Chapter V…

Chapter V

TEMPERATURE OF THE SUN

Newton was the first who attempted to measure the quantity of heat received by the earth from the sun. His object in making the experiment was to ascertain the temperature encountered by the comet of 1680 at its passage through perihelion. He found it, by multiplying the observed heating effects of direct sunshine according to the familiar rule of the "inverse squares of the distances," to be about 2,000 times that of red-hot iron.[698]

Determinations of the sun's thermal power, made with some scientific exactness, date, however, from 1837. A few days previous to the beginning of that year, Herschel began observing at the Cape of Good Hope with an "actinometer," and obtained results agreeing quite satisfactorily with those derived by Pouillet from experiments made in France some months later with a "pyrheliometer."[699] Pouillet found that the vertical rays of the sun falling on each square centimetre of the earth's surface are competent (apart from atmospheric absorption) to raise the temperature of 1.7633 grammes of water one degree Centigrade per minute. This number (1.7633) he called the "solar constant"; and the unit of heat chosen is known as the "calorie." Hence it was computed that the total amount of solar heat received during a year would suffice to melt a layer of ice covering the entire earth to a depth of 30.89 metres, or 100 feet; while the heat emitted would melt, at the sun's surface, a stratum 11.80 metres thick each minute. A careful series of observations showed that nearly half the heat incident upon our atmosphere is stopped in its passage through it.

Herschel got somewhat larger figures, though he assigned only a third as the spoil of the air. Taking a mean between his own and Pouillet's, he calculated that the ordinary expenditure of the sun per minute would have power to melt a cylinder of ice 184 feet in diameter, reaching from his surface to that of Alpha Centauri; or, putting it otherwise, that an ice-rod 45.3 miles across, continually darted into the sun with the velocity of light, would scarcely consume, in dissolving, the thermal supplies now poured abroad into space.[700] It is nearly certain that this estimate should be increased by about two-thirds in order to bring it up to the truth.

Nothing would, at first sight, appear simpler than to pass from a knowledge of solar emission--a strictly measurable quantity--to a knowledge of the solar temperature; this being defined as the temperature to which a surface thickly coated with lamp-black (that is, of standard radiating power) should be raised to enable it to send us, from the sun's distance, the amount of heat actually received from the sun. Sir John Herschel showed that heat-rays at the sun's surface must be 92,000 times as dense as when they reach the earth; but it by no means follows that either the surface emitting, or a body absorbing those heat-rays must be 92,000 times hotter than a body exposed here to the full power of the sun. The reason is, that the rate of emission--consequently the rate of absorption, which is its correlative--increases very much faster than the temperature. In other words, a body radiates or cools at a continually accelerated pace as it becomes more and more intensely heated above its surroundings.

Newton, however, took it for granted that radiation and temperature advance pari passu--that you have only to ascertain the quantity of heat received from, and the distance of a remote body in order to know how hot it is.[701] And the validity of this principle, known as "Newton's Law" of cooling, was never questioned until De la Roche pointed out, in 1812,[702] that it was approximately true only over a low range of temperature; while five years later, Dulong and Petit generalised experimental results into the rule, that while temperature grows by arithmetical, radiation increases by geometrical progression.[703] Adopting this formula, Pouillet derived from his observations on solar heat a solar temperature of somewhere between 1,461 deg. and 1,761 deg. C. Now, the higher of these points--which is nearly that of melting platinum--is undoubtedly surpassed at the focus of certain burning-glasses which have been constructed of such power as virtually to bring objects placed there within a quarter of a million of miles of the photosphere. In the rays thus concentrated, platinum and diamond become rapidly vaporised, notwithstanding the great loss of heat by absorption, first in passing through the air, and again in traversing the lens. Pouillet's maximum is then manifestly too low, since it involves the absurdity of supposing a radiating mass capable of heating a distant body more than it is itself heated.

Less demonstrably, but scarcely less surely, Mr. J. J. Waterston, who attacked the problem in 1860, erred in the opposite direction. Working up, on Newton's principle, data collected by himself in India and at Edinburgh, he got for the "potential temperature" of the sun 12,880,000 deg. Fahr.,[704] equivalent to 7,156,000 deg. C. The phrase potential temperature (for which Violle substituted, in 1876, effective temperature) was designed to express the accumulation in a single surface, postulated for the sake of simplicity, of the radiations not improbably received from a multitude of separate solar layers reinforcing each other; and might thus (it was explained) be considerably higher than the actual temperature of any one stratum.

At Rome, in 1861, Father Secchi repeated Waterston's experiments, and reaffirmed his conclusion;[705] while Soret's observations, made on the summit of Mont Blanc in 1867,[706] furnished him with materials for a fresh and even higher estimate of ten million degrees Centigrade.[707] Yet from the very same data, substituting Dulong and Petit's for Newton's law, Vicaire deduced in 1872 a provisional solar temperature of 1,398 deg.[708] This is below that at which iron melts, and we know that iron-vapour exists high up in the sun's atmosphere. The matter was taken into consideration on the other side of the Atlantic by Ericsson in 1871. He attempted to re-establish the shaken credit of Newton's principle, and arrived, by its means, at a temperature of 4,000,000 deg. Fahrenheit.[709] Subsequently, an "underrated computation," based upon observation of the quantity of heat received by his "sun motor," gave him 3,000,000 deg. And the result, as he insisted, followed inevitably from the principle that the temperature produced by radiant heat is proportional to its density, or inversely as its diffusion.[710] The principle, however, is demonstrably unsound.

In 1876 the sun's temperature was proposed as the subject of a prize by the Paris Academy of Sciences; but although the essay of M. Jules Violle was crowned, the problem was declared to remain unsolved. Violle (who adhered to Dulong and Petit's formula) arrived at an effective temperature of 1,500 deg. C., but considered that it might actually reach 2,500 deg. C., if the emissive power of the photospheric clouds fell far short (as seemed probable) of the lamp-black standard.[711] Experiments made in April and May, 1881, giving a somewhat higher result, he raised this figure to 3,000 deg. C.[712]

Appraisements so outrageously discordant as those of Waterston, Secchi, and Ericsson on the one hand, and those of the French savants on the other, served only to show that all were based upon a vicious principle. Professor F. Rosetti,[713] accordingly, of the Paduan University, at last perceived the necessity for getting out of the groove of "laws" plainly in contradiction with facts. The temperature, for instance, of the oxy-hydrogen flame was fixed by Bunsen at 2,800 deg. C.--an estimate certainly not very far from the truth. But if the two systems of measurement applied to the sun be used to determine the heat of a solid body rendered incandescent in this flame, it comes out, by Newton's mode of calculation, 45,000 deg. C.; by Dulong and Petit's, 870 deg. C.[714] Both, then, are justly discarded, the first as convicted of exaggeration, the second of undervaluation. The formula substituted by Rosetti in 1878 was tested successfully up to 2,000 deg. C.; but since, like its predecessors, it was a purely empirical rule, guaranteed by no principle, and hence not to be trusted out of sight, it was, like them, liable to break down at still higher elevations. Radiation by this new prescription increases as the square of the absolute temperature--that is, of the number of degrees counted from the "absolute zero" of -273 deg. C. Its employment gave for the sun's radiating surface an effective temperature of 20,380 deg. C. (including a supposed loss of one-half in the solar atmosphere); and setting a probable deficiency in emission (as compared with lamp-black) against a probable mutual reinforcement of superposed strata, Professor Rosetti considered "effective" as nearly equivalent to "actual" temperature. A "law of cooling," proposed by M. Stefan at Vienna in 1879,[715] was shown by Boltzmann, many years later, to have a certain theoretical validity.[716] It is that emission grows as the fourth power of absolute temperature. Hence the temperature of the photosphere would be proportional to the square root of the square root of its heating effects at a distance, and appeared, by Stefan's calculations from Violle's measures of solar radiative intensity, to be just 6,000 deg. C.; while M. H. Le Chatelier[717] derived 7,600 deg. from a formula, conveying an intricate and unaccountable relation between the temperature of an incandescent body and the intensity of its red radiations.

From a series of experiments carefully conducted at Daramona, Ireland, with a delicate thermal balance, of the kind invented by Boys and designated a "radio-micrometer," Messrs. Wilson and Gray arrived in 1893, with the aid of Stefan's Law, at a photospheric temperature of 7,400 deg. C.,[718] reduced by the first-named investigator in 1901 to 6,590 deg.[719] Dr. Paschen, of Hanover, on the other hand, ascribed to the sun a temperature of 5,000 deg. from comparisons between solar radiative intensity and that of glowing platinum;[720] while F. W. Very showed in 1895[721] that a minimum value of 20,000 deg. C. for the same datum resulted from Paschen's formula connecting temperature with the position of maximum spectral energy.

A new line of inquiry was struck out by Zoellner in 1870. Instead of tracking the solar radiations backward with the dubious guide of empirical formulae, he investigated their intensity at their source. He showed[722] that, taking prominences to be simple effects of the escape of powerfully compressed gases, it was possible, from the known mechanical laws of heat and gaseous constitution, to deduce minimum values for the temperatures prevailing in the area of their development. These came out 27,700 deg. C. for the strata lying immediately above, and 68,400 deg. C. for the strata lying immediately below the photosphere, the former being regarded as the region into which, and the latter as the region from which the eruptions took place. In this calculation, no prominences exceeding 40,000 miles (1.5') in height were included. But in 1884, G. A. Hirn of Colmar, having regard to the enormous velocities of projection observed in the interim, fixed two million degrees Centigrade as the lowest internal temperature by which they could be accounted for; although admitting the photospheric condensations to be incompatible with a higher external temperature than 50,000 deg. to 100,000 deg. C.[723]

This method of going straight to the sun itself, observing what goes on there, and inferring conditions, has much to recommend it; but its profitable use demands knowledge we are still very far from possessing. We are quite ignorant, for instance, of the actual circumstances attending the birth of the solar flames. The assumption that they are nothing but phenomena of elasticity is a purely gratuitous one. Spectroscopic indications, again, give hope of eventually affording a fixed point of comparison with terrestrial heat sources; but their interpretation is still beset with uncertainties; nor can, indeed, the expression of transcendental temperatures in degrees of impossible thermometers be, at the best, other than a futile attempt to convey notions respecting a state of things altogether outside the range of our experience.

A more tangible, as well as a less disputable proof of solar radiative intensity than any mere estimates of temperature, was provided in some experiments made by Professor Langley in 1878.[724] Using means of unquestioned validity, he found the sun's disc to radiate 87 times as much heat, and 5,300 times as much light as an equal area of metal in a Bessemer converter after the air-blast had continued about twenty minutes. The brilliancy of the incandescent steel, nevertheless, was so blinding, that melted iron, flowing in a dazzling white-hot stream into the crucible, showed "deep brown by comparison, presenting a contrast like that of dark coffee poured into a white cup." Its temperature was estimated (not quite securely)[725] at about 2,000 deg. C.; and no allowances were made, in computing relative intensities, for atmospheric ravages on sunlight, for the extra impediments to its passage presented by the smoke-laden air of Pittsburgh, or for the obliquity of its incidence. Thus, a very large balance of advantage lay on the side of the metal.

A further element of uncertainty in estimating the intrinsic strength of the sun's rays has still to be considered. From the time that his disc first began to be studied with the telescope, it was perceived to be less brilliant near the edges. Lucas Valerius, of the Lyncean Academy, seems to have been the first to note this fact, which, strangely enough, was denied by Galileo in a letter to Prince Cesi of January 25, 1613.[726] Father Scheiner, however, fully admitted it, and devoted some columns of his bulky tome to the attempt to find its appropriate explanation.[727] In 1729 Bouguer measured, with much accuracy, the amount of this darkening; and from his data, Laplace, adopting a principle of emission now known to be erroneous, concluded that the sun loses eleven-twelfths of his light through absorption in his own atmosphere.[728] The real existence of this atmosphere, which is totally distinct from the beds of ignited vapours producing the Fraunhofer lines, is not open to doubt, although its nature is still a matter of conjecture. The separate effects of its action on luminous, thermal, and chemical rays were carefully studied by Father Secchi, who in 1870[729] inferred the total absorption to be 88/100 of all radiations taken together, and added the important observation that the light from the limb is no longer white, but reddish-brown. Absorptive effects were thus seen to be unequally distributed; and they could evidently be studied to advantage only by taking the various rays of the spectrum separately, and finding out how much each had suffered in transmission.

This was done by H. C. Vogel in 1877.[730] Using a polarising photometer, he found that only 13 per cent. of the violet rays escape at the edge of the solar disc, 16 of the blue and green, 25 of the yellow, and 30 per cent. of the red. Midway between centre and limb, 88.7 of violet light and 96.7 of red penetrate the absorbing envelope, the abolition of which would increase the intensity of the sun's visible spectrum above two and a half times in the most, and once and a half times in the least refrangible parts. The nucleus of a small spot was ascertained to be of the same luminous intensity as a portion of the unbroken surface about two and a half minutes from the limb. These experiments having been made during a spot-minimum when there is reason to think that absorption is below its average strength, Vogel suggested their repetition at a time of greater activity. They were extended to the heat-rays by Edwin B. Frost. Detailed inquiries made at Potsdam in 1892[731] went to show that, were the sun's atmosphere removed, his thermal power, as regards ourselves, would be increased 1.7 times. They established, too, the practical uniformity in radiation of all parts of his disc. A confirmatory result was obtained about the same time by Wilson and Rambaut, who found that the unveiled sun would be once and a half times hotter than the actual sun.[732]

Professor Langley, now of Washington, gave to measures of the kind a refinement previously undreamt of. Reliable determinations of the "energy" of the individual spectral rays were, for the first time, rendered possible by his invention of the "bolometer" in 1880.[733] This exquisitely sensitive instrument affords the means of measuring heat, not directly, like the thermopile, but in its effects upon the conduction of electricity. It represents, in the phrase of the inventor, the finger laid upon the throttle-valve of a steam-engine. A minute force becomes the modulator of a much greater force, and thus from imperceptible becomes conspicuous. By locally raising the temperature of an inconceivably fine strip of platinum serving as the conducting-wire in a circuit, the flow of electricity is impeded at that point, and the included galvanometer records a disturbance of the electrical flow. Amounts of heat were thus detected in less than ten seconds, which, expended during a thousand years on the melting of a kilogramme of ice, would leave a part of the work still undone; and further improvements rendered this marvellous instrument capable of thrilling to changes of temperature falling short of one ten-millionth of a degree Centigrade.[734]

The heat contained in the diffraction spectrum is, with equal dispersions, barely one-tenth of that in the prismatic spectrum. It had, accordingly, never previously been found possible to measure it in detail--that is, ray by ray. But it is only from the diffraction, or normal spectrum that any true idea can be gained as to the real distribution of energy among the various constituents, visible and invisible, of a sunbeam. The effect of passage through a prism is to crowd together the red rays very much more than the blue. To this prismatic distortion was owing the establishment of a pseudo-maximum of heat in the infra-red, which disappeared when the natural arrangement by wave-length was allowed free play. Langley's bolometer has shown that the hottest part of the normal spectrum virtually coincides with its most luminous part, both lying in the orange, close to the D-line.[735] Thus the last shred of evidence in favour of the threefold division of solar radiations vanished, and it became obvious that the varying effects--thermal, luminous, or chemical--produced by them are due, not to any distinction of quality in themselves, but to the different properties of the substances they impinge upon. They are simply bearers of energy, conveyed in shorter or longer vibrations; the result in each separate case depending upon the capacity of the material particles meeting them for taking up those shorter or longer vibrations, and turning them variously to account in their inner economy.

A long series of experiments at Allegheny was completed in the summer of 1881 on the crest of Mount Whitney in the Sierra Nevada. Here, at an elevation of 14,887 feet, in the driest and purest air, perhaps, in the world, atmospheric absorptive inroads become less sensible, and the indications of the bolometer, consequently, surer and stronger. An enormous expansion was at once given to the invisible region in the solar spectrum below the red. Captain Abney had got chemical effects from undulations twelve ten-thousandths of a millimetre in length. These were the longest recognised as, or indeed believed, on theoretical grounds, to be capable of existing. Professor Langley now got heating effects from rays of above twice that wave-length, his delicate thread of platinum groping its way down nearly to thirty ten-thousandths of a millimetre, or three "microns." The known extent of the solar spectrum was thus at once more than doubled. Its visible portion covers a range of about one octave; bolometric indications already in 1884 comprised between three and four. The great importance of the newly explored region appears from the fact that three-fourths of the entire energy of sunlight reside in the infra-red, while scarcely more than one-hundredth part of that amount is found in the better known ultra-violet space.[736] These curious facts were reinforced, in 1886,[737] by further particulars learned with the help of rock-salt lenses and prisms, glass being impervious to very slow, as to very rapid vibrations. Traces were thus detected of solar heat distributed into bands of transmission alternating with bands of atmospheric absorption, far beyond the measurable limit of 5.3 microns.

In 1894, Langley described at the Oxford Meeting of the British Association[738] his new "bolographic" researches, in which the sensitive plate was substituted for the eye in recording deflections of the galvanometer responding to variations of invisible heat. Finally, in 1901,[739] he embodied in a splendid map of the infra-red spectrum 740 absorption-lines of determinate wave-lengths, ranging from 0.76 to 5.3 microns. Their chemical origin, indeed, remains almost entirely unknown, no extensive investigations having yet been undertaken of the slower vibrations distinctive of particular substances; but there is evidence that seven of the nine great bands crossing the "new spectrum" (as Langley calls it)[740] are telluric, and subject to seasonal change. Here, then, he thought, might eventually be found a sure standing-ground for vitally important previsions of famines, droughts, and bonanza-crops.

