Elementary Text-book of Physics

Front matter

ELEMENTARY

TEXT-BOOK OF PHYSICS.

BY

Introduction

INTRODUCTION.

1. Divisions of Natural Science.—Everything which can affect our senses we call matter. Any limited portion of matter, however great or small, is called a body. All bodies, together with their unceasing changes, constitute Nature.

Natural Science makes us acquainted with the properties of bodies, and with the changes, or phenomena, which result from their mutual actions. It is therefore conveniently divided into two principal sections,—Natural History and Natural Philosophy.

The former describes natural objects, classifies them according to their resemblances, and, by the aid of Natural Philosophy, points out the laws of their production and development. The latter is concerned with the laws which are exhibited in the mutual action of bodies on each other.

These mutual actions are of two kinds: those which leave the essential properties of bodies unaltered, and those which effect a complete change of properties, resulting in loss of identity. Changes of the first kind are called physical changes; those of the second kind are called chemical changes. Natural Philosophy has, therefore, two subdivisions,—Physics and Chemistry.

Physics deals with all those phenomena of matter which are not directly related to chemical changes. Astronomy is thus a branch of Physics, yet it is usually excluded from works like the present on account of its special character.

lt is not possible, however, to draw sharp lines of demarcation between the variisus departments of Natural Science, for the suc pursuit of knowledge in any one of them requires some acquaintance with the others.

2. Methods.—The ultimate basis of all our knowledge of Nature is experience,—experience resulting from the action of bodies on our senses, and the consequent affections of our minds.

When a natural phenomenon arrests our attention, we call the result an observation. Simple observations of natural phenomena only in rare instances can lead to such complete knowledge as will suffice for a full understanding of them. An observation is the more complete, the more fully we apprehend the attending circumstances. We are generally not certain that all the circumstances which we note are conditions on which the phenomenon, in a given case, depends. In such cases we modify or suppress one of the circumstances, and observe the effect on the phenomenon. If we find a corresponding modification or failure with respect to the phenomenon, we conclude that the circumstance, so modified, is a condition. We may proceed in the same way with each of the remaining circumstances, leaving all unchanged except the single one purposely modified at each trial, and always observing the effect of the modification. We thus determine the conditions on which the phenomenon depends. In other words, we bring experiment to our aid in distinguishing between the real conditions on which a phenomenon depends, and the merely accidental circumstances which may attend it.

But this is not the only use of experiment. By its aid we may frequently modify some of the conditions, known to be conditions, in such ways that the phenomenon is not arrested, but so altered in the rate with which its details pass before us that they may be easily observed. Experiment also often leads to new phenomena, and to a knowledge of activities before unobserved. Indeed, by far the greater part of our knowledge of natural phenomena has been acquired by means of experiment. To be of value, experiments must be conducted with system, and so as to trace out the whole course of the phenomenon.

Having acquired our facts by observation and experiment we seek to find out how they are related; that is, to discover the laws which connect them. The process of reasoning by which we discover such laws is called induction. As we can seldom be sure that we have apprehended all the related facts, it is clear that our inductions must generally be incomplete. Hence it follows that oonclusions reached in this way are at best only probable; yet their probability becomes very great when we can discover no outstanding fact, and especially so when, regarded provisionally as true, they enable us to predict phenomena before unknown.

In conducting our experiments, and in reasoning upon them, we are often guided by suppositions suggested by previous experience. If the course of our experiment be in accordance with our supposition, there is, so far, a presumption in its favor. So, too, in reference to our reasonings: if all our facts are seen to be consistent with some supposition not unlikely in itself, we say it thereby becomes probable. The term hypothesis is usually employed instead of supposition.

Concerning the ultimate modes of existence or action, we know nothing whatever; hence, a law of nature cannot be demonstrated in the sense that a mathematical truth is demonstrated. Yet so great is the constancy of uniform sequence with which phenomena occur in accordance with the laws which we discover, that we have no doubt respecting their validity.

When we would refer a series of ascertained laws to some common agency, we employ the term theory. Thus we find in the "wave theory " of light, based on the hypothesis of a universal ether of extreme elasticity, satisfactory explanations of the laws of reflection, refraction, difEraction, polarization, etc.

3. Measurements.—All the phenomena of Nature occur in matter, and are presented to us in time and space. Time and space are fundamental conceptions: they do not admit of definition. Matter is equally indefinable: its distinctive characteristic is its persistence in whatever state of rest or motion it may happen to have, and the resistance which it offers to any attempt to change that state. This property is called inertia. It must be carefully distinguished from inactivity.

