnetism disturbing, 346.

Atmosphere of nebulous stars, 411, 412.

—— of planets, 226, 227.

—— of the sun, its constitution, 42; indications of an absorptive surrounding the luminous, 213; the true, 224.

—— terrestrial, solar rays bent by, in lunar eclipses, 40; influence of, in solar eclipses, 41; its analysis, pressure on the surface of the globe, 117; form of, gradual decrease in density of its strata, 117, 118; influence of temperature on its density, 119; mean pressure of, variable, 120; the medium conveying sound, 129; sympathetic vibrations transmitted by, 147, 148; its action on light, falsifying vision, 153; phenomena produced by accidental changes in its strata, 155-156; effects of increased density in the stratum in the horizon, 157, 158; lunar heat absorbed by, 227; cause of the cooler air in higher regions of, 240, 241; sun’s heat modified by, 244; action of electricity in, 284; transmission of electricity by induction, 286; periodical variations of electricity in, 291; accidental developments of electricity, 291, 292; cause of variations in its magnetism, 344, 345; nebulous bodies made visible by, 421-423.

Atmospheric air, extreme elasticity of, 105.

—— pressure, effect of, on electricity, 288.

Atomic constitution determining crystalline forms, 109.

Atoms, qualities of, determining the nature of substances, 110; differences in weight of, 111.

Attraction, modes of, in spheres, in the celestial bodies, 4; determining the forms of planets, 6; determining the motions of planets, 7; solar, compelling the elliptical revolutions of planets, 8; mutual, of planets, complicating their motions, 10; interference of, disturbing the motions of heavenly bodies, 11; disturbances from the operation of reciprocal, 13; disturbances from inequality of, 14; of satellites to primaries, little disturbed, 26; disturbing force of, in spheroids, 27; its effects on Jupiter’s satellites, 28; sun’s, of the moon, 34; principle modifying the earth’s, 37; local, affecting the plumb-line, 48; comparative force of the sun’s, 57; of an external body affecting a spheroid, 79; producing tides, 91, 92; of particles of matter, 103; capillary, 113; producing annual atmospheric undulations, 121; the lunar atmosphere affected by, 226; expansive force of heat overcoming, 271; of electricities, 283; destruction of, producing electricity, 284; laws of electrical, 286-288; modes of, in static and in voltaic electricity, 317; action of planetary, on comet’s orbits, 361-363; range of solar, 365.

Aurora, the, affecting the compass, 312.

Australia, evidence of deserts in the interior of, 124; species of plants common to Europe and, 251.

Auvergne, temperature of hot springs in, 231.

Axes, change in form of masses revolving round, 6.

——, major, length of, in orbits, invariable, 20; of the orbits of Jupiter’s satellites, cause of the direct motion observed in, 28; position of, in the solar system, 65; a nutation in planetary, 66; of the moon, 68, 69; mechanical law affecting, 76.

——, optic, of crystals, 183.

Axis, greater, of the earth’s orbit, period of its revolution, 38; period of the earth’s revolution, 58; excess of Jupiter’s equatorial over his polar, 66; of rotation, proof of its being invariable, 76, 77.

——, major, of a planet’s orbit, distance from the sun measured by, 8; designation of its extremities, 9; length of, determining the form of the orbit, 10; periods of its revolutions, 17; length of, not permanently changed, 20; Jupiter’s periodically diminished, Saturn’s increased, 26; of the solar ellipse, period of its revolution, 86.

——, magnecrystallic, 349.

Azores, the, icebergs reaching, 100.

Babbage, Charles, his theory of volcanic action, 235-237; quotation from, on the nature of force, 353.

Babinet, M., his theory of dark lines observed in the solar spectrum, 163; comet’s light computed by, 359.

Babylon, eclipse observed at, 36.

Bacon, Francis, anticipation of discovery by, 32.

Baily, Mr., compression of the terrestrial spheroid calculated by, 50; density of the earth determined, 57; fictitious antiquity ascribed to Indian astronomical observations, 88.

Bali, volcanic eruption in, 233.