Atmospheric absorption had never before been studied with such precision as it was by Langley on Mount Whitney. Aided by simultaneous observations from Lone Pine, at the foot of the Sierra, he was able to calculate the intensity belonging to each ray before entering the earth's gaseous envelope--in other words, to construct an extra-atmospheric curve of energy in the spectrum. The result showed that the blue end suffered far more than the red, absorption varying inversely as wave-length. This property of stopping predominantly the quicker vibrations is shared, as both Vogel and Langley[741] have conclusively shown, by the solar atmosphere. The effect of this double absorption is as if two plates of reddish glass were interposed between us and the sun, the withdrawal of which would leave his orb, not only three or four times more brilliant, but in colour distinctly greenish-blue.[742]

The fact of the uncovered sun being blue has an important bearing upon the question of his temperature, to afford a somewhat more secure answer to which was the ultimate object of Professor Langley's persevering researches; for it is well known that as bodies grow hotter, the proportionate representation in their spectra of the more refrangible rays becomes greater. The lowest stage of incandescence is the familiar one of red heat. As it gains intensity, the quicker vibrations come in, and an optical balance of sensation is established at white heat. The final term of blue heat, as we now know, is attained by the photosphere. On this ground alone, then, of the large original preponderance of blue light, we must raise our estimate of solar heat; and actual measurements show the same upward tendency. Until quite lately, Pouillet's figure of 1.7 calories per minute per square centimetre of terrestrial surface, was the received value for the "solar constant." Forbes had, it is true, got 2.85 from observations on the Faulhorn in 1842;[743] but they failed to obtain the confidence they merited. Pouillet's result was not definitely superseded until Violle, from actinometrical measures at the summit and base of Mont Blanc in 1875, computed the intensity of solar radiation at 2.54,[744] and Crova, about the same time, at Montpellier, showed it to be above two calories.[745] Langley went higher still. Working out the results of the Mount Whitney expedition, he was led to conclude atmospheric absorption to be fully twice as effective as had hitherto been supposed. Scarcely 60 per cent., in fact, of those solar radiations which strike perpendicularly through a seemingly translucent sky, were estimated to attain the sea-level. The rest are reflected, dispersed, or absorbed. This discovery involved a large addition to the original supply so mercilessly cut down in transmission, and the solar constant rose at once to three calories. Nor did the rise stop there. M. Savelieff deduced for it a value of 3.47 from actinometrical observations made at Kieff in 1890;[746] and Knut Angstrom, taking account of the arrestive power of carbonic acid, inferred enormous atmospheric absorption, and a solar constant of four calories.[747] In other words, the sun's heat reaching the outskirts of our atmosphere is capable of doing without cessation the work of an engine of four-horse power for each square yard of the earth's surface. Thus, modern inquiries tend to render more and more evident the vastness of the thermal stores contained in the great central reservoir of our system, while bringing into fair agreement the estimates of its probable temperature. This is in great measure due to the acquisition of a workable formula by which to connect temperature with radiation. Stefan's rule of a fourth-power relation, if not actually a law of nature, is a colourable imitation of one; and its employment has afforded a practical certainty that the sun's temperature, so far as it is definable, neither exceeds 12,000 deg. C., nor falls short of 6,500 deg. C.

FOOTNOTES:

[Footnote 698: Principia, p. 498 (1st ed.).]

[Footnote 699: Comptes Rendus, t. vii., p. 24.]

[Footnote 700: Results of Astr. Observations, p. 446.]

[Footnote 701: "Est enim calor solis ut radiorum densitas, hoc est, reciproce ut quadratum distantiae locorum a sole."--Principia, p. 508 (3d ed., 1726).]

[Footnote 702: Jour. de Physique, t. lxxv., p. 215.]

[Footnote 703: Ann. de Chimie, t. vii., 1817, p. 365.]

[Footnote 704: Phil. Mag., vol. xxiii. (4th ser.), p. 505.]

[Footnote 705: Nuovo Cimento, t. xvi., p. 294.]

[Footnote 706: Comptes Rendus, t. lxv., p. 526.]

[Footnote 707: The direct result of 5-1/3 million degrees was doubled in allowance for absorption in the sun's own atmosphere. Comptes Rendus, t. lxxiv., p. 26.]

[Footnote 708: Ibid., p. 31.]

[Footnote 709: Nature, vols. iv., p. 204; v., p. 505.]

[Footnote 710: Ibid., vol. xxx., p. 467.]

[Footnote 711: Ann. de Chim., t. x. (5th ser.), p. 361.]

[Footnote 712: Comptes Rendus, t. xcvi., p. 254.]

[Footnote 713: Phil. Mag., vol. viii., p. 324, 1879.]

[Footnote 714: Ibid., p. 325.]

[Footnote 715: Sitzungsberichte, Wien, Bd. lxxix., ii., p. 391.]

[Footnote 716: Wiedemann's Annalen, Bd. xxii., p. 291; Scheiner, Strahlung und Temperatur der Sonne, p. 27.]

[Footnote 717: Comptes Rendus, March 28, 1892; _Astr. and Astrophysics_, vol. xi., p. 517.]

[Footnote 718: Phil. Trans., vol. clxxxv., p. 361.]

[Footnote 719: Proc. Roy. Society, December 12, 1901.]

[Footnote 720: Scheiner, Temp. der Sonne, p. 36.]

[Footnote 721: Astroph. Jour., vol. ii., p. 318.]

[Footnote 722: Astr. Nach., Nos. 1,815-16.]

[Footnote 723: L'Astronomie, September, 1884, p. 334.]

[Footnote 724: Amer. Jour. of Science, vol. i. (3rd ser.), p. 653.]

[Footnote 725: Young, The Sun, p. 310.]

[Footnote 726: Op., t. vi., p. 198.]

[Footnote 727: Rosa Ursina, lib. iv., p. 618.]

[Footnote 728: Mec. Cel., liv. x., p. 323.]

[Footnote 729: Le Soleil (1st ed.), p. 136.]

[Footnote 730: Monatsber., Berlin, 1877, p. 104.]

[Footnote 731: Astr. Nach., Nos. 3,105-6; Astr. and Astrophysics, vol. xi., p. 720.]

[Footnote 732: Proc. Roy. Irish Acad., vol. ii., No. 2, 1892.]

[Footnote 733: Am. Jour. of Sc., vol. xxi., p. 187.]

[Footnote 734: Amer. Jour. of Science, vol. v., p. 245, 1898.]

[Footnote 735: For J. W. Draper's partial anticipation of this result, see Ibid. vol. iv., 1872, p. 174.]

[Footnote 736: Phil. Mag., vol. xiv., p. 179, 1883.]

[Footnote 737: "The Solar and the Lunar Spectrum," _Memoirs National Acad. of Science_, vol. xxxii.; "On hitherto Unrecognised Wave-lengths," Amer. Jour. of Science, vol. xxxii., August, 1886.]

[Footnote 738: Astroph. Jour., vol. i., p. 162.]

[Footnote 739: Annals of the Smithsonian Astroph. Observatory, vol. i.; Comptes Rendus, t. cxxxi., p. 734; Astroph. Jour., vol. iii., p. 63.]

[Footnote 740: Phil. Mag., July, 1901.]

[Footnote 741: Comptes Rendus, t. xcii., p. 701.]

[Footnote 742: Nature, vol. xxvi., p. 589.]

[Footnote 743: Phil. Trans., vol. cxxxii., p. 273.]

[Footnote 744: Ann. de Chim., t. x., p. 321.]

[Footnote 745: Ibid., t. xi., p. 505.]

[Footnote 746: Comptes Rendus, t. cxii., p. 1200.]

[Footnote 747: Wied. Ann., Bd. xxxix., p. 294; Scheiner, Temperatur der Sonne, pp. 36, 38.]

Chapter VI

THE SUN'S DISTANCE

The question of the sun's distance arises naturally from the consideration of his temperature, since the intensity of the radiations emitted as compared with those received and measured, depends upon it. But the knowledge of that distance has a value quite apart from its connection with solar physics. The semi-diameter of the earth's orbit is our standard measure for the universe. It is the great fundamental datum of astronomy--the unit of space, any error in the estimation of which is multiplied and repeated in a thousand different ways, both in the planetary and sidereal systems. Hence its determination was called by Airy "the noblest problem in astronomy." It is also one of the most difficult. The quantities dealt with are so minute that their sure grasp tasks all the resources of modern science. An observational inaccuracy which would set the moon nearer to, or farther from us than she really is by one hundred miles, would vitiate an estimate of the sun's distance to the extent of sixteen million![748] What is needed in order to attain knowledge of the desired exactness is no less than this: to measure an angle about equal to that subtended by a halfpenny 2,000 feet from the eye, within a little more than a thousandth part of its value.

The angle thus represented is what is called the "horizontal parallax" of the sun. By this amount--the breadth of a halfpenny at 2,000 feet--he is, to a spectator on the rotating earth, removed at rising and setting from his meridian place in the heavens. Such, in other terms, would be the magnitude of the terrestrial radius as viewed from the sun. If we knew this magnitude with certainty and precision, we should also know with certainty and precision--the dimensions of the earth being, as they are, well ascertained--the distance of the sun. In fact, the one quantity commonly stands for the other in works treating professedly of astronomy. But this angle of parallax or apparent displacement cannot be directly measured--cannot even be perceived with the finest instruments. Not from its smallness. The parallactic shift of the nearest of the stars as seen from opposite sides of the earth's orbit, is many times smaller. But at the sun's limb, and close to the horizon, where the visual angle in question opens out to its full extent, atmospheric troubles become overwhelming, and altogether swamp the far more minute effects of parallax.

There remain indirect methods. Astronomers are well acquainted with the proportions which the various planetary orbits bear to each other. They are so connected, in the manner expressed by Kepler's Third Law, that the periods being known, it only needs to find the interval between any two of them in order to infer at once the distances separating them all from one another and from the sun. The plan is given; what we want to discover is the scale upon which it is drawn; so that, if we can get a reliable measure of the distance of a single planet from the earth, our problem is solved.

Now some of our fellow-travellers in our unending journey round the sun, come at times well within the scope of celestial trigonometry. The orbit of Mars lies at one point not more than thirty-five million miles outside that of the earth, and when the two bodies happen to arrive together in or near the favourable spot--a conjuncture which occurs every fifteen years--the desired opportunity is granted. Mars is then "in opposition," or on the opposite side of us from the sun, crossing the meridian consequently at midnight.[749] It was from an opposition of Mars, observed in 1672 by Richer at Cayenne in concert with Cassini in Paris, that the first scientific estimate of the sun's distance was derived. It appeared to be nearly eighty-seven millions of miles (parallax 9.5"); while Flamsteed deduced 81,700,000 (parallax 10") from his independent observations of the same occurrence--a difference quite insignificant at that stage of the inquiry. But Picard's result was just half Flamsteed's (parallax 20"; distance forty-one million miles); and Lahire considered that we must be separated from the hearth of our system by an interval of at least 136 million miles.[750] So that uncertainty continued to have an enormous range.

Venus, on the other hand, comes closest to the earth when she passes between it and the sun. At such times of "inferior conjunction" she is, however, still twenty-six million miles, or (in round numbers) 109 times as distant as the moon. Moreover, she is so immersed in the sun's rays that it is only when her path lies across his disc that the requisite facilities for measurement are afforded. These "partial eclipses of the sun by Venus" (as Encke termed them) are coupled together in pairs,[751] of which the components are separated by eight years, recurring at intervals alternately of 105-1/2 and 121-1/2 years. Thus, the first calculated transit took place in December, 1631, and its companion (observed by Horrocks) in the same month (N.S.), 1639. Then, after the lapse of 121-1/2 years, came the June couple of 1761 and 1769; and again after 105-1/2, the two last observed, December 8, 1874, and December 6, 1882. Throughout the twentieth century there will be no transit of Venus; but the astronomers of the twenty-first will only have to wait four years for the first of a June pair. The rarity of these events is due to the fact that the orbits of the earth and Venus do not lie in the same plane. If they did, there would be a transit each time that our twin-planet overtakes us in her more rapid circling--that is, on an average, every 584 days. As things are actually arranged, she passes above or below the sun, except when she happens to be very near the line of intersection of the two tracks.

Such an occurrence as a transit of Venus seems, at first sight, full of promise for solving the problem of the sun's distance. For nothing would appear easier than to determine exactly either the duration of the passage of a small, dark orb across a large brilliant disc, or the instant of its entry upon or exit from it. And the differences in these times (which, owing to the comparative nearness of Venus, are quite considerable), as observed from remote parts of the earth, can be translated into differences of space--that is, into apparent or parallactic displacements, whereby the distance of Venus becomes known, and thence, by a simple sum in proportion, the distance of the sun. But in that word "exactly" what snares and pitfalls lie hid! It is so easy to think and to say; so indefinitely hard to realise. The astronomers of the eighteenth century were full of hope and zeal. They confidently expected to attain, through the double opportunity offered them, to something like a permanent settlement of the statistics of our system. They were grievously disappointed. The uncertainty as to the sun's distance, which they had counted upon reducing to a few hundred thousand miles, remained at many millions.

In 1822, however, Encke, then director of the Seeberg Observatory near Gotha, undertook to bring order out of the confusion of discordant, and discordantly interpreted observations. His combined result for both transits (1761 and 1769) was published in 1824,[752] and met universal acquiescence. The parallax of the sun thereby established was 8.5776", corresponding to a mean distance[753] of 95-1/4 million miles. Yet this abolition of doubt was far from being so satisfactory as it seemed. Serenity on the point lasted exactly thirty years. It was disturbed in 1854 by Hansen's announcement[754] that the observed motions of the moon could be drawn into accord with theory only on the terms of bringing the sun considerably nearer to us than he was supposed to be.

Dr. Matthew Stewart, professor of mathematics in the University of Edinburgh, had made a futile attempt in 1763 to deduce the sun's distance from his disturbing power over our satellite.[755] Tobias Mayer of Gottingen, however, whose short career was fruitful of suggestions, struck out the right way to the same end; and Laplace, in the seventh book of the Mecanique Celeste,[756] gave a solar parallax derived from the lunar "parallactic inequality" substantially identical with that issuing from Encke's subsequent discussion of the eighteenth-century transits. Thus, two wholly independent methods--the trigonometrical, or method by survey, and the gravitational, or method by perturbation--seemed to corroborate each the upshot of the use of the other until the nineteenth century was well past its meridian. It is singular how often errors conspire to lead conviction astray.

Hansen's note of alarm in 1854 was echoed by Leverrier in 1858.[757] He found that an apparent monthly oscillation of the sun which reflects a real monthly movement of the earth round its common centre of gravity with the moon, and which depends for its amount solely on the mass of the moon and the distance of the sun, required a diminution in the admitted value of that distance by fully four million miles. Three years later he pointed out that certain perplexing discrepancies between the observed and computed places both of Venus and Mars, would vanish on the adoption of a similar measure.[758] Moreover, a favourable opposition of Mars gave the opportunity in 1862 for fresh observations, which, separately worked out by Stone and Winnecke, agreed with all the newer investigations in fixing the great unit at slightly over 91 million miles. In Newcomb's hands they gave 92-1/2 million.[759] The accumulating evidence in favour of a large reduction in the sun's distance was just then reinforced by an auxiliary result of a totally different and unexpected kind.

The discovery that light does not travel instantaneously from point to point, but takes some short time in transmission, was made by Olaus Roemer in 1675, through observing that the eclipses of Jupiter's satellites invariably occurred later, when the earth was on the far side, than when it was on the near side of its orbit. Half the difference, or the time spent by a luminous vibration in crossing the "mean radius" of the earth's orbit, is called the "light-equation"; and the determination of its precise value has claimed the minute care distinctive of modern astronomy. Delambre in 1792 made it 493 seconds. Glasenapp, a Russian astronomer, raised the estimate in 1874 to 501, Professor Harkness adopts a safe medium value of 498 seconds. Hence, if we had any independent means of ascertaining how fast light travels, we could tell at once how far off the sun is.

There is yet another way by which knowledge of the swiftness of light would lead us straight to the goal. The heavenly bodies are perceived, when carefully watched and measured, to be pushed forward out of their true places, in the direction of the earth's motion, by a very minute quantity. This effect (already adverted to) has been known since Bradley's time as "aberration." It arises from a combination of the two movements of the earth round the sun and of the light-waves through the ether. If the earth stood still, or if light spent no time on the road from the stars, such an effect would not exist. Its amount represents the proportion between the velocities with which the earth and the light-rays pursue their respective journeys. This proportion is, roughly, one to ten thousand. So that here again, if we knew the rate per second of luminous transmission, we should also know the rate per second of the earth's movement, consequently the size of its orbit and the distance of the sun.

But, until lately, instead of finding the distance of the sun from the velocity of light, there has been no means of ascertaining the velocity of light except through the imperfect knowledge possessed as to the distance of the sun. The first successful terrestrial experiments on the point date from 1849; and it is certainly no slight triumph of human ingenuity to have taken rigorous account of the delay of a sunbeam in flashing from one mirror to another. Fizeau led the way,[760] and he was succeeded, after a few months, by Leon Foucault,[761] who, in 1862, had so far perfected Wheatstone's method of revolving mirrors, as to be able to announce with authority that light travelled slower, and that the sun was in consequence nearer than had been supposed.[762] Thus a third line of separate research was found to converge to the same point with the two others.