Another essential property of matter is impenetrability, or the property of occupying space to the exclusion of other matter.

We are almost constantly obliged, in physical science, to measure the quantities with which we deal. We measure a quantity when we compare it with some standard of the same kind. A simple number expresses the result of the comparison.

If we adopt arbitrary units of length, time, and mass (or quantity of matter), we can express the measure of all other quantities in terms of these so-called fundamental units. A unit of any other quantity, thus expressed, is called a derived unit.

It is convenient, in defining the measure of derived units, to speak of the ratio between, or the product of, two dissimilar quantities, such as space and time. This must always be understood to mean the ratio between, or the product of, the numbers expressing those quantities in the fundamental units. The result of taking such a ratio or product of two dissimilar quantities is a number expressing a third quantity in terms of a derived unit.

4. Unit of Length.—The unit of length usually adopted in scientific work is the centimetre. It is the one hundredth part of the length of a certain piece of platinum, declared to be a standard by legislative act, and preserved in the archives of France. This standard, called the metre, was designed to be equal in length to one ten-millionth of the earth's quadrant.

The operation of comparing a length with the standard is often difficult of direct accomplishment. This may arise from the minuteness of the object or distance to be measured, from the distant point at which the measurement is to end being inaccessible, or from the difficulty of accurately dividing our standard into very small fractional parts. In all such cases we have recourse to indirect methods, by which the difficulties are more or less completely obviated.

The vernier enables us to estimate small fractions of the unit of length with great convenience and accuracy. It consists of an accessory piece, fitted to slide on the principal scale of the instrument to which it is applied. A portion of the accessory piece, equal to minus one or plus one divisions of the principal scale, is divided into divisions. In the former case, the divisions are numbered in the same sense as those of the principal scale; in the latter, they are numbered in the opposite sense. In either case we can measure a quantity accurately to the one nth part of one of the primary divisions of the principal scale. Fig. 1 will make the construction and use of the vernier plain.

In Fig. 1, let 0, 1, 2, 3 ... 10 be the divisions on the vernier; let 0, 1, 2, 3 . . . 10 be any set of consecutive divisions on the principal scale.

If we suppose the of the vernier to be in coincidence with the limiting point of the magnitude to be measured, it is clear that, from the position shown in the figure, we have 29.7, expressing that magnitude to the nearest tenth; and since the sixth division of the vernier coincides with a whole division of the principal scale, we have of , or of a principal division to be added: hence the whole value is 29.76.

The micrometer screw is also much employed. It consists of a carefully cut screw, accurately fitting in a nut. The head of the screw carries a graduated circle, which can turn past a fixed line. This is frequently the straight edge of a scale with divisions equal in magnitude to the pitch of the screw. These divisions will then show through how many revolutions the screw is turned in any given trial; while the divisions on the graduated circle will show the fractional part of a revolution, and consequently the fractional part of the pitch that must be added. If the screw be turned through revolutions, as shown by the scale, and through an additional fraction, as shown by the divided circle, it will pass through times the pitch of the screw, and an additional fraction of the pitch determined by the ratio of the number of divisions read from 0 on the divided circle to the whole number into which it is divided.

The cathetometer is used for measuring differences of level. A graduated scale is cut on an upright bar, which can turn about a vertical axis. Over this bar slide two accurately fitting pieces, one of which can be clamped to the bar at any point, and serve as the fixed bearing of a micrometer screw. The screw runs in a nut in the second piece, which has a vernier attached, and carries a horizontal telescope furnished with cross-hairs. The telescope having been made accurately horizontal by means of a delicate level, the cross-hairs are made to cover one of the two points, the difference of level between which is sought, and the reading upon the scale is taken; the fixed piece is then undamped, and the telescope raised or lowered until the second point is covered by the cross-hairs, and the scale reading is again taken. The difference of scale reading is the difference of level sought.

The dividing engine may be used for dividing scales or for comparing lengths. In its usual form it consists essentially of a long micrometer screw, carrying a table, which slides, with a motion accurately parallel with itself, along fixed guides, resting on a firm support. To this table is fixed an apparatus for making successive cuts upon the object to be graduated.

The object to be graduated is fastened to the fixed support. The table is carried along through any required distance determined by the motion of the screw, and the cuts can be thus made at the proper intervals.

The same instrument, furnished with microscopes and accessories, may be employed for comparing lengths with a standard. It may then be called a comparator.

The spherometer is a special form of the micrometer screw. As its name implies, it is primarily used for measuring the curvature of spherical surfaces.