Balloon, rarity of the air felt in a, 118; observations made from, 119.

Baltic, the, a tideless sea, 98; decreased atmospheric pressure on the shores of, 120.

Barlow, Mr., observations supporting his theory of electric currents, 346.

Barometer, the, principles of cohesion and attraction applied to the construction of, 113; density of the atmosphere measured by, 117; mean heights of, varying with atmospheric densities, 118; mountain heights measured by, 119, 120; atmospheric phenomena affecting, 120; used to trace the course of atmospheric waves, 121; cause of sudden fall in, before hurricanes, 127; refraction varying with, 154.

Barrow, Cape, observations on magnetic storms at, 345, 346.

Battery, voltaic, construction of, 298, 299; Professor Daniell’s improvements, 299, 300; action of, charged with water, 300; constant flow of electricity obtained by means of, 312.

——, magnetic, constructed by Dr. Faraday, 324, 325; Mr. Henley’s magneto-electric, 325; Atlantic telegraph, 326; structure of, for land telegraphs, 328; relation of heat to power of, 329; thermo-electric, 333.

Batsha, port of, tides neutralised in, 99.

Bayle, comparative density of the atmosphere in interplanetary space according to his law, 356.

Bear, Little, the, the polar star in, 82.

Becquerel, M. E., unexplained photographic phenomenon observed by, 213; phosphorescent property in the solar spectrum discovered, 216; cause of phosphorescence, 217; electricity excited by pressure, 283; light attributed to electricity by, 284; cause of phosphorescence investigated, 296; instrument comparing intensities of electricities invented, 300; crystals formed by agency of electricity, 308; thermo-electric battery constructed by, 333; effect of atmospheric on terrestrial magnetism estimated, 345.

Beehive, the, a nebulous star, 415.

Berard, M., experiments of, in polarizing heat, 264.

Berlin, line of coincidence in temperature passing through, 238.

Berne, increasing temperature of a deserted mine in, 230.

Berre, Dr., photographic pictures perfected by, 205.

Bessel, M., his calculations from measurements of arcs of the meridian, 48; calculation of the sun’s mean apparent diameter, 56; his computation of the mass of Saturn’s ring, 68; diminished obliquity of the ecliptic observed by, 81; parallax calculated, 389; his theory of Sirius’s irregular motions, 392; catalogue of double stars, 396; mass of 61 Cygni found by, 404.

Beta Lyræ, a variable star, 391; nebula between γ Lyræ and, 410.

Benzenberg, M., velocities of falling stars computed by, 423.

Biela, M., date of the discovery of his comet, 367; possibility of collision with the earth, 368; present and prospective planetary influence on, 369; becoming two distinct bodies, 369, 370.

Binary systems of stars, 395-406. See Double stars.

Biot, M., his ascent in a balloon, 118; experiments of, on the transmission of sounds through pipes, 137; liquids possessing the power of circular polarization discovered by, 190; his theory of circular polarization, 191; cause of phosphorescence in the solar spectrum investigated by, 217.

Birds, distribution of distinct species of, 255.

Birt, Mr., atmospheric waves measured by, 121, 122.

Bise, in Switzerland, cause of, 242.

Bismuth, its magnetic and electric properties, 347.

Black Sea, the, scarcely affected by tides, 98.

Bode, Baron, law of, assumed in computing Neptune’s position, 61; failing in the case of Neptune, 63.

Bond, Mr., satellite of Saturn discovered by, 32; elliptical nebula resolved, 413.

Bonnycastle, Captain, phosphorescent phenomenon observed by, 295, 296.

Bonpland, M., identical productions of the Old and New World found by, 251.

Boötes, nebulous system in, 417.

Bore, the, of the Hoogly, its origin, 94.

Botanical districts, distinct, of the globe, 251, 252.

Botto, M., thermo-electricity used in decomposition by, 333.

Bouguer, degrees of the meridian measured by, 48.

Boussingault, M., depth of the underground stratum of constant heat calculated by, 228.

Bouvard, M., atmospheric undulations estimated by, 121.

Bradley, Dr., motion of the pole of the equator discovered by, 84; his tables of refraction, 155.

Brahmins, measurement of time by, 85.

Brand, M., observation of, on meteors, 423.

Brewster, Sir David, his analysis of the solar spectrum, 161; experiments on rayless lines, 163; experiments on spectra of flames, 164; law discovered by, determining angles of polarization for light, 183; experiments on fluorescence of light, 197; line of coincidence in temperature of springs and of the atmosphere determined by, 238; temperature of a pole of maximum cold determined, 245; isogeothermal lines determined by, 246; observations on the light of fixed stars, 402.

Brighton, phenomenon caused by reflection observed from, 157.

Brinkley, Bishop, mass of the moon determined by, 56.

British Channel, height of tides in, 98.

—— Isles, atmospheric wave passing over, 121.

Brorsen, M., periods of comets discovered by, 370.

Brown, Dr. Robert, peculiar vegetation found by, in Australia, 251.

Buchan, Dr., phenomenon caused by reflection observed by, 157.

Cæsar, Julius, era computed from his reign, 85.

Cagniard de la Tour, M., instrument designed by, measuring musical notes, 143.

Calms produced by the trade-winds, 122, 123.

Calorific rays. See Rays of heat.

Calotype, the invention of, 204.

Camelopard, nebulous system in, 417.

Canaries, the, vegetation of, 252.

Canary-glass, fluorescence of light in, 196.

Cancer, the calms of, 123; the tropic of, marking the limit of the trade-winds, 126; nebulous cluster in, 415.

Canis Major, position of, 390.

—— Venatica, nebulous system in, 417.

Capillarity, theory of, 113; forces producing, 114; familiar examples of, 115; curious phenomena, 115, 116.

Capricorn, the calms of, 123; the tropic of, hurricanes changing their direction at, 126.

Carbon, its powers contrasted as a crystal and as an opaque amorphous substance, 302, 303.

Carbonate of lime. See Lime.

Carbonic oxide, its constituent parts, 111.

—— acid, proportion of, in the atmosphere, 117.

Cardinal points, the, position of continental masses with regard to, influencing temperature, 244.

Caribbean Islands, hurricanes beginning at, 126.

Castor, discovered by Sir William Herschel, 396.

Cassiopeia, star appearing and vanishing in, 392, 393.

Categat, the, consequence of its narrowness, 98.

Cauchy, M., data furnished by, for investigation of the theory of light, 201.

Cayenne, variation in length of the pendulum between Paris and, 51.

Celestial bodies: law of their mutual attraction, 4; of the solar system: law determining their attraction to the sun, 5; problem to fix the positions of, on occurrence of disturbance in their motions through counteracting attractions, 11; theory of their mutual connection and dependence, 24; mode of finding the absolute distances of, 43; distances of, computed from their parallax, 52, 54; apparent position of, affected by refraction, 153, 154; apparent infinity of, 420.

Centaur, position of, 390; brilliant double star in, 399.

Central Asia, the mountains of, their ascent by Marco Polo, 118.

Centre of gravity. See Gravity.

Centrifugal force, moon’s motions modified by, 5; influence of, on planet-forms, 6; retarding oscillations of the pendulum, 32; action of, in determining the figure of the earth, 44, 45; measurement of its intensity, 49; resolved into two forces, its action on the sea, 100.

Ceres, astronomical tables of, 63; height of her atmosphere, 226; comet of 1770 revolving beyond the orbit of, 361.

Cetus, nebulous patches crossing, 417.

Chaldeans, the, mean longitude found from observations of, 36; result of comparison of their observations with modern, 38.

Challis, Professor, Brewster’s analysis of light questioned by, 161.

Charcoal, light produced by electricity from, 302-303.

Charles V., the Emperor, observations on comets, made in his reign, 370.

Chaudes Aigues, temperature of, 231.

Chemical action of rays of the solar spectrum, 203, 207; varying maximum of energy, 208; action varying with refrangibility, 209-212; action in luminous spectrum not continuous, 213; energy an independent property of rays, 214; properties of the parathermic rays, 219; action of light maintaining vegetation, 249; affinities the source of the power of steam, 278; of electricity on oxygen, 284; eliciting voltaic electricity, 297, 300; voltaic electricity, an agent in, analysis, 307, 308.

—— combinations, theory of, 110; invariable proportions of, 111; cohesive force inducing, 112; producing combustion, 270.

—— force, the power of, 112.

—— rays, causing the deposition of dew, 269.

Chile, elevation of land by an earthquake in, 234.

China, distinct flora of, 251.

—— Sea, the, monsoons blowing over, 124.

—— ink, polarized light reflected from, 193.

Chinese, the, observations of, on the mean motions of Jupiter and Saturn, 25; proof of their early study of astronomy, 88; decimal divisions used by, 90; elements of comets computed from their observation, 365; comet of 1264 recorded by, 370.

—— Tartary, herbarium collected in, 250, 251.

Chladni, discovery of, in musical science, 145.

Christian era, traces of astronomical records before, 365.

Chromatype, the invention of, 206.

Chronology, dependent on astronomy, 87-89.

Chrysotype, the, coloured photographs obtained from, 206.

Circuit, galvanic, modes of obtaining, 332.

Circular arcs, principle with regard to their sines and cosines, a pledge for the stability of the solar system, 20.

—— motion, ratio of forces procuring, 382.

—— orbits of planets distinguished from elliptical, 8; of satellites, 27.

—— polarization of light, 189-192; of heat, 266.

Circumference of the earth, 49.

Civil time, measure of its periods, 83; not precisely adjusted to solar revolutions, 85.

Clairaut, periodic time of Halley’s comet computed by, 362, 363.

Cleavages of crystals, 109; position of, affecting the intensity of magnetic action, 350.

Climates, planetary, 225, 226; cause of the different terrestrial, 237; phenomena affecting, 239, 240; causes of variety of, 243, 244; milder, of the Polar Ocean, 245, 246; like mean annual temperatures not ensuring like, 246; compensations of irregularities, 247.

Clocks, showing apparent sidereal time, 83; regulated to show decimal time, 84; irregular action of, corrected by the laws of unequal expansion, 272.

Clouds, circling the belt of equatorial calms, 123; region of, 124; electricity evolved from, 291-292.

Cloyne, Bishop of, his calculation of the moon’s mass, 56.

Coal-measures, tropical plants in, 72, 73; age of their formation, 75.

Coal, chemical force evolved from, by combustion, 278; source of its combustible qualities, 279, 280.

“Coal Sacks” in the Milky Way, 386.

Cohesion, influence of, on matter, 105; phenomena arising from its force, 106; attraction of, overcome by the expansive power of heat, 271.

Cohesive force, properties of material molecules constituting, 103; effectual only to unite particles of like nature, 110; inducing chemical combination, 112; capillary attraction, an action of, 113.

Coins, impressions taken from, by contact, 220; by electricity, 221.

Cold, contraction caused by, 271, 272; mitigated by slow propagation of heat in air, 273; generated by voltaic electricity, 302; increasing the conducting power of the air, 345.

Colladon, M., experiments of, testing the velocity of sound, 135.

Collision between the earth and comets, possibilities, possible effects of, 367, 369.

Collodion, sensitiveness of, to light, 203; properties of, as an agent in photography, 207.

Colours, seven primary, 159; theory of the decomposition of white light into, 160; degree of refrangibility not invariable, 161; three primary, ib.; new, discovered by Sir John Herschel, 162; rays refracted without, 164; rarely homogeneous, 165; experiments on accidental and complementary, 165, 166; determined by undulations of ether, experiments, 170-175; of material substances, whence derived, 175; produced by analyzing polarized light, 186-188; varying with refrangibility of rays, 198; obtained in photography, 206; images of the solar spectrum imitating the prismatic, 208-209; of seaweeds, 253; not invariably dependent on light, ib.; affected by absorption and reflection, 268; of the electric spark, affected by the atmosphere, 289; of the voltaic spectrum, 303; of the electric spark, 304; produced by oxidation on silver, 305; of the fixed stars, 401, 402; of planetary nebulæ, 412; of nebulous clusters, 415.