Such a conspiracy of proof was not to be resisted, and at the anniversary meeting of the Royal Astronomical Society in February, 1864, the correction of the solar distance took the foremost place in the annals of the year. Lest, however, a sudden bound of four million miles nearer to the centre of our system should shake public faith in astronomical accuracy, it was explained that the change in the solar parallax corresponding to that huge leap, amounted to no more than the breadth of a human hair 125 feet from the eye![763] The Nautical Almanac gave from 1870 the altered value of 8.95", for which Newcomb's result of 8.85", adopted in 1869 in the Berlin Ephemeris, was substituted some ten years later. In astronomical literature the change was initiated by Sir Edmund Beckett in the first edition (1865) of his Astronomy without Mathematics.

If any doubt remained as to the misleading character of Encke's deduction, so long implicitly trusted in, it was removed by Powalky's and Stone's rediscussions, in 1864 and 1868 respectively, of the transit observations of 1769. Using improved determinations of the longitude of the various stations, and a selective judgment in dealing with their materials, which, however indispensable, did not escape adverse criticism, they brought out results confirmatory of the no longer disputed necessity for largely increasing the solar parallax, and proportionately diminishing the solar distance. Once more in 1890, and this time with better success, the eighteenth-century transits were investigated by Professor Newcomb.[764] Turning to account the experience gained in the interim regarding the optical phenomena accompanying such events, he elicited from the mass of somewhat discordant observations at his command, a parallax (8.79") in close agreement with the value given by sundry modes of recent research.

Conclusions on the subject, however, were still regarded as purely provisional. A transit of Venus was fast approaching, and to its arbitrament, as to that of a court of final appeal, the pending question was to be referred. It is true that the verdict in the same case by the same tribunal a century earlier had proved of so indecisive a character as to form only a starting-point for fresh litigation; but that century had not passed in vain, and it was confidently anticipated that observational difficulties, then equally unexpected and insuperable, would yield to the elaborate care and skill of forewarned modern preparation.

The conditions of the transit of December 8, 1874, were sketched out by Sir George Airy, then Astronomer-Royal, in 1857,[765] and formed the subject of eager discussion in this and other countries down to the very eve of the occurrence. In these Mr. Proctor took a leading part; and it was due to his urgent representations that provision was made for the employment of the method identified with the name of Halley,[766] which had been too hastily assumed inapplicable to the first of each transit-pair. It depends upon the difference in the length of time taken by the planet to cross the sun's disc, as seen from various points of the terrestrial surface, and requires, accordingly, the visibility of both entrance and exit at the same station. Since these were, in 1874, separated by about three and a half hours, and the interval may be much longer, the choice of posts for the successful use of the "method of durations" is a matter of some difficulty.

The system described by Delisle in 1760, on the other hand, involves merely noting the instant of ingress or egress (according to situation) from opposite extremities of a terrestrial diameter; the disparity in time giving a measure of the planet's apparent displacement, hence of its actual rate of travel in miles per minute, from which its distances severally from earth and sun are immediately deducible. Its chief attendant difficulty is the necessity for accurately fixing the longitudes of the points of observation. But this was much more sensibly felt a century ago than it is now, the improved facility and certainty of modern determinations tending to give the Delislean plan a decided superiority over its rival.

These two traditional methods were supplemented in 1874 by the camera and the heliometer. From photography, above all, much was expected. Observations made by its means would have the advantages of impartiality, multitude, and permanence. Peculiarities of vision and bias of judgment would be eliminated; the slow progress of the phenomenon would permit an indefinite number of pictures to be taken, their epochs fixed to a fraction of a second; while subsequent leisurely comparison and measurement could hardly fail, it was thought, to educe approximate truth from the mass of accumulated evidence. The use of the heliometer (much relied on by German observers) was so far similar to that of the camera that the object aimed at by both was the determination of the relative positions of the centres of the sun and Venus viewed, at the same absolute instant, from opposite sides of the globe. So that the principle of the two older methods was to ascertain the exact times of meeting between the solar and planetary limbs; that of the two modern to determine the position of the dark body already thrown into complete relief by its shining background. The former are "methods by contact," the latter "methods by projection."

Every country which had a reputation to keep or to gain for scientific zeal was forward to co-operate in the great cosmopolitan enterprise of the transit. France and Germany each sent out six expeditions; twenty-six stations were in Russian, twelve in English, eight in American, three in Italian, one in Dutch occupation. In all, at a cost of nearly a quarter of a million, some fourscore distinct posts of observation were provided; among them such inhospitable, and all but inaccessible rocks in the bleak Southern Ocean, as St. Paul's and Campbell Islands, swept by hurricanes, and fitted only for the habitation of seabirds, where the daring votaries of science, in the wise prevision of a long leaguer by the elements, were supplied with stores for many months, or even a whole year. Siberia and the Sandwich Islands were thickly beset with observers; parties of three nationalities encamped within the mists of Kerguelen Island, expressively termed the "Land of Desolation," in the sanguine, though not wholly frustrated hope of a glimpse of the sun at the right moment. M. Janssen narrowly escaped destruction from a typhoon in the China seas on his way to Nagasaki; Lord Lindsay (now Earl of Crawford and Balcarres) equipped, at his private expense, an expedition to Mauritius, which was in itself an epitome of modern resource and ingenuity.

During several years, the practical methods best suited to insure success for the impending enterprise formed a subject of European debate. Official commissions were appointed to receive and decide upon evidence; and experiments were in progress for the purpose of defining the actual circumstances of contacts, the precise determination of which constituted the only tried, though by no means an assuredly safe road to the end in view. In England, America, France, and Germany, artificial transits were mounted, and the members of the various expeditions were carefully trained to unanimity in estimating the phases of junction and separation between a moving dark circular body and a broad illuminated disc. In the previous century, a formidable and prevalent phenomenon, which acquired notoriety as the "Black Drop" or "Black Ligament," had swamped all pretensions to rigid accuracy. It may be described as substituting adhesion for contact, the limbs of the sun and planet, instead of meeting and parting with the desirable clean definiteness, clinging together as if made of some glutinous material, and prolonging their connection by means of a dark band or dark threads stretched between them. Some astronomers ascribed this baffling appearance entirely to instrumental imperfections; others to atmospheric agitation; others again to the optical encroachment of light upon darkness known as "irradiation." It is probable that all these causes conspired, in various measure, to produce it; and it is certain that its conspicuous appearance may, by suitable precautions, be obviated.

The organisation of the British forces reflected the utmost credit on the energy and ability of Lieutenant-Colonel Tupman, who was responsible for the whole. No useful measure was neglected. Each observer went out ticketed with his "personal equation," his senses drilled into a species of martial discipline, his powers absorbed, so far as possible, in the action of a cosmopolitan observing machine. Instrumental uniformity and uniformity of method were obtainable, and were attained; but diversity of judgment unhappily survived the best-directed efforts for its extirpation.

The eventful day had no sooner passed than telegrams began to pour in, announcing an outcome of considerable, though not unqualified success. The weather had proved generally favourable; the manifold arrangements had worked well; contacts had been plentifully observed; photographs in lavish abundance had been secured; a store of materials, in short, had been laid up, of which it would take years to work out the full results by calculation. Gradually, nevertheless, it came to be known that the hope of a definitive issue must be abandoned. Unanimity was found to be as remote as ever. The dreaded "black ligament" gave, indeed, less trouble than was expected; but another appearance supervened which took most observers by surprise. This was the illumination due to the atmosphere of Venus. Astronomers, it is true, were not ignorant that the planet had, on previous occasions, been seen girdled with a lucid ring; but its power to mar observations by the distorting effect of refraction had scarcely been reckoned with. It proved, however, to be very great. Such was the difficulty of determining the critical instant of internal contact, that (in Colonel Tupman's words) "observers side by side, with adequate optical means, differed as much as twenty or thirty seconds in the times they recorded for phenomena which they have described in almost identical language."[767]

Such uncertainties in the data admitted of a corresponding variety in the results. From the British observations of ingress and egress Sir George Airy[768] derived, in 1877, a solar parallax of 8.76" (corrected to 8.754"), indicating a mean distance of 93,375,000 miles. Mr. Stone obtained a value of ninety-two millions (parallax 8.88"), and held any parallax less than 8.84" or more than 8.93" to be "absolutely negatived" by the documents available.[769] Yet, from the same, Colonel Tupman deduced 8.81",[770] implying a distance 700,000 miles greater than Stone had obtained. The best French observations of contacts gave a parallax of about 8.88"; French micrometric measures the obviously exaggerated one of 9.05".[771]

Photography, as practised by most of the European parties, was a total failure. Utterly discrepant values of the microscopic displacements designed to serve as sounding lines for the solar system, issued from attempts to measure even the most promising pictures. "You might as well try to measure the zodiacal light," it was remarked to Sir George Airy. Those taken on the American plan of using telescopes of so great focal length as to afford, without further enlargement, an image of the requisite size, gave notably better results. From an elaborate comparison of those dating from Vladivostock, Nagasaki, and Pekin, with others from Kerguelen and Chatham Islands, Professor D. P. Todd, of Amherst College, deduced a solar distance of about ninety-two million miles (parallax 8.883" +-0.034"),[772] and the value was much favoured by concurrent evidence.

On the whole, estimates of the great spatial unit cannot be said to have gained any security from the combined effort of 1874. A few months before the transit, Mr. Proctor considered that the uncertainty then amounted to 1,448,000 miles;[773] five years after the transit, Professor Harkness judged it to be still 1,575,950 miles;[774] yet it had been hoped that it would have been brought down to 100,000. As regards the end for which it had been undertaken, the grand campaign had come to nothing. Nevertheless, no sign of discouragement was apparent. There was a change of view, but no relaxation of purpose. The problem, it was seen, could be solved by no single heroic effort, but by the patient approximation of gradual improvements. Astronomers, accordingly, looked round for fresh means or more refined expedients for applying those already known. A new phase of exertion was entered upon.

On September 5, 1877, Mars came into opposition near the part of his orbit which lies nearest to that of the earth, and Dr. Gill (now Sir David) took advantage of the circumstance to appeal once more to him for a decision on the quaestio vexata of the sun's distance. He chose, as the scene of his labours, the Island of Ascension, and for their plan a method recommended by Airy in 1857,[775] but never before fairly tried. This is known as the "diurnal method of parallaxes." Its principle consists in substituting successive morning and evening observations from the same spot, for simultaneous observations from remote spots, the rotation of the earth supplying the necessary difference in the points of view. Its great advantage is that of unity in performance. A single mind, looking through the same pair of eyes, reinforced with the same optical appliances, is employed throughout, and the errors inseparable from the combination of data collected under different conditions are avoided. There are many cases in which one man can do the work of two better than two men can do the work of one. The result of Gill's skilful determinations (made with Lord Lindsay's heliometer) was a solar parallax of 8.78", corresponding to a distance of 93,080,000 miles.[776] The bestowal of the Royal Astronomical Society's gold medal stamped the merit of this distinguished service.

But there are other subjects for this kind of inquiry besides Mars and Venus. Professor Galle of Breslau suggested in 1872[777] that some of the minor planets might be got to repay astronomers for much disinterested toil spent in unravelling their motions, by lending aid to their efforts towards a correct celestial survey. Ten or twelve come near enough, and are bright enough for the purpose; in fact, the absence of sensible magnitude is one of their chief recommendations, since a point of light offers far greater facilities for exact measurement than a disc. The first attempt to work this new vein was made at the opposition of Phocaea in 1872; and from observations of Flora in the following year at twelve observatories in the northern and southern hemispheres, Galle deduced a solar parallax of 8.87".[778] At Mauritius in 1874, Lord Lindsay and Sir David Gill applied the "diurnal method" to Juno, then conveniently situated for the purpose; and the continued use of similar occasions affords an unexceptionable means for improving knowledge of the sun's distance. They frequently recur; they need no elaborate preparation; a single astronomer armed with a heliometer can do all the requisite work. Dr. Gill, however, organized a more complex plan of operations upon Iris in 1888, and upon Victoria and Sappho in 1889. A novel method was adopted. Its object was to secure simultaneous observations made from opposite sides of the globe just when the planet lay in the plane passing through the centre of the earth and the two observers, the same pair of reference-stars being used on each occasion. The displacements caused by parallax were thus in a sense doubled, since the star to which the planet seemed approximated in the northern hemisphere, showed as if slightly removed from it in the southern, and vice versa. As the planet pursued its course, fresh star-couples came into play, during the weeks that the favourable period lasted. In these determinations, only heliometers were employed. Dr. Elkin, of Yale college, co-operated throughout, and the heliometers of Dresden, Gottingen, Bamberg, and Leipzig, shared in the work, while Dr. Auwers of Berlin was Sir David Gill's personal coadjutor at the Cape. Voluminous data were collected; meridian observations of the stars of reference for Victoria occupied twenty-one establishments during four months; the direct work of triangulation kept four heliometers in almost exclusive use for the best part of a year; and the ensuing toilsome computations, carried out during three years at the Cape Observatory, filled two bulky tomes[779] with their details. Gill's final result, published in 1897, was a parallax of 8.802", equivalent to a solar distance of 92,874,000; and it was qualified by a probable error so small that the value might well have been accepted as definitive but for an unlooked-for discovery. The minor planet Eros, detected August 14, 1898, was found to pursue a course rendering it an almost ideal intermediary in solar parallax-determinations. Once in thirty years, it comes within fifteen million miles of the earth; and although the next of these choice epochs must be awaited for some decades, an opposition too favourable to be neglected occurred in 1900. At an International Conference, accordingly, held at Paris in July of that year, a plan of photographic operations was concerted between the representatives of no less than 58 observatories.[780] Its primary object was to secure a large stock of negatives showing the planet with the comparison-stars along the route traversed by it from October, 1900, to March, 1901,[781] and this at least was successfully attained. Their measurement will in due time educe the apparent displacements of the moving object as viewed simultaneously from remote parts of the earth; and the upshot should be a solar parallax adequate in accuracy to the exigent demands of the twentieth century.

The second of the nineteenth-century pair of Venus-transits was looked forward to with much abated enthusiasm. Russia refused her active co-operation in observing it, on the ground that oppositions of the minor planets were trigonometrically more useful, and financially far less costly; and her example was followed by Austria; while Italian astronomers limited their sphere of action to their own peninsula. Nevertheless, it was generally held that a phenomenon which the world could not again witness until it was four generations older should, at the price of any effort, not be allowed to pass in neglect.

The persuasion of its importance justified the summoning of an International Conference at Paris in 1881, from which, however, America, preferring independent action, held aloof. It was decided to give Delisle's method another trial; and the ambiguities attending and marring its use were sought to be obviated by careful regulations for insuring agreement in the estimation of the critical moments of ingress and egress.[782] But in fact (as M. Puiseux had shown[783]), contacts between the limbs of the sun and planet, so far from possessing the geometrical simplicity attributed to them, are really made up of a prolonged succession of various and varying phases, impossible either to predict or identify with anything like rigid exactitude. Sir Robert Ball compared the task of determining the precise instant of their meeting or parting, to that of telling the hour with accuracy on a watch without a minute hand; and the comparison is admittedly inadequate. For not only is the apparent movement of Venus across the sun extremely slow, being but the excess of her real motion over that of the earth; but three distinct atmospheres--the solar, terrestrial, and Cytherean--combine to deform outlines and mask the geometrical relations which it is desired to connect with a strict count of time.

The result was very much what had been expected. The arrangements were excellent, and were only in a few cases disconcerted by bad weather. The British parties, under the experienced guidance of Mr. Stone, the late Radcliffe observer, took up positions scattered over the globe, from Queensland to Bermuda; the Americans collected a whole library of photographs; the Germans and Belgians trusted to the heliometer; the French used the camera as an adjunct to the method of contacts. Yet little or no approach was made to solving the problem. Thus, from 606 measures of Venus on the sun, taken with a new kind of heliometer at Santiago in Chili, M. Houzeau, of the Brussels Observatory, derived a solar parallax of 8.907", and a distance of 91,727,000 miles.[784] But the "probable errors" of this determination amounted to 0.084" either way: it was subject to a "more or less" of 900,000, or to a total uncertainty of 1,800,000 miles. The "probable error" of the English result, published in 1887, was less formidable,[785] yet the details of the discussion showed that no great confidence could be placed in it. The sun's distance came out 92,560,000 miles; while 92,360,000 was given by Professor Harkness's investigation of 1,475 American photographs.[786] Finally, Dr. Auwers deduced from the German heliometric measures the unsatisfactorily small value of 92,000,000 miles.[787] The transit of 1882 had not, then, brought about the desired unanimity.

The state and progress of knowledge on this important topic were summed up by Faye and Harkness in 1881.[788] The methods employed in its investigation fall (as we have seen) into three separate classes--the trigonometrical, the gravitational, and the "phototachymetrical"--an ungainly adjective used to describe the method by the velocity of light. Each has its special difficulties and sources of error; each has counter-balancing advantages. The only trustworthy result from celestial surveys, was at that time furnished by Gill's observations of Mars in 1877. But the method by lunar and planetary disturbances is unlike all the others in having time on its side. It is this which Leverrier declared with emphasis must inevitably prevail, because its accuracy is continually growing.[789] The scarcely perceptible errors which still impede its application are of such a nature as to accumulate year by year; eventually, then, they will challenge, and must receive, a more and more perfect correction. The light-velocity method, however, claimed, and for some years justified, M. Faye's preference.

By a beautiful series of experiments on Foucault's principle, Michelson fixed in 1879 the rate of luminous transmission at 299,930 (corrected later to 299,910) kilometres a second.[790] This determination was held by Professor Todd to be entitled to four times as much confidence as any previous one; and if the solar parallax of 8.758" deduced from it by Professor Harkness errs somewhat by defect, it is doubtless because Glasenapp's "light-equation," with which it was combined, errs slightly by excess. But all earlier efforts of the kind were thrown into the shade by Professor Newcomb's arduous operations at Washington in 1880-1882.[791] The scale upon which they were conducted was in itself impressive. Foucault's entire apparatus in 1862 had been enclosed in a single room; Newcomb's revolving and fixed mirrors, between which the rays of light were to run their timed course, were set up on opposite shores of the Potomac, at a distance of nearly four kilometres. This advantage was turned to the utmost account by ingenuity and skill in contrivance and execution; and the deduced velocity of 299,860 kilometres = 186,328 miles a second, had an estimated error (30 kilometres) only one-tenth that ascribed by Cornu to his own result in 1874.

Just as these experiments were concluded in 1882, M. Magnus Nyren, of St. Petersburg, published an elaborate investigation of the small annular displacements of the stars due to the successive transmission of light, involving an increase of Struve's "constant of aberration" from 20.445" to 20.492". And from the new value, combined with Newcomb's light-velocity, was derived a valuable approximation to the sun's distance, concluded at 92,905,021 miles (parallax = 8.794"). Yet it is not quite certain that Nyren's correction was an improvement. A differential method of determining the amount of aberration, struck out by M. Loewy of Paris,[792] avoids most of the objections to the absolute method previously in vogue; and the upshot of its application in 1891 was to show that Struve's constant might better be retained than altered, Loewy's of 20.447" varying from it only to an insignificant extent. Professor Hall had, moreover, deduced nearly the same value (20.454") from the Washington observations since 1862, of Alpha Lyrae (Vega); whence, in conjunction with Newcomb's rate of light transmission, he arrived at a solar parallax of 8.81".[793] Inverting the process, Sir David Gill in 1897 derived the constant from the parallax. If the earth's orbit have a mean radius, as found by him, of 92,874,000 miles, then, he calculated, the aberration of light--Newcomb's measures of its velocity being supposed exact--amounts to 20.467". This figure can need very slight correction.

Professor Harkness surveyed in 1891,[794] from an eclectic point of view, the general situation as regarded the sun's parallax. Convinced that no single method deserved an exclusive preference, he reached a plausible result through the combination, on the principle of least squares--that is, by the mathematical rules of probability--of all the various quantities upon which the great datum depends. It thus summed up and harmonised the whole of the multifarious evidence bearing upon the point, and, as modified in 1894,[795] falls very satisfactorily into line with the Cape determination. We may, then, at least provisionally, accept 92,870,000 miles as the length of our measuring-rod for space. Nor do we hazard much in fixing 100,000 miles as the outside limit of its future correction.

FOOTNOTES:

[Footnote 748: Airy, Month. Not., vol. xvii., p. 210.]

[Footnote 749: Mars comes into opposition once in about 780 days; but owing to the eccentricity of both orbits, his distance from the earth at those epochs varies from thirty-five to sixty-two million miles.]

[Footnote 750: J. D. Cassini, Hist. Abregee de la Parallaxe du Soleil, p. 122, 1772.]

[Footnote 751: The present period of coupled eccentric transits will, in the course of ages, be succeeded by a period of single, nearly central transits. The alignments by which transits are produced, of the earth, Venus, and the sun, close to the place of intersection of the two planetary orbits, now occur, the first a little in front of, the second, after eight years less two and a half days, a little behind the node. But when the first of these two meetings takes place very near the node, giving a nearly central transit, the second falls too far from it, and the planet escapes projection on the sun. The reason of the liability to an eight-yearly recurrence is that eight revolutions of the earth are accomplished in only a very little more time than thirteen revolutions of Venus.]

[Footnote 752: Die Entfernung der Sonne: Fortsetzung, p. 108. Encke slightly corrected his results of 1824 in Berlin Abh., 1835, p. 295.]

[Footnote 753: Owing to the ellipticity of its orbit, the earth is nearer to the sun in January than in June by 3,100,000 miles. The quantity to be determined, or "mean distance," is that lying midway between these extremes--is, in other words, half the major axis of the ellipse in which the earth travels.]

[Footnote 754: Month. Not., vol. xv., p. 9.]

[Footnote 755: The Distance of the Sun from the Earth determined by the Theory of Gravity, Edinburgh, 1763.]

[Footnote 756: Opera, t. iii., p. 326.]

[Footnote 757: Comptes Rendus, t. xlvi., p. 882. The parallax 8.95" derived by Leverrier from the above-described inequality in the earth's motion, was corrected by Stone to 8.91". Month. Not., vol. xxviii., p. 25.]

[Footnote 758: Month. Not., vol. xxxv., p. 156.]

[Footnote 759: Wash. Obs., 1865, App. ii., p. 28.]

[Footnote 760: Comptes Rendus, t. xxix., p. 90.]

[Footnote 761: Ibid., t. xxx., p. 551.]

[Footnote 762: Ibid., t. lv., p. 501. The previously admitted velocity was 308 million metres per second; Foucault reduced it to 298 million. Combined with Struve's "constant of aberration" this gave 8.86" for the solar parallax, which exactly agreed with Cornu's result from a repetition of Fizeau's experiments in 1872. Comptes Rendus, t. lxxvi., p. 338.]

[Footnote 763: Month. Not., vol. xxiv., p. 103.]

[Footnote 764: Astr. Papers of the American Ephemeris, vol. ii., p. 263.]

[Footnote 765: Month. Not., vol. xvii., p. 208.]

[Footnote 766: Because closely similar to that proposed by him in Phil. Trans. for 1716.]

[Footnote 767: Month. Not., vol. xxxviii., p. 447.]

[Footnote 768: Ibid., p. 11.]

[Footnote 769: Ibid., p. 294.]

[Footnote 770: Ibid., p. 334.]

[Footnote 771: Comptes Rendus, t. xcii., p. 812.]

[Footnote 772: Observatory, vol. v., p. 205.]

[Footnote 773: Transits of Venus, p. 89 (1st ed.).]

[Footnote 774: Am. Jour. of Sc., vol. xx., p. 393.]

[Footnote 775: Month. Not., vol. xvii., p. 219.]

[Footnote 776: Mem. Roy. Astr. Soc., vol. xlvi., p. 163.]

[Footnote 777: Astr. Nach., No. 1,897.]

[Footnote 778: Hilfiker, Bern Mittheilungen, 1878, p. 109.]

[Footnote 779: Annals of the Cape Observatory, vols. vi., vii.]

[Footnote 780: Rapport sur l'Etat de l'Observatoire de Paris pour l'Annee 1900, p. 7.]

[Footnote 781: Observatory, vol. xxiii., p. 311; Newcomb, _Astr. Jour._, No. 480.]

[Footnote 782: Comptes Rendus, t. xciii., p. 569.]

[Footnote 783: Ibid., t. xcii., p. 481.]

[Footnote 784: Bull. de l'Acad., t. vi., p. 842.]

[Footnote 785: Month. Not., vol. xlviii., p. 201.]

[Footnote 786: Astr. Jour., No. 182.]

[Footnote 787: Astr. Nach., No. 3,066.]

[Footnote 788: Comptes Rendus, t. xcii., p. 375; Am. Jour. of Sc., vol. xxii., p. 375.]

[Footnote 789: Month. Not., vol. xxxv., p. 401.]

[Footnote 790: Am. Jour. of Sc., vol. xviii., p. 393.]

[Footnote 791: Nature, vol. xxxiv., p. 170; Astron. Papers of the American Ephemeris, vol. ii., p. 113.]

[Footnote 792: Comptes Rendus, t. cxii., p. 549.]

[Footnote 793: Astr. Journ., Nos. 169, 170]

[Footnote 794: The Solar Parallax and its Related Constants, Washington, 1891.]

[Footnote 795: Astr. and Astrophysics, vol. xiii., p. 626.]

Chapter VII

PLANETS AND SATELLITES

Johann Hieronymus Schroeter was the Herschel of Germany. He did not, it is true, possess the more brilliant gifts of his rival. Herschel's piercing discernment, comprehensive intelligence, and inventive splendour were wanting to him. He was, nevertheless, the founder of descriptive astronomy in Germany, as Herschel was in England.

Born at Erfurt in 1745, he prosecuted legal studies at Gottingen, and there imbibed from Kaestner a life-long devotion to science. From the law, however, he got the means of living, and, what was to the full as precious to him, the means of observing. Entering the sphere of Hanoverian officialism in 1788, he settled a few years later at Lilienthal, near Bremen, as "Oberamtmann," or chief magistrate. Here he built a small observatory, enriched in 1785 with a seven-foot reflector by Herschel, then one of the most powerful instruments to be found anywhere out of England. It was soon surpassed, through his exertions, by the first-fruits of native industry in that branch. Schrader of Kiel transferred his workshops to Lilienthal in 1792, and constructed there, under the superintendence and at the cost of the astronomical Oberamtmann, a thirteen-foot reflector, declared by Lalande to be the finest telescope in existence, and one twenty-seven feet in focal length, probably as inferior to its predecessor in real efficiency as it was superior in size.

Thus, with instruments of gradually increasing power, Schroeter studied during thirty-four years the topography of the moon and planets. The field was then almost untrodden; he had but few and casual predecessors, and has since had no equal in the sustained and concentrated patience of his hourly watchings. Both their prolixity and their enthusiasm are faithfully reflected in his various treatises. Yet the one may be pardoned for the sake of the other, especially when it is remembered that he struck out a substantially new line, and that one of the main lines of future advance. Moreover, his infectious zeal communicated itself; he set the example of observing when there was scarcely an observer in Germany; and under his roof Harding and Bessel received their training as practical astronomers.

But he was reserved to see evil days. Early in 1813 the French under Vandamme occupied Bremen. On the night of April 20, the Vale of Lilies was, by their wanton destructiveness, laid waste with fire; the Government offices were destroyed, and with them the chief part of Schroeter's property, including the whole stock of his books and writings. There was worse behind. A few days later, his observatory, which had escaped the conflagration, was broken into, pillaged, and ruined. His life was wrecked with it. He survived the catastrophe three years without the means to repair, or the power to forget it, and gradually sank from disappointment into decay, terminated by death, August 29, 1816. He had, indeed, done all the work he was capable of; and though not of the first quality, it was far from contemptible. He laid the foundation of the comparative study of the moon's surface, and the descriptive particulars of the planets laboriously collected by him constituted a store of more or less reliable information hardly added to during the ensuing half century. They rested, it is true, under some shadow of doubt; but the most recent observations have tended on several points to rehabilitate the discredited authority of the Lilienthal astronomer. We may now briefly resume, and pursue in its further progress, the course of his studies, taking the planets in the order of their distances from the sun.

In April, 1792, Schroeter saw reason to conclude, from the gradual degradation of light on its partially illuminated disc, that Mercury possesses a tolerably dense atmosphere.[796] During the transit of May 7, 1799, he was, moreover, struck with the appearance of a ring of softened luminosity encircling the planet to an apparent height of three seconds, or about a quarter of its own diameter.[797] Although a "mere thought" in texture, it remained persistently visible both with the seven-foot and the thirteen-foot reflectors, armed with powers up to 288. It had a well-marked grayish boundary, and reminded him, though indefinitely fainter, of the penumbra of a sun-spot. A similar appendage had been noticed by De Plantade at Montpellier, November 11, 1736, and again in 1786 and 1789 by Prosperin and Flaugergues; but Herschel, on November 9, 1802, saw the preceding limb of the planet projected on the sun cut the luminous solar clouds with the most perfect sharpness.[798] The presence, however, of a "halo" was unmistakable in 1832, when Professor Moll, of Utrecht, described it as a "nebulous ring of a darker tinge approaching to the violet colour."[799] Again, to Huggins and Stone, November 5, 1868, it showed as lucid and most distinct. No change in the colour of the glasses used, or the powers applied, could get rid of it, and it lasted throughout the transit.[800] It was next seen by Christie and Dunkin at Greenwich, May 6, 1878,[801] and with much precision of detail by Trouvelot at Cambridge (U.S.).[802] Professor Holden, on the other hand, noted at Hastings-on-Hudson the total absence of all anomalous appearances.[803] Nor could any vestige of them be perceived by Barnard at Lick on November 10, 1894.[804] Various effects of irradiation and diffraction were, however, observed by Lowell and W. H. Pickering at Flagstaff;[805] and Davidson was favoured at San Francisco with glimpses of the historic aureola,[806] as well as of a central whitish spot, which often accompanies it. That both are somehow of optical production can scarcely be doubted.

Nothing can be learned from them regarding the planet's physical condition. Airy showed that refraction in a Mercurian atmosphere could not possibly originate the noted aureola, which must accordingly be set down as "strictly an ocular nervous phenomenon."[807] It is the less easy to escape from this conclusion that we find the virtually airless moon capable of exhibiting a like appendage. Professor Stephen Alexander, of the United States Survey, with two other observers, perceived, during the eclipse of the sun of July 18, 1860, the advancing lunar limb to be bordered with a bright band;[808] and photographic effects of the same kind appear in pictures of transits of Venus and partial solar eclipses.

The spectroscope affords little information as to the constitution of Mercury. Its light is of course that of the sun reflected, and its spectrum is consequently a faint echo of the Fraunhofer spectrum. Dr. H. C. Vogel, who first examined it in April, 1871, suspected traces of the action of an atmosphere like ours,[809] but, it would seem, on slight grounds. It is, however, certainly very poor in blue rays. More definite conclusions were, in 1874,[810] derived by Zoellner from photometric observations of Mercurian phases. A similar study of the waxing and waning moon had afforded him the curious discovery that light-changes dependent upon phase vary with the nature of the reflecting surface, following a totally different law on a smooth homogeneous globe and on a rugged and mountainous one. Now the phases of Mercury--so far as could be determined from only two sets of observations--correspond with the latter kind of structure. Strictly analogous to those of the moon, they seem to indicate an analogous mode of surface-formation. This conclusion was fully borne out by Mueller's more extended observations at Potsdam during the years 1885-1893.[811] Practical assurance was gained from them that the innermost planet has a rough rind of dusky rock, absorbing all but 17 per cent. of the light poured upon it by the fierce adjacent sun. Its "albedo," in other words, is 0.17,[812] which is precisely that ascribed to the moon. The absence of any appreciable Mercurian atmosphere followed almost necessarily from these results.

On March 26, 1800, Schroeter, observing with his 13-foot reflector in a peculiarly clear sky, perceived the southern horn of Mercury's crescent to be quite distinctly blunted.[813] Interception of sunlight by a Mercurian mountain rather more than eleven English miles high explained the effect to his satisfaction. By carefully timing its recurrence, he concluded rotation on an axis in a period of 24 hours 4 minutes. The first determination of the kind rewarded twenty years of unceasing vigilance. It received ostensible confirmation from the successive appearances of a dusky streak and blotch in May and June, 1801.[814] These, however, were inferred to be no permanent markings on the body of the planet, but atmospheric formations, the streak at times drifting forwards (it was thought) under the fluctuating influence of Mercurian breezes. From a rediscussion of these somewhat doubtful observations Bessel inferred that Mercury rotates on an axis inclined 70 deg. to the plane of its orbit in 24 hours 53 seconds.

The rounded appearance of the southern horn seen by Schroeter was more or less doubtfully caught by Noble (1864), Burton, and Franks (1877);[815] but was obvious to Mr. W. F. Denning at Bristol on the morning of November 5, 1882.[816] That the southern polar regions are usually less bright than the northern is well ascertained; but the cause of the deficiency remains dubious. If inequalities of surface are in question, they must be on a considerable scale; and a similar explanation might be given of the deformations of the "terminator"--or dividing-line between darkness and light in the planet's phases--first remarked by Schroeter, and again clearly seen by Trouvelot in 1878 and 1881.[817] The displacement, during four days, of certain brilliant and dusky spaces on the disc indicated to Mr. Denning in 1882 rotation in about twenty-five hours; while the general aspect of the planet reminded him of that of Mars.[818] But the difficulties in the way of its observation are enormously enhanced by its constant close attendance on the sun.

In his sustained study of the features of Mercury, Schroeter had no imitator until Schiaparelli took up the task at Milan in 1882. His observations were made in daylight. It was found that much more could be seen, and higher magnifying powers used, high up in the sky near the sun, than at low altitudes, through the agitated air of morning or evening twilight. A notable discovery ensued.[819] Following the planet hour by hour, instead of making necessarily brief inspections at intervals of about a day, as previous observers had done, it was found that the markings faintly visible remained sensibly fixed, hence, that there was no rotation in a period at all comparable with that of the earth. And after long and patient watching, the conclusion was at last reached that Mercury turns on his axis in the same time needed to complete a revolution in his orbit. One of his hemispheres, then, is always averted from the sun, as one of the moon's hemispheres from the earth, while the other never shifts from beneath his torrid rays. The "librations," however, of Mercury are on a larger scale than those of the moon, because he travels in a more eccentric path. The temporary inequalities arising between his "even pacing" on an axis and his alternately accelerated and retarded elliptical movement occasion, in fact, an oscillation to and fro of the boundaries of light and darkness on his globe over an arc of 47 deg. 22', in the course of his year of 88 days. Thus the regions of perpetual day and perpetual night are separated by two segments, amounting to one-fourth of the entire surface, where the sun rises and sets once in 88 days. Else there is no variation from the intense glare on one side of the globe, and the nocturnal blackness on the other.

To Schiaparelli's scrutiny, Mercury appeared as a "spotty globe," enveloped in a tolerably dense atmosphere. The brownish stripes and streaks, discerned on his rose-tinged disc, and judged to be permanent, were made the basis of a chart. They were not indeed always equally well seen. They disappeared regularly near the limb, and were at times veiled even when centrally situated. Some of them had been clearly perceived by De Ball at Bothkamp in 1882.[820]

Mr. Lowell followed Schiaparelli's example by observing Mercury in the full glare of noon. "The best time to study him," he remarked, "is when planetary almanacs state 'Mercury invisible.'" A remarkable series of drawings executed, some at Flagstaff in 1896, the remainder at Mexico in 1897, supplied grounds for the following, among other, conclusions.[821] Mercury rotates synchronously with its revolution--that is, once in 88 days--on an axis sensibly perpendicular to its orbital plane. No certain signs of a Mercurian atmosphere are visible. The globe is seamed and furrowed with long narrow markings, explicable as cracks in cooling. It is, and always was, a dead world. From micrometrical measures, moreover, the inferences were drawn that the planet's mass has a probable value about 1/20 that of the earth, while its mean density falls considerably short of the terrestrial standard.

The theory of Mercury's movements has always given trouble. In Lalande's,[822] as in Maestlin's time, the planet seemed to exist for no other purpose than to throw discredit on astronomers; and even to Leverrier's powerful analysis it long proved recalcitrant. On the 12th of September, 1869, however, he was able to announce before the Academy of Sciences[823] the terms of a compromise between observation and calculation. They involved the addition of a new member to the solar system. The hitherto unrecognised presence of a body about the size of Mercury itself revolving at somewhat less than half its mean distance from the sun (or, if farther, then of less mass, and vice versa), would, it was pointed out, produce exactly the effect required, of displacing the perihelion of the former planet 38" a century more than could otherwise be accounted for. The planes of the two orbits, however, should not lie far apart, as otherwise a nodal disturbance would arise not perceived to exist. It was added that a ring of asteroids similarly placed would answer the purpose equally well, and was more likely to have escaped notice.

Upon the heels of this forecast followed promptly a seeming verification. Dr. Lescarbault, a physician residing at Orgeres, whose slender opportunities had not blunted his hopes of achievement, had, ever since 1845, when he witnessed a transit of Mercury, cherished the idea that an unknown planet might be caught thus projected on the solar background. Unable to observe continuously until 1858, he, on March 26, 1859, saw what he had expected--a small perfectly round object slowly traversing the sun's disc. The fruitless expectation of reobserving the phenomenon, however, kept him silent, and it was not until December 22, after the news of Leverrier's prediction had reached him, that he wrote to acquaint him with his supposed discovery.[824] The Imperial Astronomer thereupon hurried down to Orgeres, and by personal inspection of the simple apparatus used, by searching cross-examination and local inquiry, convinced himself of the genuine character and substantial accuracy of the reported observation. He named the new planet "Vulcan," and computed elements giving it a period of revolution slightly under twenty days.[825] But it has never since been seen. M. Liais, director of the Brazilian Coast Survey, thought himself justified in asserting that it never had been seen. Observing the sun for twelve minutes after the supposed ingress recorded at Orgeres, he noted those particular regions of its surface as "tres uniformes d'intensite."[826] He subsequently, however, admitted Lescarbault's good faith, at first rashly questioned. The planet-seeking doctor was, in truth, only one among many victims of similar illusions.

Waning interest in the subject was revived by a fresh announcement of a transit witnessed, it was asserted, by Weber at Peckeloh, April 4, 1876.[827] The pseudo-planet, indeed, was detected shortly afterwards on the Greenwich photographs, and was found to have been seen by M. Ventosa at Madrid in its true character of a sun-spot without penumbra; but Leverrier had meantime undertaken the investigation of a list of twenty similar dubious appearances, collected by Haase, and republished by Wolf in 1872.[828] From these, five were picked out as referring in all likelihood to the same body, the reality of whose existence was now confidently asserted, and of which more or less probable transits were fixed for March 22, 1877, and October 15, 1882.[829] But, widespread watchfulness notwithstanding, no suspicious object came into view at either epoch.

The next announcement of the discovery of "Vulcan" was on the occasion of the total solar eclipse of July 29, 1878.[830] This time it was stated to have been seen at some distance south-west of the obscured sun, as a ruddy star with a minute planetary disc; and its simultaneous detection by two observers--the late Professor James C. Watson, stationed at Rawlins (Wyoming Territory), and Professor Lewis Swift at Denver (Colorado)--was at first readily admitted. But their separate observations could, on a closer examination, by no possibility be brought into harmony, and, if valid, certainly referred to two distinct objects, if not to four; each astronomer eventually claiming a pair of planets. Nor could any one of the four be identified with Lescarbault's and Leverrier's Vulcan, which, if a substantial body revolving round the sun, must then have been found on the east side of that luminary.[831] The most feasible explanation of the puzzle seems to be that Watson and Swift merely saw each the same two stars in Cancer: haste and excitement doing the rest.[832] Nevertheless, they strenuously maintained their opposite conviction.[833]

Intra-Mercurian planets have since been diligently searched for when the opportunity of a total eclipse offered, especially during the long obscuration at Caroline Island. Not only did Professor Holden "sweep" in the solar vicinity, but Palisa and Trouvelot agreed to divide the field of exploration, and thus make sure of whatever planetary prey there might be within reach; yet with only negative results. Photographic explorations during recent eclipses have been equally fruitless. Belief in the presence of any considerable body or bodies within the orbit of Mercury is, accordingly, at a low ebb. Yet the existence of the anomaly in the Mercurian movements indicated by Leverrier has been made only surer by further research.[834] Its elucidation constitutes one of the "pending problems" of astronomy.

* * * * *

From the observation at Bologna in 1666-67 of some very faint spots, Domenico Cassini concluded a rotation or libration of Venus--he was not sure which--in about twenty-three hours.[835] By Bianchini in 1726 the period was augmented to twenty-four days eight hours. J. J. Cassini, however, in 1740, showed that the data collected by both observers were consistent with rotation in twenty-three hours twenty minutes.[836] So the matter rested until Schroeter's time. After watching nine years in vain, he at last, February 28, 1788, perceived the ordinarily uniform brightness of the planet's disc to be marbled with a filmy streak, which returned periodically to the same position in about twenty-three hours twenty-eight minutes. This approximate estimate was corrected by the application of a more definite criterion. On December 28, 1789, the southern horn of the crescent Venus was seen truncated, an outlying lucid point interrupting the darkness beyond. Precisely the same appearance recurred two years later, giving for the planet's rotation a period of 23h. 21m.[837] To this only twenty-two seconds were added by De Vico, as the result of over 10,000 observations made with the Cauchoix refractor of the Collegio Romano, 1839-41.[838] The axis of rotation was found to be much more bowed towards the orbital plane than that of the earth, the equator making with it an angle of 53 deg. 11'.

These conclusions inspired, it is true, much distrust, consequently there were no received ideas on the subject to be subverted. Nevertheless, a shock of surprise was felt at Schiaparelli's announcement, early in 1890,[839] that Venus most probably rotates after the fashion just previously ascribed to Mercury. A continuous series of observations, from November, 1877, to February, 1878, with their records in above a hundred drawings, supplied the chief part of the data upon which he rested his conclusions. They certainly appeared exceptionally well-grounded; and the doubts at first qualifying them were removed by a fresh set of determinations in July, 1895.[840] Most observers had depended, in their attempts to ascertain the rotation-period of Venus, upon evanescent shadings, most likely of atmospheric origin, and scarcely recognisable from day to day. Schiaparelli fixed his attention upon round, defined, lustrously white spots, the presence of which near the cusps of the illuminated crescent has been attested for close upon two centuries. His steady watch over them showed the invariability of their position with regard to the terminator; and this is as much as to say that the regions of day and night do not shift on the surface of the planet. In other words, she keeps the same face always turned towards the sun. Moreover, since her orbit is nearly circular, libratory effects are very small. They amount in fact to only just one-thirtieth of those serving to modify the severe contrasts of climate in Mercury.

Confirmatory evidence of Schiaparelli's result for Venus is not wanting. Thus, observations irreconcilable with a swift rate of rotation were made at Bothkamp in 1871 by Vogel and Lohse;[841] and a drawing executed by Professor Holden with the great Washington reflector, December 15, 1877, showed the same markings in the positions recorded at Milan to have been occupied by them eight hours previously. Further, a series of observations, carried out by M. Perrotin at Nice, May 15 to October 4, 1890, and from Mount Mounier in 1895-6, with the special aim of testing the inference of synchronous rotation and revolution, proved strongly corroborative of it.[842] A remarkable collection of drawings made by Mr. Lowell in 1896 appeared decisive in its favour;[843] Tacchini at Rome,[844] Mascari at Catania and Etna,[845] Cerulli at Terano,[846] obtained in 1892-6 evidence similar in purport. On the other hand, Niesten of Brussels found reason to revert to Vico's discarded elements for the planet's rotation;[847] and Trouvelot,[848] Stanley Williams,[849] Villiger,[850] and Leo Brenner,[851] so far agreed with him as to adopt a period of approximately twenty-four hours. Finally, E. Von Oppolzer suggested an appeal to the spectroscope;[852] and Belopolsky secured in 1900[853] spectrograms apparently marked by the minute displacements corresponding to a rapid rate of axial movement. But they were avowedly taken only as an experiment, with unsuitable apparatus; and the desirable verification of their supposed import is not yet forthcoming. Until it is, Schiaparelli's period of 225 days must be allowed to hold the field.

Effects attributed to great differences of level in the surface of Venus have struck many observers. Francesco Fontana at Naples in 1643 noticed irregularities along the inner edge of the crescent.[854] Lahire in 1700 considered them--regard being had to difference of distance--to be much more strongly marked than those visible in the moon.[855] Schroeter's assertions to the same effect, though scouted with some unnecessary vehemence by Herschel,[856] have since been repeatedly confirmed; amongst others by Maedler, De Vico, Langdon, who in 1873 saw the broken line of the terminator with peculiar distinctness through a veil of auroral cloud;[857] by Denning,[858] March 30, 1881, despite preliminary impressions to the contrary, as well as by C. V. Zenger at Prague, January 8, 1883. The great mountain mass, presumed to occasion the periodical blunting of the southern horn, was precariously estimated by the Lilienthal observer to rise to the prodigious height of nearly twenty-seven miles, or just five times the elevation of Mount Everest! Yet the phenomenon persists, whatever may be thought of the explanation. Moreover, the speck of light beyond, interpreted as the visible sign of a detached peak rising high enough above the encircling shadow to catch the first and last rays of the sun, was frequently discerned by Baron Van Ertborn in 1876;[859] while an object near the northern horn of the crescent, strongly resembling a lunar ring-mountain, was delineated both by De Vico in 1841 and by Denning forty years later.

We are almost equally sure that Venus, as that the earth is encompassed with an atmosphere. Yet, notwithstanding luminous appearances plainly due to refraction during the transits both of 1761 and 1769, Schroeter, in 1792, took the initiative in coming to a definite conclusion on the subject.[860] It was founded, first, on the rapid diminution of brilliancy towards the terminator, attributed to atmospheric absorption; next, on the extension beyond a semicircle of the horns of the crescent; lastly, on the presence of a bluish gleam illuminating the early hours of the Cytherean night with what was taken to be genuine twilight. Even Herschel admitted that sunlight, by the same effect through which the heavenly bodies show visibly above our horizons while still geometrically below them, appeared to be bent round the shoulder of the globe of Venus. Ample confirmation of the fact has since been afforded. At Dorpat in May, 1849, the planet being within 3 deg. 26' of inferior conjunction, Maedler found the arms of waning light upon the disc to embrace no less than 240 deg. of its extent;[861] and in December, 1842, Mr. Guthrie, of Bervie, N.B., actually observed, under similar conditions, the whole circumference to be lit up with a faint nebulous glow.[862] The same curious phenomenon was intermittently seen by Mr. Leeson Prince at Uckfield in September, 1861;[863] but with more satisfactory distinctness by Mr. C. S. Lyman of Yale College,[864] before and after the conjunction of December 11, 1866, and during nearly five hours previous to the transit of 1874, when the yellowish ring of refracted light showed at one point an approach to interruption, possibly through the intervention of a bank of clouds. Again, on December 2, 1898, Venus being 1 deg. 45' from the sun's centre, Mr. H. N. Russell, of the Halsted Observatory, descried the coalescence of the cusps, and founded on the observation a valuable discussion of such effects.[865] Taking account of certain features in the case left unnoticed by Neison[866] and Proctor,[867] he inferred from them the presence of a Cytherean atmosphere considerably less refractive than our own, although possibly, in its lower strata, encumbered with dust or haze.

Similar appearances are conspicuous during transits. But while the Mercurian halo is characteristically seen on the sun, the "silver thread" round the limb of Venus commonly shows on the part off the sun. There are, however, instances of each description in both cases. Mr. Grant, in collecting the records of physical phenomena accompanying the transits of 1761 and 1769, remarks that no one person saw both kinds of annulus, and argues a dissimilarity in their respective modes of production.[868] Such a dissimilarity probably exists, in the sense that the inner section of the ring is illusory, the outer, a genuine result of the bending of light in a gaseous envelope; but the distinction of separate visibility has not been borne out by recent experience. Several of the Australian observers during the transit of 1874 witnessed the complete phenomenon. Mr. J. Macdonnell, at Eden, saw a "shadowy nebulous ring" surround the whole disc when ingress was two-thirds accomplished; Mr. Tornaghi, at Goulburn, perceived a halo, entire and unmistakable, at half egress.[869] Similar observations were made at Sydney,[870] and were renewed in 1882 by Lescarbault at Orgeres, by Metzger in Java, and by Barnard at Vanderbilt University.[871]

Spectroscopic indications of aqueous vapour as present in the atmosphere of Venus, were obtained in 1874 and 1882, by Tacchini and Ricco in Italy, and by Young in New Jersey.[872] Janssen, however, who made a special study of the point subsequently to the transit of 1882, found them much less certain than he had anticipated;[873] and Vogel, by repeated examinations, 1871-73, could detect only the very slightest variations from the pattern of the solar spectrum. Some additions there indeed seem to be in the thickening of a few water and oxygen-lines; but so nearly evanescent as to induce the persuasion that most of the light we receive from Venus has traversed only the tenuous upper portion of its atmosphere.[874] It is reflected, at any rate, with comparatively slight diminution. On the 26th and 27th of September, 1878, a close conjunction gave Mr. James Nasmyth the rare opportunity of watching Venus and Mercury for several hours side by side in the field of his reflector; when the former appeared to him like clean silver, the latter as dull as lead or zinc.[875] Yet the light incident upon Mercury is, on an average, three and a half times as strong as the light reaching Venus. Thus, the reflective power of Venus must be singularly strong. And we find, accordingly, from a combination of Zoellner's with Mueller's results, that its albedo is but little inferior to that of new-fallen snow; in other words, it gives back 77 per cent. of the luminous rays impinging upon it.

This extraordinary brilliancy would be intelligible were it permissible to suppose that we see nothing of the planet but a dense canopy of clouds. But the hypothesis is discountenanced by the Flagstaff observations, and is irreconcilable with the visibility of mountainous elevations, and permanent surface-markings. To Mr. Lowell these were so distinct and unchanging as to furnish data for a chart of the Cytherean globe, and the peculiar arrangement of divergent shading exhibited in it cannot off-hand be set down as unreal, in view of Perrotin's earlier discernment of analogous linear traces. Gruithuisen's "snow-caps,"[876] however--it is safe to say--do not exist as such; although shining regions near the poles form a well-attested trait of the strange Cytherean landscape.

The "secondary," or "ashen light," of Venus was first noticed by Riccioli in 1643; it was seen by Derham about 1715, by Kirch in 1721, by Schroeter and Harding in 1806;[877] and the reality of the appearance has since been authenticated by numerous and trustworthy observations. It is precisely similar to that of the "old moon in the new moon's arms"; and Zenger, who witnessed it with unusual distinctness, January 8, 1883,[878] supposes it due to the same cause--namely, to the faint gleam of reflected earth-light from the night-side of the planet. When we remember, however, that "full earth-light" on Venus, at its nearest, has little more than 1/12000 its intensity on the moon, we see at once that the explanation is inadequate. Nor can Professor Safarik's,[879] by phosphorescence of the warm and teeming oceans with which Zoellner[880] regarded the globe of Venus as mainly covered, be seriously entertained. Vogel's suggestion is more plausible. He and O. Lohse, at Bothkamp, November 3 to 11, 1871, saw the dark hemisphere partially illuminated by secondary light, extending 30 deg. from the terminator, and thought the effect might be produced by a very extensive twilight.[881] Others have had recourse to the analogy of our aurorae, and J. Lamp suggested that the grayish gleam, visible to him at Bothkamp, October 21 and 26, 1887,[882] might be an accompaniment of electrical processes connected with the planet's meteorology. Whatever the origin of the phenomenon, it may serve, on a night-enwrapt hemisphere, to dissipate some of the thick darkness otherwise encroached upon only by "the pale light of stars."

Venus was once supposed to possess a satellite. But belief in its existence has died out. No one, indeed, has caught even a deceptive glimpse of such an object during the last 125 years. Yet it was repeatedly and, one might have thought, well observed in the seventeenth and eighteenth centuries. Fontana "discovered" it in 1645; Cassini--an adept in the art of seeing--recognised it in 1672, and again in 1686; Short watched it for a full hour in 1740 with varied instrumental means; Tobias Mayer in 1759, Montaigne in 1761; several astronomers at Copenhagen in March, 1764, noted what they considered its unmistakable presence; as did Horrebow in 1768. But M. Paul Stroobant,[883] who in 1887 submitted all the available data on the subject to a searching examination, identified Horrebow's satellite with Theta Librae, a fifth-magnitude star; and a few other apparitions were, by his industry, similarly explained away. Nevertheless, several withstood all efforts to account for them, and together form a most curious case of illusion. For it is quite certain that Venus has no such conspicuous attendant.

* * * * *

The third planet encountered in travelling outward from the sun is the abode of man. He has in consequence opportunities for studying its physical habitudes altogether different from the baffling glimpse afforded to him of the other members of the solar family. Regarding the earth, then, a mass of knowledge so varied and comprehensive has been accumulated as to form a science--or rather several sciences--apart. But underneath all lie astronomical relations, the recognition and investigation of which constitute one of the most significant intellectual events of the present century.

It is indeed far from easy to draw a line of logical distinction between items of knowledge which have their proper place here, and those which should be left to the historian of geology. There are some, however, of which the cosmical connections are so close that it is impossible to overlook them. Among these is the ascertainment of the solidity of the globe. At first sight it seems difficult to conceive what the apparent positions of the stars can have to do with subterranean conditions; yet it was from star measurements alone that Hopkins, in 1839, concluded the earth to be solid to a depth of at least 800 or 1,000 miles.[884] His argument was, that if it were a mere shell filled with liquid, precession and nutation would be much larger than they are observed to be. For the shell alone would follow the pull of the sun and moon on its equatorial girdle, leaving the liquid behind; and being thus so much the lighter, would move the more readily. There is, it is true, grave reason to doubt whether this reasoning corresponds with the actual facts of the case;[885] but the conclusion to which it led has been otherwise affirmed and extended.

Indications of an identical purport have been derived from another kind of external disturbance, affecting our globe through the same agencies. Lord Kelvin (then Sir William Thomson) pointed out in 1862[886] that tidal influences are brought to bear on land as well as on water, although obedience to them is perceptible only in the mobile element. Some bodily distortion of the earth's figure must, however, take place, unless we suppose it of absolute or "preternatural" rigidity, and the amount of such distortion can be determined from its effect in diminishing oceanic tides below their calculated value. For if the earth were perfectly plastic to the stresses of solar and lunar gravity, tides--in the ordinary sense--would not exist. Continents and oceans would swell and subside together. It is to the difference in the behaviour of solid and liquid terrestrial constituents that the ebb and flow of the waters are due.

Six years later, the distinguished Glasgow professor suggested that this criterion might, by the aid of a prolonged series of exact tidal observations, be practically applied to test the interior condition of our planet.[887] In 1882, accordingly, suitable data extending over thirty-three years having at length become available, Mr. G. H. Darwin performed the laborious task of their analysis, with the general result that the "effective rigidity" of the earth's mass must be at least as great as that of steel.[888]

Ratification from an unexpected quarter has lately been brought to this conclusion. The question of a possible mobility in the earth's axis of rotation has often been mooted. Now at last it has received an affirmative reply. Dr. Kuestner detected, in his observations of 1884-85, effects apparently springing from a minute variation in the latitude of Berlin. The matter having been brought before the International Geodetic Association in 1888, special observations were set on foot at Berlin, Potsdam, Prague, and Strasbourg, the upshot of which was to bring plainly to view synchronous, and seemingly periodic fluctuations of latitude to the extent of half a second of arc. The reality of these was verified by an expedition to Honolulu in 1891-92, the variations there corresponding inversely to those simultaneously determined in Europe.[889] Their character was completely defined by Mr. S. C. Chandler's discussion in October, 1891.[890] He showed that they could be explained by supposing the pole of the earth to describe a circle with a radius of thirty feet in a period of fourteen months. Confirmation of this hypothesis was found by Dr. B. A. Gould in the Cordoba observations,[891] and it was provided with a physical basis through the able co-operation of Professor Newcomb.[892] The earth, owing to its ellipsoidal shape, should, apart from disturbance, rotate upon its "axis of figure," or shortest diameter; since thus alone can the centrifugal forces generated by its spinning balance each other. Temporary causes, however, such as heavy falls of snow or rain limited to one continental area, the shifting of ice-masses, even the movements of winds, may render the globe slightly lop-sided, and thus oblige it to forsake its normal axis, and rotate on one somewhat divergent from it. This "instantaneous axis" (for it is incessantly changing) must, by mathematical theory, revolve round the axis of figure in a period of 306 days. Provided, that is to say, the earth were a perfectly rigid body. But it is far from being so; it yields sensibly to every strain put upon it; and this yielding tends to protract the time of circulation of the displaced pole. The length of its period, then, serves as a kind of measure of the plasticity of the globe; which, according to Newcomb's and S. S. Hough's independent calculations,[893] seems to be a little less than that of steel. In an earth compacted of steel, the instantaneous axis would revolve in 441 days; in the actual earth, the process is accomplished in 428 days. By this new path, accordingly, astronomers have been led to an identical estimate of the consistence of our globe with that derived from tidal investigations.

Variations of latitude are intrinsically complex. To produce them, an incalculable interplay of causes must be at work, each with its proper period and law of action.[894] All the elements of the phenomenon are then in a perpetual state of flux,[895] and absorb for their continual redetermination, the arduous and combined labours of many astronomers. Nor is this trouble superfluous. Minute in extent though they be, the shiftings of the pole menace the very foundations of exact celestial science; their neglect would leave the entire fabric insecure. Just at the beginning of the present century they reached a predicted minimum, but are expected again to augment their range after the year 1902. The interesting suggestion has been made by Mr. J. Halm that such fluctuations are, in some obscure way, affected by changes in solar activity, and conform like them to an eleven-year cycle.[896]

In a paper read before the Geological Society, December 15, 1830,[897] Sir John Herschel threw out the idea that the perplexing changes of climate revealed by the geological record might be explained through certain slow fluctuations in the eccentricity of the earth's orbit, produced by the disturbing action of the other planets. Shortly afterwards, however, he abandoned the position as untenable;[898] and it was left to the late Dr. James Croll, in 1864[899] and subsequent years, to reoccupy and fortify it. Within restricted limits (as Lagrange and, more certainly and definitely, Leverrier proved), the path pursued by our planet round the sun alternately contracts, in the course of ages, into a moderate ellipse, and expands almost to a circle, the major axis, and consequently the mean distance, remaining invariable. Even at present, when the eccentricity approaches a minimum, the sun is nearer to us in January than in July by above three million miles, and some 850,000 years ago this difference was more than four times as great. Dr. Croll brought together[900] a mass of evidence to support the view, that, at epochs of considerable eccentricity, the hemisphere of which the winter, occurring at aphelion, was both intensified and prolonged, must have undergone extensive glaciation; while the opposite hemisphere, with a short, mild winter, and long, cool summer, enjoyed an approach to perennial spring. These conditions were exactly reversed at the end of 10,500 years, through the shifting of the perihelion combined with the precession of the equinoxes, the frozen hemisphere blooming into a luxuriant garden as its seasons came round to occur at the opposite sites of the terrestrial orbit, and the vernal hemisphere subsiding simultaneously into ice-bound rigour.[901] Thus a plausible explanation was offered of the anomalous alternations of glacial and semi-tropical periods, attested, on incontrovertible geological evidence, as having succeeded each other in times past over what are now temperate regions. They succeeded each other, it is true, with much less frequency and regularity than the theory demanded; but the discrepancy was overlooked or smoothed away. The most recent glacial epoch was placed by Dr. Croll about 200,000 years ago, when the eccentricity of the earth's orbit was 3.4 times as great as it is now. At present a faint representation of such a state of things is afforded by the southern hemisphere. One condition of glaciation in the coincidence of winter with the maximum of remoteness from the sun, is present; the other--a high eccentricity--is deficient. Yet the ring of ice-bound territory hemming in the southern pole is well known to be far more extensive than the corresponding region in the north.

The verification of this ingenious hypothesis depends upon a variety of intricate meteorological conditions, some of which have been adversely interpreted by competent authorities.[902] What is still more serious, its acceptance seems precluded by time-relations of a simple kind. Dr. Wright[903] has established with some approach to certainty that glacial conditions ceased in Canada and the United States about ten or twelve thousand years ago. The erosive action of the Falls of Niagara qualifies them to serve as a clepsydra, or water-clock on a grand scale; and their chronological indications have been amply corroborated elsewhere and otherwise on the same continent. The astronomical Ice Age, however, should have been enormously more antique. No reconciliation of the facts with the theory appears possible.

The first attempt at an experimental estimate of the "mean density" of the earth was Maskelyne's observation in 1774 of the deflection of a plumb-line through the attraction of Schehallien. The conclusion thence derived, that our globe weighs 4-1/2 times as much as an equal bulk of water,[904] was not very exact. It was considerably improved upon by Cavendish, who, in 1798, brought into use the "torsion-balance" constructed for the same purpose by John Michell. The resulting estimate of 5.48 was raised to 5.66 by Francis Baily's elaborate repetition of the process in 1838-42. From experiments on the subject made in 1872-73 by Cornu and Baille the slightly inferior value of 5.56 was derived; and it was further shown that the data collected by Baily, when corrected for a systematic error, gave practically the same result (5.55).[905] M. Wilsing's of 5.58, obtained at Potsdam in 1889,[906] nearly agreed with it; while Professor Poynting, by means of a common balance, arrived at a terrestrial mean density of 5.49.[907] Professor Boys next entered the field with an exquisite apparatus, in which a quartz fibre performed the functions of a torsion-rod; and the figure 5.53 determined by him, and exactly confirmed by Dr. Braun's research at Mariaschein, Bohemia, in 1896,[908] may be called the standard value of the required datum. Newton's guess at the average weight of the earth as five or six times that of water has thus been curiously verified.

Operations for determining the figure of the earth were carried out during the last century on an unprecedented scale. The Russo-Scandinavian arc, of which the measurement was completed under the direction of the elder Struve in 1855, reached from Hammerfest to Ismailia on the Danube, a length of 25 deg. 20'. But little inferior to it was the Indian arc, begun by Lambton in the first years of the century, continued by Everest, revised and extended by Walker. Both were surpassed in compass by the Anglo-French arc, which embraced 28 deg.; and considerable segments of meridians near the Atlantic and Pacific shores of North America were measured under the auspices of the United States Coast Survey. But these operations shrink into insignificance by comparison with Sir David Gill's grandiose scheme for uniting two hemispheres by a continuous network of triangulation. The history of geodesy in South Africa began with Lacaille's measurements in 1752. They were repeated and enlarged in scope by Sir Thomas Maclear in 1841-48; and his determinations prepared the way for a complete survey of Cape Colony and Natal, executed during the ten years 1883-92 by Colonel Morris, R.E., under the direction of Sir David Gill.[909] Bechuanaland and Rhodesia were subsequently included in the work; and the Royal Astronomer obtained, in 1900, the support of the International Geodetic Association for its extension to the mouth of the Nile. Nor was this the limit of his design. By carrying the survey along the Levantine coast, connection can be established with Struve's system, and the magnificent amplitude of 105 deg. will be given to the conjoined African and European arcs. Meantime, the French have undertaken the remeasurement of Bouguer's Peruvian arc, and a corresponding Russo-Swedish[910] enterprise is progressing in Spitzbergen; so that abundant materials will ere long be provided for fresh investigations of the shape and size of our planet. The smallness of the outstanding uncertainty can be judged of by comparing J. B. Listing's[911] with General Clarke's[912] results, published in the same year (1878). Listing stated the dimensions of the terrestrial spheroid as follows: Equatorial radius = 3,960 miles; polar radius = 3,947 miles; ellipticity = 1/288.5. Clarke's corresponding figures were: 3,963 and 3,950 miles, giving an ellipticity of 1/293.5. The value of the latter fraction at present generally adopted is 1/292; that is to say, the thickness of the protuberant equatorial ring is held to be 1/292 of the equatorial radius. From astronomical considerations, it is true, Newcomb estimated the ratio at 1/308;[913] but for obtaining this particular datum, geodetical methods are unquestionably to be preferred.

* * * * *

The moon possesses for us a unique interest. She in all probability shared the origin of the earth; she perhaps prefigures its decay. She is at present its minister and companion. Her existence, so far as we can see, serves no other purpose than to illuminate the darkness of terrestrial nights, and to measure, by swiftly-recurring and conspicuous changes of aspect, the long span of terrestrial time. Inquiries stimulated by visible dependence, and aided by relatively close vicinity, have resulted in a wonderfully minute acquaintance with the features of the single lunar hemisphere open to our inspection.

Selenography, in the modern sense, is little more than a hundred years old. It originated with the publication in 1791 of Schroeter's Selenotopographische Fragmente.[914] Not but that the lunar surface had already been diligently studied, chiefly by Hevelius, Cassini, Riccioli, and Tobias Mayer; the idea, however, of investigating the moon's physical condition, and detecting symptoms of the activity there of natural forces through minute topographical inquiry, first obtained effect at Lilienthal. Schroeter's delineations, accordingly, imperfect though they were, afforded a starting-point for a comparative study of the superficial features of our satellite.

The first of the curious objects which he named "rills" was noted by him in 1787. Before 1801 he had found eleven; Lohrmann added 75; Maedler 55; Schmidt published in 1866 a catalogue of 425, of which 278 had been detected by himself;[915] and he eventually brought the number up to nearly 1,000. They are, then, a very persistent lunar feature, though wholly without terrestrial analogue. There is no difference of opinion as to their nature. They are quite obviously clefts in a rocky surface, 100 to 500 yards deep, usually a couple of miles across, and pursuing straight, curved, or branching tracks up to 150 miles in length. As regards their origin, the most probable view is that they are fissures produced in cooling; but Neison inclines to consider them rather as dried watercourses.[916]

On February 24, 1792, Schroeter perceived what he took to be distinct traces of a lunar twilight, and continued to observe them during nine consecutive years.[917] They indicated, he thought, the presence of a shallow atmosphere, about 29 times more tenuous than our own. Bessel, on the other hand, considered that the only way of "saving" a lunar atmosphere was to deny it any refractive power, the sharpness and suddenness of star-occultations negativing the possibility of gaseous surroundings of greater density (admitting an extreme supposition) than 1/500 that of terrestrial air.[918] Newcomb places the maximum at 1/400. Sir John Herschel concluded "the non-existence of any atmosphere at the moon's edge having 1/1980 part of the density of the earth's atmosphere."[919]

This decision was fully borne out by Sir William Huggins's spectroscopic observation of the disappearance behind the moon's limb of the small star Eta Piscium, January 4, 1865.[920] Not the slightest sign of selective absorption or unequal refraction was discernible. The entire spectrum went out at once, as if a slide had suddenly dropped over it. The spectroscope has uniformly told the same tale; for M. Thollon's observation during the total solar eclipse at Sohag of a supposed thickening at the moon's rim, of certain dark lines in the solar spectrum, is now acknowledged to have been illusory. Moonlight, analysed with the prism, is found to be pure reflected sunlight, diminished in quantity, owing to the low reflective capability of the lunar surface, to less than one-fifth its incident intensity, but wholly unmodified in quality.

Nevertheless, the diameter of the moon appeared from the Greenwich observations discussed by Airy in 1865[921] to be 4" smaller than when directly measured; and the effect would be explicable by refraction in a lunar atmosphere 2,000 times thinner than our own at the sea-level. But the difference was probably illusory. It resulted in part, if not wholly, from the visual enlargement by irradiation of the bright disc of the moon. Professor Comstock, employing the 16-inch Clark equatoreal of the Washburn Observatory, found in 1897 the refractive displacements of occulted stars so trifling as to preclude the existence of a permanent lunar atmosphere of much more than 1/5000 the density of the terrestrial envelope.[922] The possibility, however, was admitted that, on the illuminated side of the moon, temporary exhalations of aqueous vapour might arise from ice-strata evaporated by sun-heat. Meantime, some renewed evidence of actual crepuscular gleams on the moon had been gathered by MM. Paul and Prosper Henry of the Paris Observatory, as well as by Mr. W. H. Pickering, in the pure air of Arequipa, at an altitude of 8,000 feet above the sea.[923] An occultation of Jupiter, too, observed by him August 12, 1892,[924] was attended with a slight flattening of the planet's disc through the effect, it was supposed, of lunar refraction--but of refraction in an atmosphere possessing, at the most, 1/4000 the density at the sea-level of terrestrial air, and capable of holding in equilibrium no more than 1/250 of an inch of mercury. Yet this small barometric value corresponds, Mr. Pickering remarks, "to a pressure of hundreds of tons per square mile of the lunar surface." The compression downward of gaseous strata on the moon should, in any case, proceed very gradually, owing to the slight power of lunar gravity,[925] and they might hence play an important part in the economy of our satellite while evading spectroscopic and other tests. Thus--as Mr. Ranyard remarked[926]--the cliffs and pinnacles of the moon bear witness, by their unworn condition, to the efficiency of atmospheric protection against meteoric bombardment; and Mr. Pickering shows that it could be afforded by such a tenuous envelope as that postulated by him.

The first to emulate Schroeter's selenographical zeal was Wilhelm Gotthelf Lohrmann, a land-surveyor of Dresden, who, in 1824, published four out of twenty-five sections of the first scientifically executed lunar chart, on a scale of 37-1/2 inches to a lunar diameter. His sight, however, began to fail three years later, and he died in 1840, leaving materials from which the work was completed and published in 1878 by Dr. Julius Schmidt, late director of the Athens Observatory. Much had been done in the interim. Beer and Maedler began at Berlin in 1830 their great trigonometrical survey of the lunar surface, as yet neither revised nor superseded. A map, issued in four parts, 1834-36, on nearly the same scale as Lohrmann's, but more detailed and authoritative, embodied the results. It was succeeded, in 1837, by a descriptive volume bearing the imposing title, Der Mond; oder allgemeine vergleichende Selenographie. This summation of knowledge in that branch, though in truth leaving many questions open, had an air of finality which tended to discourage further inquiry.[927] It gave form to a reaction against the sanguine views entertained by Hevelius, Schroeter, Herschel and Gruithuisen as to the possibilities of agreeable residence on the moon, and relegated the "Selenites," one of whose cities Schroeter thought he had discovered, and of whose festal processions Gruithuisen had not despaired of becoming a spectator, to the shadowy land of the Ivory Gate. All examples of change in lunar formations were, moreover, dismissed as illusory. The light contained in the work was, in short, a "dry light," not stimulating to the imagination. "A mixture of a lie," Bacon shrewdly remarks, "doth ever add pleasure." For many years, accordingly, Schmidt had the field of selenography almost to himself.

Reviving interest in the subject was at once excited and displayed by the appointment, in 1864, of a Lunar Committee of the British Association. The indirect were of greater value than the direct fruits of its labours. An English school of selenography rose into importance. Popularity was gained for the subject by the diffusion of works conspicuous for ingenuity and research. Nasmyth's and Carpenter's beautifully illustrated volume (1874) was succeeded, after two years, by a still more weighty contribution to lunar science in Mr. Neison's well-known book, accompanied by a map, based on the survey of Beer and Maedler, but adding some 500 measures of positions, besides the representation of several thousand new objects. With Schmidt's Charte der Gebirge der Mondes, Germany once more took the lead. This splendid delineation, built upon Lohrmann's foundation, embraced the detail contained in upwards of 3,000 original drawings, representing the labour of thirty-four years. No less than 32,856 craters are represented in it, on a scale of seventy-five inches to a diameter. An additional help to lunar inquiries was provided at the same time in this country by the establishment, through the initiative of the late Mr. W. R. Birt, of the Selenographical Society.

But the strongest incentive to diligence in studying the rugged features of our celestial helpmate has been the idea of probable or actual variation in them. A change always seems to the inquisitive intellect of man like a breach in the defences of Nature's secrets, through which it may hope to make its way to the citadel. What is desirable easily becomes credible; and thus statements and rumours of lunar convulsions have successively, during the last hundred years, obtained credence, and successively, on closer investigation, been rejected. The subject is one as to which illusion is peculiarly easy. Our view of the moon's surface is a bird's-eye view. Its conformation reveals itself indirectly through irregularities in the distribution of light and darkness. The forms of its elevations and depressions can be inferred only from the shapes of the black, unmitigated shadows cast by them. But these shapes are in a state of perpetual and bewildering fluctuation, partly through changes in the angle of illumination, partly through changes in our point of view, caused by what are called the moon's "librations."[928] The result is, that no single observation can be exactly repeated by the same observer, since identical conditions recur only after the lapse of a great number of years.

Local peculiarities of surface, besides, are liable to produce perplexing effects. The reflection of earth-light at a particular angle from certain bright summits completely, though temporarily, deceived Herschel into the belief that he had witnessed, in 1783 and 1787, volcanic outbursts on the dark side of the moon. The persistent recurrence, indeed, of similar appearances under circumstances less amenable to explanation inclined Webb to the view that effusions of native light actually occur.[929] More cogent proofs must, however, be adduced before a fact so intrinsically improbable can be admitted as true.

But from the publication of Beer and Maedler's work until 1866, the received opinion was that no genuine sign of activity had ever been seen, or was likely to be seen, on our satellite; that her face was a stereotyped page, a fixed and irrevisable record of the past. A profound sensation, accordingly, was produced by Schmidt's announcement, in October, 1866, that the crater "Linne," in the Mare Serenitatis, had disappeared,[930] effaced, as it was supposed, by an igneous outflow. The case seemed undeniable, and is still dubious. Linne had been known to Lohrmann and Maedler, 1822-32, as a deep crater, five or six miles in diameter, the third largest in the dusky plain known as the "Mare Serenitatis"; and Schmidt had observed and drawn it, 1840-43, under a practically identical aspect. Now it appears under high light as a whitish spot, in the centre of which, as the rays begin to fall obliquely, a pit, scarcely two miles across, emerges into view.[931] The crateral character of this comparatively minute depression was detected by Father Secchi, February 11, 1867.

This is not all. Schroeter's description of Linne, as seen by him November 5, 1788, tallies quite closely with modern observation;[932] while its inconspicuousness in 1797 is shown by its omission from Russell's lunar globe and maps.[933] We are thus driven to adopt one of two suppositions: either Lohrmann, Maedler, and Schmidt were entirely mistaken in the size and importance of Linne, or a real change in its outward semblance supervened during the first half of the century, and has since passed away, perhaps again to recur. The latter hypothesis seems the more probable: and its probability is strengthened by much evidence of actual obscuration or variation of tint in other parts of the lunar surface, more especially on the floor of the great "walled plain" named "Plato."[934] From a re-examination with a 13-inch refractor at Arequipa in 1891-92, of this region, and of the Mare Serenitatis, Mr. W. H. Pickering inclines to the belief that lunar volcanic action, once apparently so potent, is not yet wholly extinct.[935]

An instance of an opposite kind of change was alleged by Dr. Hermann J. Klein of Cologne in March, 1878.[936] In Linne the obliteration of an old crater had been assumed; in "Hyginus N.," the formation of a new crater was asserted. Yet, quite possibly, the same cause may have produced the effects thought to be apparent in both. It is, however, far from certain that any real change has affected the neighbourhood of Hyginus. The novelty of Klein's observation of May 19, 1877, may have consisted simply in the detection of a hitherto unrecognised feature. The region is one of complex formation, consequently of more than ordinary liability to deceptive variations in aspect under rapid and entangled fluctuations of light and shade.[937] Moreover, it seems to be certain, from Messrs. Pratt and Capron's attentive study, that "Hyginus N." is no true crater, but a shallow, saucer-like depression, difficult of clear discernment.[938] Under suitable illumination, nevertheless, it contains, and is marked by, an ample shadow.[939]

In both these controverted instances of change, lunar photography was invoked as a witness; but, notwithstanding the great advances made in the art by De la Rue in this country, by Draper, and, above all, by Rutherford in America, without decisive results. Investigations of the kind began to assume a new aspect in 1890, when Professor Holden organised them at the Lick Observatory.[940] Autographic moon-pictures were no longer taken casually, but on system; and Dr. Weinek's elaborate study, and skilful reproductions of them at Prague,[941] gave them universal value. They were designed to provide materials for an atlas on the scale of Beer and Maedler's, of which some beautiful specimen-plates have been issued. At Paris, in 1894, with the aid of a large "equatoreal coude," a work of similar character was set on foot by MM. Loewy and Puiseux. Its progress has been marked by the successive publication of five instalments of a splendid atlas, on a scale of about eight feet to the lunar diameter, accompanied by theoretical dissertations, designed to establish a science of "selenology." The moon's formations are thus not only delineated under every variety of light-incidence, but their meaning is sought to be elicited, and their history and mutual relations interpreted.[942] Henceforth, at any rate, the lunar volcanoes can scarcely, without notice taken, breathe hard in their age-long sleep.

Melloni was the first to get undeniable heating effects from moonlight. His experiments, made on Mount Vesuvius early in 1846,[943] were repeated with like result by Zantedeschi at Venice four years later. A rough measure of the intensity of those effects was arrived at by Piazzi Smyth at Guajara, on the Peak of Teneriffe, in 1856. At a distance of fifteen feet from the thermomultiplier, a Price's candle was found to radiate just twice as much heat as the full moon.[944] Then, after thirteen years, in 1869-72, an exact and extensive series of observations on the subject were made by the present Earl of Rosse. The lunar radiations, from the first to the last quarter, displayed, when concentrated with the Parsonstown three-foot mirror, appreciable thermal energy, increasing with the phase, and largely due to "dark heat," distinguished from the quicker-vibrating sort by inability to traverse a plate of glass. This was supposed to indicate an actual heating of the surface, during the long lunar day of 300 hours, to about 500 deg. F.[945] (corrected later to 197 deg.),[946] the moon thus acting as a direct radiator no less than as a reflector of heat. But the conclusion was very imperfectly borne out by Dr. Boeddicker's observations with the same instrument and apparatus during the total lunar eclipse of October 4, 1884.[947] This initial opportunity of measuring the heat phases of an eclipsed moon was used with the remarkable result of showing that the heat disappeared almost completely, though not quite simultaneously, with the light. Confirmatory evidence of the extraordinary promptitude with which our satellite parts with heat already to some extent appropriated, was afforded by Professor Langley's bolometric observations at Allegheny of the partial eclipse of September 23, 1885.[948] Yet it is certain that the moon sends us a perceptible quantity of heat on its own account, besides simply throwing back solar radiations. For in February, 1885, Professor Langley succeeded, after many fruitless attempts, in getting measures of a "lunar heat-spectrum." The incredible delicacy of the operation may be judged of from the statement that the sum-total of the thermal energy dispersed by his rock-salt prisms was insufficient to raise a thermometer fully exposed to it one-thousandth of a degree Centigrade! The singular fact was, however, elicited that this almost evanescent spectrum is made up of two superposed spectra, one due to reflection, the other, with a maximum far down in the infra-red, to radiation.[949] The corresponding temperature of the moon's sunlit surface Professor Langley considers to be about that of freezing water.[950] Repeated experiments having failed to get any thermal effects from the dark part of the moon, it was inferred that our satellite "has no internal heat sensible at the surface"; so that the radiations from the lunar soil giving the low maximum in the heat-spectrum, "must be due purely to solar heat which has been absorbed and almost immediately re-radiated." Professor Langley's explorations of the terra incognita of immensely long wave-lengths where lie the unseen heat-emissions from the earth into space, led him to the discovery that these, contrary to the received opinion, are in good part transmissible by our atmosphere, although they are completely intercepted by glass. Another important result of the Allegheny work was the abolition of the anomalous notion of the "temperature of space," fixed by Pouillet at -140 deg. C. For space in itself can have no temperature, and stellar radiation is a negligible quantity. Thus, it is safe to assume "that a perfect thermometer suspended in space at the distance of the earth or moon from the sun, but shielded from its rays, would sensibly indicate the absolute zero,"[951] ordinarily placed at -273 deg. C.

A "Prize Essay on the Distribution of the Moon's Heat" (The Hague), 1891, by Mr. Frank W. Very, who had taken an active part in Professor Langley's long-sustained inquiry, embodies the fruits of its continuation. They show the lunar disc to be tolerably uniform in thermal power. The brighter parts are also indeed hotter, but not much. The traces perceived of a slight retention of heat by the substances forming the lunar surface, agreed well with the Parsonstown observations of the total eclipse of the moon, January 28, 1888.[952] For they brought out an unmistakable divergence between the heat and light phases. A curious decrease of heat previous to the first touch of the earth's shadow upon the lunar globe remains unexplained, unless it be admissible to suppose the terrestrial atmosphere capable of absorbing heat at an elevation of 190 miles. The probable range of temperature on the moon was discussed by Professor Very in 1898.[953] He concluded it to be very wide. Hotter than boiling water under the sun's vertical rays, the arid surface of our dependent globe must, he found, cool in the 14-day lunar night to about the temperature of liquid air.

Although that fundamental part of astronomy known as "celestial mechanics" lies outside the scope of this work, and we therefore pass over in silence the immense labours of Plana, Damoiseau, Hansen, Delaunay, G. W. Hill, and Airy in reconciling the observed and calculated motions of the moon, there is one slight but significant discrepancy which is of such importance to the physical history of the solar system, that some brief mention must be made of it.

Halley discovered in 1693, by examining the records of ancient eclipses, that the moon was going faster then than 2,000 years previously--so much faster, as to have got ahead of the place in the sky she would otherwise have occupied, by about two of her own diameters. It was one of Laplace's highest triumphs to have found an explanation of this puzzling fact. He showed, in 1787, that it was due to a very slow change in the ovalness of the earth's orbit, tending, during the present age of the world, to render it more nearly circular. The pull of the sun upon the moon is thereby lessened; the counter-pull of the earth gets the upper hand; and our satellite, drawn nearer to us by something less than an inch each year,[954] proportionately quickens her pace. Many thousands of years hence the process will be reversed; the terrestrial orbit will close in at the sides, the lunar orbit will open out under the growing stress of solar gravity, and our celestial chronometer will lose instead of gaining time.

This is all quite true as Laplace put it; but it is not enough. Adams, the virtual discoverer of Neptune, found with surprise in 1853 that the received account of the matter was "essentially incomplete," and explained, when the requisite correction was introduced, only half the observed acceleration.[955] What was to be done with the remaining half? Here Delaunay, the eminent French mathematical astronomer, unhappily drowned at Cherbourg in 1872 by the capsizing of a pleasure-boat, came to the rescue.[956]

It is obvious to anyone who considers the subject a little attentively, that the tides must act to some extent as a friction-brake upon the rotating earth. In other words, they must bring about an almost infinitely slow lengthening of the day. For the two masses of water piled up by lunar influence on the hither and farther sides of our globe, strive, as it were, to detach themselves from the unity of the terrestrial spheroid, and to follow the movements of the moon. The moon, accordingly, holds them against the whirling earth, which revolves like a shaft in a fixed collar, slowly losing motion and gaining heat, eventually dissipated through space.[957] This must go on (so far as we can see) until the periods of the earth's rotation and of the moon's revolution coincide. Nay, the process will be continued--should our oceans survive so long--by the feebler tide-raising power of the sun, ceasing only when day and night cease to alternate, when one side of our planet is plunged in perpetual darkness and the other seared by unchanging light.

Here, then, we have the secret of the moon's turning always the same face towards the earth. It is that in primeval times, when the moon was liquid or plastic, an earth-raised tidal wave rapidly and forcibly reduced her rotation to its present exact agreement with her period of revolution. This was divined by Kant[958] nearly a century before the necessity for such a mode of action presented itself to any other thinker. In a weekly paper published at Koenigsberg in 1754, the modern doctrine of "tidal friction" was clearly outlined by him, both as regards its effects actually in progress on the rotation of the earth, and as regards its effects already consummated on the rotation of the moon--the whole forming a preliminary attempt at what he called a "natural history" of the heavens. His sagacious suggestion, however, remained entirely unnoticed until revived--it would seem independently--by Julius Robert Mayer in 1848;[959] while similar, and probably original, conclusions were reached by William Ferrel of Allensville, Kentucky, in 1858.[960]

Delaunay was not then the inventor or discoverer of tidal friction; he merely displayed it as an effective cause of change. He showed reason for believing that its action in checking the earth's rotation, far from being, as Ferrel had supposed, completely neutralised by the contraction of the globe through cooling, was a fact to be reckoned with in computing the movements, as well as in speculating on the history, of the heavenly bodies. The outstanding acceleration of the moon was thus at once explained. It was explained as apparent only--the reflection of a real lengthening, by one second in 100,000 years, of the day. But on this point the last word has not yet been spoken.

Professor Newcomb undertook in 1870 the onerous task of investigating the errors of Hansen's Lunar Tables as compared with observations prior to 1750. The results, published in 1878,[961] proved somewhat perplexing. They tend, in general, to reduce the amount of acceleration left unaccounted for by Laplace's gravitational theory, and proportionately to diminish the importance of the part played by tidal friction. But, in order to bring about this diminution, and at the same time conciliate Alexandrian and Arabian observations, it is necessary to reject as total the ancient solar eclipses known as those of Thales and Larissa. This may be a necessary, but it must be admitted to be a hazardous expedient. Its upshot was to indicate a possibility that the observed and calculated values of the moon's acceleration might after all prove to be identical; and the small outstanding discrepancy was still further diminished by Tisserand's investigation, differently conducted, of the same Arabian eclipses discussed by Newcomb.[962] The necessity of having recourse to a lengthening day is then less pressing than it seemed some time ago; and the effect, if perceptible in the moon's motion, should, M. Tisserand remarked, be proportionately so in the motions of all the other heavenly bodies. The presence of the apparent general acceleration that should ensue can be tested with most promise of success, according to the same authority, by delicate comparisons of past and future transits of Mercury.

Newcomb further showed that small residual irregularities are still found in the movements of our satellite, inexplicable either by any known gravitational influence, or by any uniform value that could be assigned to secular acceleration.[963] If set down to the account of imperfections in the "time-keeping" of the earth, it could only be on the arbitrary supposition of fluctuations in its rate of going themselves needing explanation. This, it is true, might be found in very slight changes of figure,[964] not altogether unlikely to occur. But into this cloudy and speculative region astronomers for the present decline to penetrate. They prefer, if possible, to deal only with calculable causes, and thus to preserve for their "most perfect of sciences" its special prerogative of assured prediction.

FOOTNOTES:

[Footnote 796: Neueste Beytraege zur Erweiterung der Sternkunde, Bd. iii., p. 14 (1800).]

[Footnote 797: Ibid., p. 24.]

[Footnote 798: Phil. Trans., vol. xciii., p. 215.]

[Footnote 799: Mem. Roy. Astr. Soc., vol. vi., p. 116.]

[Footnote 800: Month. Not., vol. xix., pp. 11, 25.]

[Footnote 801: Ibid., vol. xxxviii., p. 398.]

[Footnote 802: Am. Jour. of Sc., vol. xvi., p. 124.]

[Footnote 803: Wash. Obs. for 1876, Part ii., p. 34.]

[Footnote 804: Pop. Astr., vol. ii., p. 168; Astr. Jour., No. 335.]

[Footnote 805: Astr. and Astrophysics, vol. xiii., p. 866.]

[Footnote 806: Ibid., p. 867.]

[Footnote 807: Month. Not., vol. xxiv., p. 18.]

[Footnote 808: Ibid., vol. xxiii., p. 234 (Challis).]

[Footnote 809: Untersuchungen ueber die Spectra der Planeten, p. 9.]

[Footnote 810: Sirius, vol. vii., p. 131.]

[Footnote 811: Potsdam Publ., No. 30; Astr. Nach., No. 3,171; Frost, Astr. and Astrophysics, vol. xii., p. 619.]

[Footnote 812: Zoellner and Winnecke made it=O.13, Astr. Nach., No. 2,245.]

[Footnote 813: Neueste Beytraege, Bd. iii., p. 50.]

[Footnote 814: Astr. Jahrbuch, 1804, pp. 97-102.]

[Footnote 815: Webb, Celestial Objects, p. 46 (4th ed.).]

[Footnote 816: L'Astronomie, t. ii., p. 141.]

[Footnote 817: Observations sur les Planetes Venus et Mercure, p. 87.]

[Footnote 818: Observatory, vol. vi., p. 40.]

[Footnote 819: Atti dell' Accad. dei Lincei, t. v. ii., p. 283, 1889; Astr. Nach., No. 2,944.]

[Footnote 820: Astr. Nach. No. 2,479.]

[Footnote 821: Memoirs Amer. Acad., vol. xii., No. 4, p. 464.]

[Footnote 822: Hist. de l'Astr., p. 682.]

[Footnote 823: Comptes Rendus, t. xlix., p. 379.]

[Footnote 824: Comptes Rendus, t. l., p. 40.]

[Footnote 825: Ibid., p. 46.]

[Footnote 826: Astr. Nach., Nos. 1,248 and 1,281.]

[Footnote 827: Comptes Rendus, t. lxxxiii., pp. 510, 561.]

[Footnote 828: Handbuch der Mathematik, Bd. ii., p. 327.]

[Footnote 829: Comptes Rendus, t. lxxxiii., p. 721.]

[Footnote 830: Nature, vol. xviii., pp. 461, 495, 539.]

[Footnote 831: Oppolzer, Astr. Nach., No. 2,239.]

[Footnote 832: Ibid., Nos. 2,253-4 (C. H. F. Peters).]

[Footnote 833: Ibid., Nos. 2,263 and 2,277. See also Tisserand in Ann. Bur. des Long., 1882, p. 729.]

[Footnote 834: See J. Bauschinger's Untersuchungen (1884), summarised in Bull. Astr., t. i., p. 506, and Astr. Nach., No. 2,594. Newcomb finds the anomalous motion of the perihelion to be even larger (43" instead of 38") than Leverrier made it. Month. Not., February, 1884, p. 187. Harzer's attempt to account for it in Astr. Nach., No. 3,030, is more ingenious than successful.]

[Footnote 835: Jour. des Scavans, December, 1667, p. 122.]

[Footnote 836: Elemens d'Astr., p. 525. Cf. Chandler, Pop. Astr., February, 1897, p. 393.]

[Footnote 837: _Beobachtungen ueber die sehr betraechtlichen Gebirge und Rotation der Venus_, 1792, p. 35. Schroeter's final result in 1811 was 23h. 21m. 7.977s. Monat. Corr., Bd. xxv., p. 367.]

[Footnote 838: Astr. Nach., No. 404.]

[Footnote 839: Rendiconti del R. Istituto Lombardo, t. xxiii., serie ii.]

[Footnote 840: Astr. Nach., No. 3,304.]

[Footnote 841: Bothkamp Beobachtungen, Heft ii., p. 120.]

[Footnote 842: Comptes Rendus, t. cxi., p. 542; t. cxxii., p. 395.]

[Footnote 843: Month. Not., vol. lvii., p. 402; Astr. Nach., No. 3,406.]

[Footnote 844: Mem. Spettroscopisti Italiani, t. xxv., p. 93; Nature, vol. liii., p. 306.]

[Footnote 845: Astr. Nach., No. 3,329.]

[Footnote 846: Ibid.]

[Footnote 847: Bull. de l'Acad. de Belgique, t. xxi., p. 452, 1891.]

[Footnote 848: Observations sur les Planetes Venus et Mercure, 1892.]

[Footnote 849: Astr. Nach., No. 3,300.]

[Footnote 850: Ibid., No. 3,332.]

[Footnote 851: Ibid., No. 3,314.]

[Footnote 852: Ibid., No. 3,170.]

[Footnote 853: Ibid., No. 3,641. The velocity of a point on the equator of Venus, if Brenner's period of 23h. 57m. were exact, would be 0.28 miles per second; but the displacements due to this rate would be doubled by reflection.]

[Footnote 854: Novae Observationes, p. 92.]

[Footnote 855: Mem. de l'Ac., 1700, p. 296.]

[Footnote 856: Phil. Trans., vol. lxxxiii., p. 201.]

[Footnote 857: Webb, Cel. Objects, p. 58.]

[Footnote 858: Month. Not., vol. xlii., p. 111.]

[Footnote 859: Bull. Ac. de Bruxelles, t. xliii., p. 22.]

[Footnote 860: Phil. Trans., vol. lxxxii., p. 309; Aphroditographische Fragmente, p. 85 (1796).]

[Footnote 861: Astr. Nach., No. 679.]

[Footnote 862: Month. Not., vol. xiv., p. 169.]

[Footnote 863: Ibid., vol. xxiv., p. 25.]

[Footnote 864: Am. Jour. of Sc., vol. xliii., p. 129 (2d ser.); vol. ix., p. 47 (3d ser.).]

[Footnote 865: Astroph. Jour., vol. ix., p. 284.]

[Footnote 866: Month. Not., vol. xxxvi., p. 347.]

[Footnote 867: Old and New Astronomy, p. 448.]

[Footnote 868: Hist. Phys. Astr., p. 431.]

[Footnote 869: Mem. Roy. Astr. Soc., vol. xlvii., pp. 77, 84.]

[Footnote 870: Astr. Reg., vol. xiii., p. 132.]

[Footnote 871: L'Astronomie, t. ii., p. 27; Astr. Nach., No. 2,021; Am. Jour. of Sc., vol. xxv., p. 430.]

[Footnote 872: Mem. Spettr. Ital., Dicembre, 1882; Am. Jour. of Sc., vol. xxv., p. 328.]

[Footnote 873: Comptes Rendus, t. cxvi., p. 288.]

[Footnote 874: Vogel, Spectra der Planeten, p. 15.]

[Footnote 875: Nature, vol. xix., p. 23.]

[Footnote 876: Nova Acta Acad. Naturae Curiosorum, Bd. x., 239.]

[Footnote 877: Astr. Jahrbuch, 1809, p. 164.]

[Footnote 878: Month Not., vol. xliii., p. 331.]

[Footnote 879: Report Brit. Ass., 1873, p. 407. The paper contains a valuable record of observations of the phenomenon.]

[Footnote 880: Photom. Untersuchungen, p. 301.]

[Footnote 881: Bothkamp Beobachtungen, Heft ii., p. 126.]

[Footnote 882: Astr. Nach., No. 2,818.]

[Footnote 883: Memoires de l'Acad. de Bruxelles, t. xlix., No. 5, 4to; Astr. Nach., No. 2,809; f. Schorr, Der Venusmond, 1875.]

[Footnote 884: Phil. Trans., 1839, 1841, 1842.]

[Footnote 885: Delaunay objected (Comptes Rendus, t. lxvii., p. 65) that the viscosity of the contained liquid (of which Hopkins took no account) would, where the movements were so excessively slow as those of the earth's axis, almost certainly cause it to behave like a solid. Lord Kelvin, however (Report Brit. Ass., 1876, ii., p. 1), considered Hopkins's argument valid as regards the comparatively quick solar semi-annual and lunar fortnightly nutations.]

[Footnote 886: Phil. Trans., cliii., p. 573.]

[Footnote 887: Report Brit. Ass., 1868, p. 494.]

[Footnote 888: Ibid., 1882, p. 474.]

[Footnote 889: Albrecht, Astr. Nach., No. 3,131.]

[Footnote 890: Astr. Jour., Nos. 248, 249.]

[Footnote 891: Ibid., No. 258.]

[Footnote 892: Month. Not., vol. lii., p. 336.]

[Footnote 893: Astr. Nach., No. 3,097; Phil. Trans., vol. clxxxvi., A., p. 469; Proc. Roy. Soc., vol. lix.]

[Footnote 894: See Chandler's searching investigations, Astr. Jour., Nos. 329, 344, 351, 392, 402, 406, 412, 446, 489, 490, 494, 495.]

[Footnote 895: Rees, Pop. Astr., No. 74, 1900.]

[Footnote 896: Nature, vol. lxi., p. 447; see also A. V. Baecklund, Astr. Nach., No. 3,787.]

[Footnote 897: Trans. Geol. Soc., vol. iii. (2d ser.), p. 293.]

[Footnote 898: See his Treatise on Astronomy, p. 199 (1833).]

[Footnote 899: Phil. Mag., vol. xxviii. (4th ser.), p. 121.]

[Footnote 900: Climate and Time, 1875; Discussions on Climate and Cosmology, 1885.]

[Footnote 901: See for a popular account of the theory, Sir R. Ball's The Cause of an Ice Age, 1892.]

[Footnote 902: See A. Woeikof, Phil. Mag., vol. xxi., p. 223.]

[Footnote 903: The Ice Age in North America, London, 1890.]

[Footnote 904: Phil. Trans., vol. lxviii., p. 783.]

[Footnote 905: Comptes Rendus, t. lxxvi., p. 954.]

[Footnote 906: Potsdam Publ., Nos. 22, 23.]

[Footnote 907: Phil. Trans., vol. clxxxii., p. 565; Adams Prize Essay for 1893.]

[Footnote 908: Denkschriften Akad. der Wiss. Wien, Bd. lxiv.; quoted by Poynting. Nature, vol. lxii., p. 404.]

[Footnote 909: Report on the Geodetic Survey of S. Africa, 1894.]

[Footnote 910: Nature, vol. lxii., p. 622; Hollis, Observatory, vol. xxiii., p. 337; Poincare, Comptes Rendus, July 23, 1900.]

[Footnote 911: Astr. Nach., No. 2,228.]

[Footnote 912: Young's Gen. Astr., p. 601.]

[Footnote 913: Astr. Constants, p. 195.]

[Footnote 914: The second volume was published at Gottingen in 1802.]

[Footnote 915: Ueber Rillen auf dem Monde, p. 13. Cf. The Moon, by T. Gwyn Elger, p. 20. W. H. Pickering, Harvard Annals, vol. xxxii., p. 249.]

[Footnote 916: The Moon, p. 73.]

[Footnote 917: Selen. Fragm., Th. ii., p. 399.]

[Footnote 918: Astr. Nach., No. 263 (1834); Pop. Vorl., pp. 615-620 (1838).]

[Footnote 919: Outlines of Astr., par. 431.]

[Footnote 920: Month. Not., vol. xxv., p. 61.]

[Footnote 921: Month. Not., vol. xxv., p. 264.]

[Footnote 922: Astroph. Jour., vol. vi., p. 422.]

[Footnote 923: Harvard Annals, vol. xxxii., p. 81.]

[Footnote 924: Astr. and Astrophysics, vol. xi., p. 778.]

[Footnote 925: Neison, The Moon, p. 25.]

[Footnote 926: Knowledge, vol. xvii., p. 85.]

[Footnote 927: Neison, The Moon, p. 104.]

[Footnote 928: The combination of a uniform rotational with an unequal orbital movement causes a slight swaying of the moon's globe, now east, now west, by which we are able to see round the edges of the averted hemisphere. There is also a "parallactic" libration, depending on the earth's rotation; and a species of nodding movement--the "libration in latitude"--is produced by the inclination of the moon's axis to her orbit, and by her changes of position with regard to the terrestrial equator. Altogether, about 2/11 of the invisible side come into view.]

[Footnote 929: Cel. Objects, p. 58 (4th ed.).]

[Footnote 930: Astr. Nach., No. 1,631.]

[Footnote 931: Cf. Leo Brenner, Naturwiss. Wochenschrift, January 13, 1895; Jour. Brit. Astr. Ass., vol. v., pp. 29, 222.]

[Footnote 932: Respighi, Les Mondes, t. xiv., p. 294; Huggins, Month. Not., vol. xxvii., p. 298.]

[Footnote 933: Birt, Ibid., p. 95.]

[Footnote 934: Report Brit. Ass., 1872, p. 245.]

[Footnote 935: Observatory, vol. xv., p. 250.]

[Footnote 936: Astr. Reg., vol. xvi., p. 265; Astr. Nach., No. 2,275.]

[Footnote 937: Lindsay and Copeland, Month. Not., vol. xxxix., p. 195.]

[Footnote 938: Observatory, vols. ii., p. 296; iv., p. 373. N. E. Green (Astr. Reg., vol. xvii., p. 144) concluded the object a mere "spot of colour," dark under oblique light.]

[Footnote 939: Webb, Cel. Objects, p. 101.]

[Footnote 940: Publ. Lick Observatory, vol. iii., p. 7.]

[Footnote 941: Ibid., p. 21; Mee, Knowledge, vol. xviii., p. 135.]

[Footnote 942: Comptes Rendus, t. cxxii., p. 967; Bull. Astr., August, 1899; Ann. Bureau des Long., 1898; Nature, vols. lii., p. 439; lvi., p. 280; lix., p. 304; lx., p. 491; Astroph. Jour. vol. vi., p. 51.]

[Footnote 943: Comptes Rendus, t. xxii., p. 541.]

[Footnote 944: Phil. Trans., vol. cxlviii., p. 502.]

[Footnote 945: Proc. Roy. Soc., vol. xvii., p. 443.]

[Footnote 946: Phil. Trans., vol. clxiii., p. 623.]

[Footnote 947: Trans. R. Dublin Soc., vol. iii., p. 321.]

[Footnote 948: Science, vol. vii., p. 9.]

[Footnote 949: Amer. Jour. of Science, vol. xxxviii., p. 428.]

[Footnote 950: "The Temperature of the Moon," Memoirs National Acad. of Sciences, vol. iv., p. 193, 1889.]

[Footnote 951: Temperature of the Moon, p. iii.; see also App. ii., p. 206.]

[Footnote 952: Trans. R. Dublin Soc., vol. iv., p. 481, 1891; Rosse, Proc. Roy. Institution, May 31, 1895.]

[Footnote 953: Astroph. Jour., vol. viii., pp. 199, 265.]

[Footnote 954: Airy, Observatory, vol. iii., p. 420.]

[Footnote 955: Phil. Trans., vol. cxliii., p. 397; Proc. Roy. Soc., vol. vi., p. 321.]

[Footnote 956: Comptes Rendus, t. lxi., p. 1023.]

[Footnote 957: Professor Darwin calculated that the heat generated by tidal friction in the course of lengthening the earth's period of rotation from 23 to 24 hours, equalled 23 million times the amount of its present annual loss by cooling. Nature, vol. xxxiv., p. 422.]

[Footnote 958: Saemmtl. Werke (ed. 1839), Th. vi., pp. 5-12. See also C. J. Monro's useful indications in Nature, vol. vii., p. 241.]

[Footnote 959: Dynamik des Himmels, p. 40.]

[Footnote 960: Gould's Astr. Jour., vol. iii., p. 138.]

[Footnote 961: Wash. Obs. for 1875, vol. xxii., App. ii.]

[Footnote 962: Comptes Rendus, t. cxiii., p. 669; Annuaire, Paris, 1892.]

[Footnote 963: Newcomb, Pop. Astr. (4th ed.), p. 101.]

[Footnote 964: Sir W. Thomson, Report Brit. Ass., 1876, p. 12.]