It consists of a screw with a large head, divided into a great number of parts, turning in a nut supported on three legs terminating in points, which form the vertices of an equilateral triangle. The axis of revolution of the screw is perpendicular to the plane of the triangle, and passes through its centre. The screw ends in a point which may be brought into the same piano with the points of the legs. This is done by placing the legs on a truly plane surface, and turning the screw till its point is just in contact with the surface. The sense of touch will enable one to decide with great nicety when the screw is turned far enough. If, now, we note the reading of the divided scale and also that of the divided head, and then raise the screw, by turning it backward, so that the given curved surface may exactly coincide with the four points, we can compute the radius of curvature from the difference of the two readings and the known length of the side of the triangle formed by the points of the tripod.

5. Unit of Time.— The unit of time is the mean time second, which is the of a mean solar day. We employ the clock, regulated by the pendulum or the chronometer balance, to indicate seconds. The clock, while sufficiently accurate for ordinary use, must for exact investigations be frequently corrected by astronomical observations.

Smaller intervals of time than the second are measured by causing some vibrating body, as a tuning-fork, to trace its path along some suitable surface, on which also are recorded the beginning and end of the interval of time to be measured. The number of vibrations traced while the event is occurring determines its duration in known parts of a second.

In estimating the duration of certain phenomena giving rise to light, the revolving mirror may be employed. By its use, with proper accessories, intervals as small as forty billionths of a second have been estimated.

6. Unit of Mass.— The unit of mass usually adopted in scientific work is the gram. It is equal to the one-thousandth part of a certain piece of platinum, called the kilogram, preserved as a standard in the archives of France. This standard was intended to be equal in mass to one cubic decimetre of water at its greatest density.

Masses are compared by means of the balance, the construction of which will be discussed hereafter.

7. Measurement of Angles.— Angles are usually measured by reference to a divided circle graduated on the system of division upon which the ordinary trigonometrical tables are based. A pointer or an arm turns about the centre of the circle, and the angle between two of its positions is measured in degrees on the arc of the circle. For greater accuracy, the readings may be made by the help of a vernier. To facilitate the measurement of an angle subtended at the centre of the circle by two distant points, a telescope with cross-hairs is mounted on the movable arm.

In theoretical discussions the unit of angle often adopted is the radian, that is, the angle subtended by the arc of a cirule equal to its radius. In terms of this unit, a semi-circumference equals π = 3.141592. The radian, measured in degrees, is 57° 17' 44.8."

8. Dimensions of Units.— Any derived unit may be represented by the product of certain powers of the symbols representing the fundamental units of length, mass, and time.

Any equation showing what powers of the fundamental units enter into the expression for the derived unit is called its dimensional equation. In a dimensional equation time is represented by , length by , and mass by . To indicate the dimensions of any quantity, the symbol representing that quantity is enclosed in brackets.

For example, the unit of area varies as the square of the unit of length; hence its dimensional equation is . In like manner, the dimensional equation for volume is .

9. Systems of Units.— The system of units adopted in this book, and generally employed in scientific work, based upon the centimetre, gram, and second, as fundamental units, is called the centimetre-gram-second system or the C. G. S. system. A system based upon the foot, grain, and second was formerly much used in England. One based upon the millimetre, milligram, and second is still sometimes used in Germany.

Heat, Chapter II. Transfer of Heat

CHAPTER II.

TRANSFER OF HEAT.

172. Transfer of Heat.—In the preceding discussions it has been assumed that heat may be transferred from one body to another, and that if two bodies in contact be at different temperatures, heat will be transferred from the hotter to the colder body. In general, if transfer of heat be possible in any system, heat will pass from the hotter to the colder parts of the system, and the temperature of the system will tend to become uniform. There are three ways in which this transfer is accomplished, called respectively convection, conduction, and radiation.

173. Convection.—If a vessel containing any fluid be heated at the bottom, the bottom layers become less dense than those above, producing a condition of instability. The lighter portions of the fluid rise, and the heavier portions from above, coming to the bottom, are in their turn heated. Hence continuous currents are caused. This process is called convection. By this process, masses of fluid, although fluids are poor conductors, may be rapidly heated. Water is often heated in a reservoir at a distance from the source of heat by the circulation produced in pipes leading to the source of heat and back. The winds and the great currents of the ocean are convection currents. An interesting result follows from the fact that water has a maximum density (§ 190). When the water of lakes cools in winter, currents are set up and maintained, so long as the surface water becomes more dense by cooling, or until the whole mass reaches 4°. Any further cooling makes the surface water lighter. It therefore remains at the surface, and its temperature rapidly falls to the freezing-point, while the great mass of the water remains at the temperature of its maximum density.