Columbus, beds of algæ found by, 253.

Column, capillary, forces producing changes in its form, 114, 115.

Coma Berenices, a nebulous cluster, 415; nebulous zone passing, 416, 417.

Combustion, cause of, 270; defined, 304.

Comets, attraction by the sun of, 5; disturbances in the motion of, a key to the nature of the ethereal medium, 22; retrograde motion in, 33; passing through Jupiter’s satellites, 69; return of, to their perihelia, furnishing historical data, 88; existence of the luminous ether demonstrated by, 168, 169; terrestrial atmosphere unaffected by, 358; amount of their light computed, 358, 359; passages of, through the solar system, 359; velocity, paths of, 359, 360; proof of the return of, 360; disturbing action of planets on their orbits, 361; of 1770, an example, 361, 362; computed return of Halley’s, 362, 363; aspects, records of Halley’s, 363-365; discoveries made by the revolutions of, 365; of the solar system, Encke’s, 365, 366; Biela’s, possibility of collision with, 367, 370; periods of various, 370; cause of their brilliancy, 371; velocity, sun’s influence on, 371, 372; of 1843, 372, 373; their constitution, 373, 374; of 1811, its luminous envelopes, 374, 375; sudden convulsions in, 375; tails, 375-377; causes assigned for contraction of diameter in, 377, 378; Donati’s, 378, 379; nature of their light, 379-381; computations of their numbers, 381, 382; orbits of, 383; nebula resembling, 413.

Compass, mariner’s, phenomena disturbing, 312; intensity of a galvanic current measured by, 315.

Compression of the terrestrial spheroid, calculations of, 48-51; cause of the great, in Jupiter, 66; measures of, from pressure of superincumbent mass, 78; effect of, on magnetic action, 351.

Concord, a, in music, 142.

Conductors of electricity, 284, 285; lightning, 293; molecular structure determining the power of, 303.

Conic sections, conditions compelling bodies in space to move in, 5; principle determining their nature, 11.

Constellations, nearest the sun, 390; where the orbit of the solar system lies, 406; occupied by the nebulous system, 417.

Contraction caused by cold, 271, 272.

Cook, Captain, object of his first voyage, 53.

Cooper, Mr., list of missing stars drawn up by, 395.

Copper, electricity communicated to plates of, 220; lightning-conductors of, 293; action of an electro-magnet on, 351, 352.

Cordier, temperature of mines observed by, 228.

Cordilleras, effect on temperature of their table-lands, 241.

Corn, a, field used to illustrate the propagation of sound, 129, 130.

Cornwall, hot-springs in mines of, 229.

Corona Australis, nebula in, 414.

Corpuscular theory of light, 167; phenomena disproving, 171, 175, 176.

Coseguina, volcanic irruption of, 233.

Coulomb, instrument measuring electrical intensity, invented by, 287.

Creation, vastness and magnificence of, 2.

Crimea, cause of the great storm in the, 122.

Cross, Mr., voltaic battery with constant action invented by, 300.

Cross, the Southern, vacant patches of the Milky Way near, 386.

Crystallization defined, 106; forms of, their variety affected by temperature, 107, 108; permanent and variable forms, 108, 109; cleavages in, 109; common to all substances, ib.; by the agency of electricity, 308, 309.

Crystals, conditions determining their forms, 107-109; optic axes of, 183; used in polarizing light, 186, 188; changes in, effected by compression, 189; transmission of rays of heat by, 258; expansion of, by heat, 272, 273; formed by electricity, 308; action of magnetism in, 349, 350; circumstances determining the set of, 350, 351; effect of temperature on magnetized, 352.

Cumming, Professor, experiments of, in thermo-electricity, 333.

Currents, two great, setting from each pole towards the equator, 100; proving the rotation of winds, 124, 125.

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