174. Conduction.—If one end of a metal rod be heated, it is found that the heat travels along the rod, since those portions at a distance from the source of heat finally become warm. This process of transfer of heat from molecule to molecule of a body, while the molecules themselves retain their relative places, is called conduction.

In the discussion of the transfer of heat by conduction it is assumed as a principle, borne out by experiment, that the flow of heat between two very near parallel planes, drawn in a substance, is proportional to the difference of temperature between those planes, or that the flow of heat across a plane is proportional to the rate of fall of temperature across that plane.

175. Flow of Heat across a Wall.—The simplest body in which the flow of heat can be studied is a wall of homogeneous material bounded by two parallel infinite planes, one of which is kept at the temperature and the other at the temperature we represent the distance between the planes or the thickness of the wall by We suppose that the flow of heat across this wall has continued so long that it has become steady, or that the temperatures at all points have assumed flnal values. Manifestly the temperature at all points in any plane parallel with the faces of the wall is the same, and the same amount of heat passes across any one such plane as passes across any other. We conclude therefore by the fundamental principle assumed (§ 174) that the rate of change of temperature across each plane in the wall is the same, or that the change of temperature throughout the wall from one face to the other is uniform; the rate of change of temperature is therefore given by where it has been assumed that is the higher temperature. If represent the distance of any plane in the wall from the hotter surface, the fall of temperature between it and the hotter surface is and the temperature of the plane is The confirmation by experiment of this law of temperature distribution in a wall is a warrant for our assumption of the fundamental principle of the flow of heat.

176. Conductivity.—If, now, we consider a prism extending across the wall, bounded by planes perpendicular to the exposed surfaces, and represent the area of its exposed bases by the quantity of heat which flows in a time through this prism may be represented by where is a constant depending upon the material of which the wall is composed. is the conductivity of the substance, and may be defined as the quantity of heat which in unit time flows through a section of unit area in a wall of the substance whose thickness is unity, when its exposed surfaces are maintained at a difference of temperature of one degree; or, in other words, it is the quantity of heat which in unit time flows through a section of unit area in a substance, where the rate of fall of temperature at that section is unity. In the above discussions the temperatures and are taken as the actual temperatures of the surfaces of the wall. If the colder surface of the wall be exposed to air of temperature to which the heat which traverses it is given up, will be greater than The difference will depend upon the quantity of heat which flows, and upon the facility with which the surface parts with heat.

177. Flow of Heat along a Bar.—If a prism of a substance have one of its bases maintained at a temperature while the other base and the sides are exposed to air at a lower temperature, the conditions of uniform fall of temperature no longer exist, and the amount of heat'which flows through the different sections is no longer the same: but the amount of heat which flows through any section is still proportional to the rate of fall of temperature at that section, and is equal to the heat which escapes from the portion of the bar beyond the section.

178. Measurement of Conductivity.—A bar heated at one end furnishes a convenient means of measuring conductivity. In Fig. 69 let represent a bar heated at Let the ordinates , represent the excess of temperatures above the temperature of the air at the points from which they are drawn. These temperatures may be determined by means of thermometers inserted in cavities in the bar, or by means of a thermopile. Draw the curve through the summits of the ordinates. The inclination of this curve at any point represents the rate of fall of temperature at that point. The ordinates to the line drawn tangent to the curve at the point show what would be the temperatures at various points of the bar if the fall were uniform and at the same rate as at It shows that, at the rate of fall at the bar would at be at the temperature of the air; or, in the length the fall of temperature would equal the amount represented by The rate of fall is, therefore, If represent the quantity of heat passing the section at in the unit time, we have, from § 176, is equal to the quantity of heat that escapes in unit time from all that portion of the bar beyond It may be found by heating a short piece of the same bar to a high temperature, allowing it to cool under the same conditions that surround the bar and observing its temperature from minute to minute as it falls. These observations furnish the data for computing the quantity of heat which escapes per minute from unit length of the bar at different temperatures. It is then easy to compute the amount of heat that escapes per minute from each portion, , etc., of the bar beyond each portion being taken so short that its tempera throughout may, without sensible error, be considered uniform and the same as that at its middle point. Summing up all these quantities, we obtain the quantity which passes the section in the unit time. Then 179. Conductivity diminishes as Temperature rises.—By the method described above, Forbes determined the conductivity of a bar of iron at points at different distances from the heated end, and found that the conductivity is not the same at all temperatures, but is greater as the temperature is lower.

180. Conductivity of Crystals.—The conductivity of crystals of the isometric system is the same in all directions, but in crystals of the other systems it is not so. In a crystal of Iceland spar the conductivity is greatest in the direction of the axis of symmetry, and equal in all directions in a plane at right angles to that axis.

181. Conductivity of Non-homogeneous Solids.—De la Rive and De Candolle were the first to show that wood conducts heat better in the direction of the fibres than at right angles to them. Tyndall, by experimenting upon cubes cut from wood, has shown that the conductivity has a maximum value parallel to the fibres, a minimum value at right angles to the fibres and parallel to the annual layers. Feathers, fur, and the materials of clothing are poor conductors because of their want of continuity.

182. Conductivity of Liquids.—The conductivity of liquids can be measured, in the same way as that of solids, by noting the fall of temperature at various distances from the source of heat in a column of liquid heated at the top. Great care must be taken in these experiments to avoid errors due to convection currents.

Liquids are generally poor conductors.

183. Radiation.—We have now considered those cases in which there is a transfer of heat between bodies in contact. Heat is also transferred between bodies not in contact. This is effected by a process called radiation, which will be subsequently considered.

Magnetism and Electricity, Chapter IV. Chemical Relations of the Current

CHAPTER IV.

CHEMICAL RELATIONS OF THE CURRENT.

279. Electrolysis.—It has been already mentioned that, in certain cases, the existence of an electrical current in a circuit is accompanied by the decomposition into their constituents of chemical compounds forming part of the circuit. This process, called electrolysis, must now be considered more fully. It is one of those treated generally in § 277, in which work other than heating the circuit is done by the current. That work is done by the decomposition of a body the constituents of which, if left to themselves, tend to recombine, is evident from the fact that, if they be allowed to recombine, the combination is always attended with the evolution of heat or the appearance of some other form of energy. The amount of heat developed, or the energy gained, is, of course, the measure of the energy lost by combination or necessary to decomposition.

Those bodies which exhibit electrolysis are always such as have considerable freedom of motion among their molecules. Ordinarily, they are liquids or solids in solution or fused. The discharge through gases is also probably accompanied by electrolysis. Bodies which can be decomposed were called by Faraday, to whom the nomenclature of this subject is due, electrolytes. The current is usually introduced into the electrolyte by solid terminals called electrodes. The one at the higher potential is called the positive electrode or anode; the other, the negative electrode, or cathode. The two constituents into which the electrolyte is decomposed are called ions. One of them appears at the anode and is called the anion, the other at the cathode and is called the cation.

For the sake of clearness we will describe some typical cases of electrolysis. The original observation of the evolution of gas when the current was passed through a drop of water, made by Nicholson and Carlisle, was soon modified by Carlisle in a way which is still generally in use. Two platinum electrodes are immersed in water slightly acidulated with sulphuric acid, and tubes are arranged above them so that the gases evolved can be collected separately. When the current is passing, bubbles of gas appear on the electrodes. When they are collected and examined, the gas which appears at the anode is found to be oxygen, and that which appears at the cathode to be hydrogen. The quantities evolved are in the proportion to form water. This appears to be a simple decomposition of water into its constituents, but it is probable that the acid in the water is first decomposed, and that the constituents of water are evolved by a secondary chemical reaction.

An experiment performed by Davy, by which he discovered the elements potassium and sodium, is a good example of simple electrolysis. He fused caustic potash in a platinum dish, which was made the anode, and immersed in the fused mass a platinum wire as cathode. Oxygen was then evolved at the anode, and the metal potassium was deposited on the cathode. This is the type of a large number of decompositions.

If, in a solution of zinc sulphate, a plate of copper be made the anode and a plate of zinc the cathode, there will be zinc deposited on the cathode and copper taken from the anode, so that, after the process has continued for a time, the solution will contain a quantity of cupric sulphate. This is a case similar to the electrolysis of acidulated water, in which the simple decomposition of the electrolyte is modified by secondary chemical reactions.

If two copper electrodes be immersed in a solution of cupric sulphate, copper will be removed from the anode and deposited on the cathode, without any important change occuring in the character or concentration of the electrolyte. This is an example of the special case in which the secondary reactions in the electrolyte exactly balance the work done by the current in decomposition, so that on the whole no chemical work is done.

280. Faraday's Laws.—The researches of Faraday in electrolysis developed two laws, which are of great importance in the theory of chemistry as well as in electricity: