Fig.14.Fig. 14.
Fig. 14.
But the most wonderful of these mechanical arrangements is the machine for analysing the curves drawn by a self-registering tide gauge, so as to exhibit the constants of the harmonic curves, and thus enable the prediction of tidal heights to be carried out either by the tide-predicting machine, or by calculation. One day in 1876, Thomson remarked to his brother, James Thomson, then Professor of Engineering at Glasgow, that all he required for the construction of a tidal analyser was a form of integrating machine more satisfactory for his purpose than the usual type of integrator employed by surveyors and naval architects. James Thomson at once replied that he had invented, a long time before, what he called a disk-globe-cylinder-integrator. This consisted of a brass disk, with its plane inclined to the horizontal, which could be turned about its axis by a wheel gearing in teeth on the edge of the disk, and driven by the operator in a manner which will presently appear. Parallel and close to the disk, but not touching it, was placed a horizontal cylinderof brass, about 2 inches in diameter (called the registering cylinder), and between the disk and this cylinder was laid a metal ball about 2½ inches in diameter. When the disk was kept at rest, and the ball was rolled along between the cylinder and disk, the trace of its rolling on the latter was a straight horizontal line passing through the centre. Supposing then that the point of contact of the ball with the disk was on one side, at a distance from the centre, and that the disk was then turned, the ball was by the friction between it and the disk made to roll, and so to turn the cylinder. The angular velocity of rolling, and therefore the angular velocity of the cylinder, was proportional to the speed of the part of the disk in contact with it, that is, toy. It was also proportional to the speed of turning of the disk.
The mode by which this machine effects an integration will now be evident. Imagine the area to be found to lie between a curve and a straight datum line, drawn on a band of paper. This is stretched on a large cylinder, with the datum line round the cylinder. We call this the paper-cylinder. The distances of the different points of the curve from the datum line are values ofy. A horizontal bar parallel to the cylinder carries a fork at one end and a projecting style at the other. The globe just fits between the prongs of the fork, and when the bar is moved in the direction of its length carries the ball along the disk and cylinder. When the style at the other end is on the datum line, the centre of the ball is at the centre of the disk, and the turning of the disk does not turn the cylinder. When the bar is displaced in the line of its own length to bring the style from the datum line to a point on the curve, the ball is displaceda distancey, and there is a corresponding turning of the cylinder by the action of the ball. In the use of the instrument the paper-cylinder is turned by the operator while the style is kept on the curve, and the disk is turned by the gearing already referred to, which is driven by a shaft geared with that of the paper-cylinder. Thus the displacement of the ball is alwaysy, the ordinate of the curve, and for any displacementdxalong the datum line, the registering cylinder is turned through an angle proportional toydx. Thus any finite angle turned through is proportional to the integral ofydxfor the corresponding part of the curve: a scale round one end of the registering cylinder gives that angle. Thomson immediately perceived that this extremely ingenious integrating machine was just what he required for his purpose. The curve of tidal heights drawn (on a reduced scale, of course) by a tide-gauge, is really the resultant of a large number of simple curves, represented by a series of harmonic terms, the coefficients of which are certain integrals. The problem is the evaluation of these integrals; and the method usually employed is to obtain them by measurement of ordinates of the curve and an elaborate process of calculation. But one of them is simply the integral area between the curve and the datum line corresponding to the mean water level, and the others are the integrals of quantities of the typeysinnx.dx, whereyis the ordinate of the curve, andna number inversely proportional to the period of the tidal constituent represented by the term.
All that was necessary, in order to give the integral of a termysinnx.dx, was to make the disk oscillate about its axis as the paper-cylinder was turned throughan angle proportional tox. Thus one disk, globe, and cylinder was arranged exactly as has been described for the integral ofydx, and with this as many others as there were harmonic terms to be evaluated from the curve were combined as follows. The disks were placed all in one plane with their centres all on one horizontal line, and the cylinders with their axes also in line, and a single sliding bar, with a fork for each globe, gave in each case the displacementyfrom the centre of the disk.
The requisite different speeds of oscillation were given to the disks by shafts geared with the paper-cylinder, by trains of wheels cut with the proper number of teeth for the speed required.
Thus the angles turned through by the registering cylinders when a curve on the paper-cylinder was passed under the style were proportional to the integrals required, and it was only necessary to calibrate the graduation of the scales of these cylinders by means of known curves to obtain the integrals in proper units.
One of these machines, which analyses four harmonic constituents, is in the Natural Philosophy Department at Glasgow; a much larger machine, to analyse a tidal curve containing five pairs of harmonic terms, or eleven constituents in all, was made for the British Association Committee on Tidal Observations, and is probably now in the South Kensington Museum.
But still more remarkable applications which Thomson made of his brother's integrating machine were to the mechanical integration of linear differential equations, with variable coefficients, to the integration of the general linear differential equation of any order,and, finally, to the integration of any differential equation of any order.
These applications were all made in a few days, almost in a few hours, after James Thomson first described the elementary machine, and papers containing descriptions of the combinations required were at once dictated by Thomson to his secretary, and despatched for publication. Very possibly he had thought out the applications to some extent before; but it is unlikely that he had done so in detail. But, even if it were so, the connection of a series of machines by the single controlling bar, and the production of the oscillations of the disks, all controlled, as they were, by the motion of a simple point along the curve, so as to give the required Fourier coefficients, were almost instantaneous, and afford an example of invention amounting to inspiration.
There should be noticed here also the geometrical slide for use in safety-valves, cathetometers and other instruments, and the hole-slot-and-plane mode of so supporting an instrument now used in all laboratories. These were Thomson's inventions, and their importance is insisted on in theNatural Philosophy.
In Part II, the principal subjects treated are attractions, elasticity, such great hydrostatical examples as the equilibrium theory of the tides and the equilibrium of rotating liquid spheroids, and such problems of astronomical and terrestrial dynamics as the distribution of matter in the earth, with the bearing on this subject of the precession of the equinoxes, tidal friction, the earth's rigidity, the effects of elastic tides, the secular cooling of the earth, the age of the earth, andthe "age of the sun's heat." Of these, with the exception of the age of the earth, we shall not attempt to give any account. The importance of the original contributions to elasticity contained in the book is indicated by the large space devoted to theNatural Philosophyin Professor Karl Pearson's continuation of Todhunter'sHistory of Elasticity. The heavy task of editing Part II was performed mainly by Sir George Darwin, who made many notable additions from his own researches to the matter contained in the first edition.
In the next chapter an attempt will be made to present Thomson's views on the subject of the age of the earth. These, when they were published, attracted much attention, and received a good deal of hostile criticism from geologists and biologists, whose processes they were deemed to restrict to an entirely inadequate period of time.
Thomson in his lectures and otherwise gave a great deal of attention to the motion of gyrostats, and to the effect of the inclusion of gyrostats in a system on its properties. Reference has been made to the treatment of "gyrostatic domination" in "Thomson and Tait." A gyrostat consists of a disk or wheel with a massive rim, which revolves within a case or framework, by which the whole arrangement can be moved about, or supported, without interfering with the wheel. The ordinary toy consisting of wheel with a massive rim, and a light frame, is an example. But much larger and more carefully made instruments, in which the wheelis entirely enclosed, give the most interesting experiments. The body seems to have its properties entirely altered by the rotation of the wheel, and of course the case prevents any outward change from being visible.
Fig. 15.Fig. 15.
Fig. 15.
Figure 15 shows one form of gyrostat mounted on a horizontal frame, held in the hands of an experimenter. The axis of the fly-wheel is vertical within the tubular part of the case; the fly-wheel is within the part on which is engraved an arrow-head to show the direction of rotation. Round the case in the plane of the wheel is a projecting rim sharpened to an edge, on which the gyrostat can be supported in other experiments. To the rim are screwed two projecting pivots, which can turn in bearings on the two sides of the frame as shown. The centre of mass of the wheel is on the level of these pivots, so that the instrument will remain with either end of the axis up.
If the fly-wheel be not in rotation, the experimenter can carry the arrangement about, and the fly-wheel and case move with it as if the gyrostat were merelyan ordinary rigid body. But now remove the gyrostat from the frame, and set the wheel in rotation. This is done by an endless cord wrapped round a small pulley fast on the axle (to which access is obtained by a hole just opposite in the case) and passed also round a larger pulley on the shaft of a motor. When the motor is started the cord must be tightened only very gently at first, so that it slips on the pulley, otherwise the motor would be retarded, and possibly burned by the current. The fly-wheel gradually gets up speed, and then the cord can be brought quite tight so that no slipping occurs. When the speed is great enough the cord is cut with a stroke from a sharp knife and runs out.
The gyrostat is now replaced on its pivots in the frame, with its axis vertical, and moved about as it was before. If the experimenter, holding the frame as shown, turns round in the direction of the arrow, which is that of rotation, nothing happens. If, however, he turns round the other way, the gyrostat immediately turns on its pivots so as to point the other end of the axis up. If the experimenter continues his turning motion, the gyrostat is now quiescent: for it is being carried round now in the direction of rotation. Thus, with no gravitational stability at all (since the centre is on a level with the pivots) the gyrostat is in stable equilibrium when carried round in the direction of rotation, but is in unstable equilibrium when carried round the opposite way.
Thus, if the observer knew nothing of the rotation of the fly-wheel, and could see and feel only the outside of the case, the behaviour of the instrument might well appear very astonishing.
This is a case of what Thomson and Tait call "gyrostatic domination," which is treated very fully in their Sections 345 (vi) to 345 (xxviii) of Part I. It may be remarked here that this case of motion may be easily treated mathematically in an exceedingly elementary manner, and the instability of the one case, and the stability of the other, made clear to the beginner who has only a notion of the composition of angular momenta about different axes.
A year or two ago it was suggested by Professor Pickering, of Harvard, that the fact that the outermost satellite of Saturn revolves in the direction opposite to the planet's rotation, may be due to the fact that originally Saturn rotated in the direction of the motion of this moon, but inasmuch as his motion round the sun was opposite in direction to his rotation, he was turned, so to speak, upside down, like the gyrostat! The other satellites, it is suggested, were thrown off later, as their revolution is direct. Professor Pickering refers to an experiment (similar to that described above) which he gives as new. Thomson had shown this experiment for many years, as an example of the general discussion in "Thomson and Tait," and its theory had already been explicitly published.21
Many other experiments with gyrostats used to be shown by Thomson to visitors. Many of these are indicated in "Thomson and Tait." The earth's precessional motion is a gyrostatic effect due to the differential attraction of the sun, which tends to bring the plane of the equator into coincidence with the ecliptic, and so alters the direction of the axis of rotation. Old students will remember the balancedglobe—with inclined material axis rolling round a horizontal ring—by which the kinematics of the motion could be studied, and the displacement of the equinoxes on the ecliptic traced.
Fig. 16.Fig. 16.
Fig. 16.
Another example of the gyrostatic domination discussed in "Thomson and Tait" is given in the very remarkable address entitled "A Kinetic Theory of Matter," which Sir William Thomson delivered to Section A of the British Association at Montreal, in 1884. Figure 16 shows an ordinary double "coach spring," the upper and lower members of which carry two hooked rods as shown. If the upper hook is attached to a fixed support, and a weight is hung on the lower, the spring will be drawn out, and the arrangement will be in equilibrium under a certain elongation. If the weight be pulled down furtherand then left to itself, it will vibrate up and down in a period depending upon the equilibrium elongation produced by the weight. The same thing will happen if a spiral spring be substituted for the coach spring. A spherical case, through which the hooked rods pass freely, hides the internal parts from view.
Fig. 17.Fig. 17.
Fig. 17.
Figure 17 shows two hooked rods, as in the former case, attached by swivels to two opposite corners of a frame formed of four rods jointed together at their ends. Each of these is divided in the middle for the insertion of a gyrostat, the axis of which is pivoted on the adjacent ends of the two halves of the rod. A spherical case, indicated by the circle, again hides the internal arrangement from inspection, but permits the hooked rods to move freely up and down. The swivels allow the frame, gyrostats and all, to be turned about the line of the hooks.
If now the gyrostats be not in rotation, the frame will be perfectly limp, and will not in the least resist pull applied by a weight. But if the gyrostats be rotated in the directions shown by the circles, with arrowheads drawn round the rods, there will be angular momentum of the whole system about the line joining the hooks, and if a weight or a force be applied to pull out the frame along that line, the pull will be resisted just as it was in the other case by the spring. Moreover, equilibrium will be obtained with an elongation proportional to the weight hung on, and small oscillations will be performed just as if there were a spring in the interior instead of the gyrostats.
According as the frame is pulled out, or shortened, the angular momentum of the gyrostats about the line joining the hooks is increased or diminished, and the frame, carrying the gyrostats with it, turns about the swivels in one direction or the other, at the rate necessary to maintain the angular momentum at a constant value. But this will not be perceived from without.
The rotation of the fly-wheels thus gives to the otherwise limp frame the elasticity which the spring possesses; without dissection of the model the difference cannot be perceived. This illustrates Thomson's idea that the elasticity of matter may be due to motion of molecules or groups of molecules of the body, imbedded in a connecting framework, deformed by applied forces as in this model, and producing displacements which are resisted in consequence of the motion.
And here may be mentioned also Thomson's explanation of the phenomenon, discovered by Faraday, of the rotation of the plane of a beam of polarised lightwhich is passed along the lines of force of a magnetic field. This rotation is distinct altogether from that which is produced when polarised light is passed along a tube filled with a solution of sugar or tartaric acid. If the ray be reflected after passage, and made to retraverse the medium, the rotation is annulled in the latter case, it is doubled in the former. This led Thomson to the view that in sugar, tartaric acid, quartz, etc., the turning is due to the structure of the substance, and in the magnetic field to rotation already existing in the medium. He used to say that a very large number of minute spiral cavities all in the same direction, and all right-handed or all left-handed, in the sugar or quartz, would give the effect; on the other hand, the magnetic phenomenon could only be produced by some arrangement analogous to a very large number of tops, or gyrostats, imbedded in the medium with their axes all in one direction (or preponderatingly so) and all turning the same way. The rotation of these tops or gyrostats Thomson supposed to be caused by the magnetic field, and to be essentially that which constitutes the magnetisation of the medium.
Let the frame of the gyrostatic spring-balance described above, turn round the line joining the hooks so as to exactly compensate, by turning in the opposite direction, the angular momentum about that line given by the fly-wheels; then the arrangement will have no angular momentum on the whole; and a large number of such balances, all very minute and hooked together, will form a substance without angular momentum in any part. But now by the equivalent of a magnetic force along the lines of the hooks, let a different angularturning of the frames be produced; the medium will possess a specific angular momentum in every part. If a wave of transverse vibrations which are parallel to one direction (that is, if the wave be plane-polarised) enter the medium in the direction of the axes of the frames, the direction of vibration will be turned as the wave proceeds, that is, the plane of polarisation will be turned round.
More recent research has shown an effect of a magnetic field on the spectrum of light produced in the field, and viewed with a spectroscope in a direction at right angles to the field—the Zeeman effect, as it is called—and the explanation of this effect by equations of moving electric charges, which are essentially gyrostatic equations, is suggestive of an analogy or correspondence between the systems of moving electrons which constitute these charges, and some such gyrostatic molecules as Thomson imagined. It has been pointed out that the Zeeman effect, in its simple forms at least, can be exactly imitated by the motion of an ordinary pendulum having a gyrostat in its bob, with its axis directed along the suspension rod.22
In the ten years from 1863 to 1873 Thomson was extremely busy with literary work. In 1872, five years after the publication of the treatise onNatural Philosophy, and just before the appearance of theElements, Messrs. Macmillan & Co. published for him a collection of memoirs entitledReprint of Papers onElectrostatics and Magnetism. The volume contains 596 pages, and the subjects dealt with range from the "Uniform Motion of Heat and its Connection with the Mathematical Theory of Electricity" (the paper already described in Chapter II above) and the discussion of Electrometers and Electrostatic Measuring Instruments, to a complete mathematical theory of magnetism. The subject of electrostatics led naturally to the consideration of electrical measuring instruments as they existed forty years ago (about 1867), and their replacement by others, the indications of which from day to day should be directly comparable, and capable of being interpreted in absolute units. Down to that time people had been obliged to content themselves with gold-leaf electroscopes, and indeed it was impossible for accuratemeasuringinstruments to be invented until a system of absolute units had been completely worked out. The task of fixing upon definitions of units and of realising them in suitable standards had been begun by the British Association, and it was as part of the Report of that Committee to the Dundee Meeting in 1867 that Thomson's paper on Electrometers first appeared.
It was there pointed out that an electrometer is essentially an instrument for measuring differences of electric potential between conductors, by means of effects of electrostatic force. Such a difference is what a gold-leaf electroscope indicates for its gold leaves and the walls surrounding the air-space in which they are suspended. As electroscopes used to be constructed, these walls were made of glass imperfectly covered, if at all, by conducting material, and the electroscope was quite indefinite and uncertain in its action. Theinstrument was also, as made, quite insensitive. Recently, however, it has been rehabilitated in reputation, and brought into use as a very sensitive indicator of effects of radio-activity.
Thomson described in this paper six species of electrometers of his own devising. The best known of these are his quadrant electrometer and his attracted-disk electrometers. The former is to be found in some form or other in every laboratory nowadays, and need not be described in detail. The action is of two conductors—the two pairs of opposite quadrants of a shallow, horizontal, cylindrical box, made by dividing the box into four by two slits at right angles—upon an electrified slip of aluminium suspended by a two-thread suspension within the box, with its length along one of the slits. The two pairs of opposite quadrants are at the potential difference to be measured, and the slip of aluminium, or "needle," has each end urged round from a quadrant at higher potential towards one at a lower, and these actions conspire to turn the slip against its tendency to return to the position in which the two threads are in one plane. Thus the deflection (measured by the displacement of a reflected ray of light used as index) gives an indication of the amount of the potential difference.
The electrification of the "needle" was kept up by enclosing the quadrantal box within an electrified Leyden jar, to the interior coating of which contact is made by a platinum wire, depending from the needle to sulphuric acid contained in the jar. The whole apparatus was enclosed in a conducting case connected to earth. This made its action perfectly definite. Variations of this electrification of the jar were shownby an attached attracted-disk electrometer, the principle of which we shall merely indicate.
The quadrant electrometer has now been vastly increased in sensibility by the use of a single quartz fibre as suspension. By the invention of this fibre, which is exceedingly strong and is, moreover, so definite in its elastic properties that it comes back at once exactly to its former zero state after twist, Mr. C. V. Boys has increased the delicacy of all kinds of suspended indicators many fold. But it ought to be remembered that a Dolezalek electrometer, with some hundred or more times the sensibility of the bifilar instrument, was only made possible by its predecessor.
Attracted-disk-electrometers simply measure, either by weighing or by the deflection of a spring, the attractive force between two parallel disks at different potentials. From the determination of this force, and the measurement of the distance between the disks (or better, of an alteration of the distance) a difference of potentials can be determined, and a unit for it obtained, which is in direct and known relation to ordinary dynamical units. Thomson's "Absolute Electrometer" was designed specially for accurate determinations of this kind. Another form, called the Long Range Electrometer, was devised for the measurement of the potentials of the charged conductors in electric machines and Leyden jars.
Accurate determinations of the sparking resistance between parallel plates charged to different potentials in air were made by means of attracted-disk-electrometers in the course of some important experiments described in theElectrostatics and Magnetism. These results have been much referred to in later researches.
A small attracted-disk-electrometer was used as indicated above to keep a watch on the electrification of the Leyden jar of the quadrant instrument, and a small induction machine was added, by turning which the operator could make good any loss of charge of the jar.
This electrical machine was an example of an apparatus on precisely the same principle as the Voss or Wimshurst machines of the present day. In it by a set of moving carriers, influenced by conductors, the charges of the latter were increased according to a compound interest principle only interfered with by leakage to the air or by the supports. Several forms of this machine, on the same principle, were constructed by Thomson, and described in 1868; but he afterwards found that he had been anticipated by C. F. Varley in 1860. Still later it was discovered that a similar instrument had been made a century before by Nicholson, and called by him the "Revolving Doubler."
The experiments which Thomson made on atmospheric electricity at the old College tower, and by means of portable electrometers in Arran and elsewhere, can only be mentioned. They led no doubt to some improvements on electrometers which he made, the method of bringing the nozzle of a water-dropper, or a point on a portable electrometer to the potential of the air, by the inductive action on a stream of water-drops in the one case, or the particles of smoke from a burning match in the other. He invented a self-acting machine, worked by a stream of water-drops, for accumulating electric charges, on the principle of the revolving doubler. It was this apparently thatled to the machines with revolving carriers, to which reference has been made above.
The mathematical theory of magnetism which Thomson gave in 1849, in thePhil. Trans. R.S., was, when completed by various later papers, a systematic discussion of the whole subject, including electromagnetism and diamagnetism. To a large extent the ground covered by the 1849 paper had been traversed before by Poisson, and partially by Murphy and Green; but Thomson stated that one chief object of his memoir was to formally construct the theory without reference to the two magnetic fluids, by means of which the facts of experiment and conclusions of theory had so far been expressed. He found it, however, convenient to introduce the idea of positive and negative magnetic matter (attracting and repelling as do charges of positive and negative electricity), which are to be regarded as always present in equal amounts, not only in a magnet as a whole, but in every portion of a magnet; and at first sight this might appear like a return to the magnetic fluids. But it amounts on the whole rather to a conception of a magnet as a conglomeration of doublets of magnetic matter (that is, very close, equal and inseparable charges of the two kinds of matter), the arrangement of which can be changed by the action of magnetic force. This idea is set forth now in all the books on magnetism and electricity. There can be no doubt that the systematic presentment of the subject by Thomson, and the theorems and ideas of magnetic force and magnetic permeability by which he rendered the clear, and therefore mathematical, notions of Faraday explicitly quantitative, had much influence in furthering theprogress of electrical science, and so leading on the one hand to the electromagnetic theories of Maxwell, and on the other to modern research on the magnetic properties of iron, and to the correct ideas which now prevail as to construction of dynamo-electric machines and motors.
Fromhis student days throughout his life, Lord Kelvin took a keen interest in geological questions. He was always an active member of the Geological Society of Glasgow, and was its president for twenty-one years (1872-1893). The distribution of heat in the substance of the earth was the subject of his inaugural dissertation as Professor of Natural Philosophy; and previously, as a student, he had written an essay on "The Figure of the Earth," for which he had been awarded a University Gold Medal. He never ceased to ponder over the problems of terrestrial physics, and he wrote much on the subject. His papers are to be found as Appendices to Thomson and Tait'sNatural Philosophy, and in vol. ii of hisPopular Lectures and Addresses, which is devoted to geology and general physics.
His conclusions regarding the age of the earth have been referred to in the last chapter. The first allusion to the subject was contained (see p.65above) in his inaugural dissertation "De Caloris distributione in Terræ Corpus"; but he returned to it again in a communication made to the Royal Society of Edinburgh in December, 1865, and entitled "The Doctrine of Uniformity in Geology briefly refuted." On February 27, 1868, he delivered to the Geological Society ofGlasgow an address entitled "On Geological Time," in which the necessity for limiting geological and other changes to an almost infinitesimal fraction of the vast periods at that time demanded was insisted on, and which gave rise to much discussion.
The address began with a protest against the old uniformitarian view of geological changes as expressed by Playfair in hisIllustrations of the Huttonian Theory. The first objection taken to the idea that "in the continuation of the different species of animals and vegetables that inhabit the earth, we discern neither a beginning nor an end; in the planetary motions where geometry has carried the eye so far, both into the future and the past, we discover no mark either of the commencement or the termination of the present order" is, that the stability of the motions of the heavenly bodies, to which reference is made in this statement, is founded upon what is essentially an approximate calculation, which leaves out, by intention, the consideration of frictional resistance.
He points out, for example, that the friction which accompanies the relative motion of the waters of the earth and the land is attended by the production of heat, and that, by the doctrine of the conservation of energy, heat cannot be produced without a disappearance of an equivalent quantity of energy, either of motion or of position. The chief source of this energy is the earth's rotation. Since the earth turns under the moon and the tidal spheroid—that is, the earth's shape as distorted by the heaping up of the waters in the tides—remains on the whole stationary with respect to the moon, the solid matter of the earth turns under the distribution of the water, heldmore or less fixed by the moon, as does a fly-wheel under a stationary friction band round its rim. Then just as the band held fixed retards the fly-wheel, so the earth must be retarded in its rotation by this water-brake. In the earth's rotation there is a store of kinetic energy which, roughly estimated, would not be exhausted in less than ten million million years, although drawn upon continuously by friction, or other actions, at the rate of one million horse-power; so that, no immediate catastrophe, such as that we should be involved in by the stoppage or considerable retardation of the spinning motion of the earth, is possible. But it was pointed out by Thomson that the best results of astronomical observation show that the earth would in one hundred years fall behind a perfect time-keeper, with which its rotation kept pace at the beginning of the time, by about twenty seconds. The tendency is to make the earth turn slower, and the moon to increase its distance and move more slowly in its orbit, but with a resultant effect towards coincidence of the period of the earth's rotation with that of revolution of the moon round the earth. After this coincidence has been attained, however, the solar tides will tend to make the moon fall in towards the earth.
If then the earth be rotating more and more slowly, as time goes on, at present, it must have been rotating more rapidly in past time. A thousand million years ago, at the present rate of retardation, the earth must have been rotating one seventh part of its speed faster than it is rotating at present, and this would give for centrifugal force at the surface one thousand million years ago, greater than the centrifugal force at present, in the ratio of 64 to 49. Apparently therefore theearth must have solidified at a much later date than that epoch, a date when it was rotating much more nearly with the angular speed which it has now; otherwise the figure of the earth would have deviated much more from the spherical form than it actually does. On the other hand, one hundred million years ago centrifugal force would be only three per cent. greater than it is at present, and consolidation of the earth at that less remote period would give a shape to the earth not very different from that which it now possesses. The argument therefore from tidal retardation would cut down the time available for geological and biological changes to something not much more than one hundred million years, perhaps to less.
A second argument for limitation of the time available for such processes is derived from the sun's heat. The sun cannot be regarded as a miraculous body producing its light and heat from nothing. Changes of the constitution of the sun must be continually proceeding, to account for its enormous radiation of energy into space, a radiation of which only an infinitesimal part is received by the bodies of the solar system, and a still more minute portion by the earth. The effects of the sun's light and heat on the earth show how enormous must be the quantity of energy lost from the sun in a year. How is this loss of energy to be accounted for? What is the physical change which gives rise to it? In 1854 Thomson put forward the theory that the sun's heat is kept up by the falling in of meteors on the sun's surface, but he afterwards saw reason to abandon that view. Helmholtz had advocated the theory that the sun was a body heated by the coming together of the matter composing it by itsmutual attraction, a process which, although the sun is now a continuous mass, is to be regarded as still going on. It is easy to calculate the exhaustion of potential energy caused by the coming together of the matter of the sun from universal dispersion through infinite space to a sphere of uniform density of the present size of the sun. The result is about as much energy as would be generated by burning seven million million million million million tons of coal. The amount radiated in each hour is about as much as would be generated by burning something like nine tons of coal every hour on every square yard of the sun's surface. It is certain that the sun must be still contracting, and if it contracts sufficiently to just make good this expenditure by the further exhaustion of potential energy involved in the closer aggregation of the matter, it must diminish in radius in each year by as much as 130 feet.
The amount of energy generated by the falling together of the matter of the sun from universal diffusion to the dimensions which the sun has at present, is only about 13,000,000 times the amount now radiated per annum. In Thomson's paper Pouillet's estimate of the energy radiated per second is used, and this number is raised to 20,000,000. Taking the latter estimate, the whole potential energy exhausted by the condensation of the sun's mass to uniform density would suffice for only 20,000,000 years' supply. But the sun is undoubtedly of much greater density in the central parts than near the surface, and so the energy exhausted must be much greater than that stated above. This will raise the number of years provided for. On the other hand, a considerable amount of energy wouldbe dissipated during the process of condensation, and this would reduce the period of radiation estimated. Thomson suggests that 50,000,000, or 100,000,000, years is a possible estimate.
It is not unlikely that the rate of radiation in past time, when the sun had not nearly condensed to its present size, was so much less than it is at present that the period suggested above may have to be considerably augmented. Another source of radiation, which seems to be regarded by some authorities as a probable, if not a certain, one, has been suggested in recent years—the presence of radio-active substances in the sun. So far as we know, Lord Kelvin did not admit that this source of radiation was worthy of consideration; but of course, granted its existence to an extent comparable with the energy derivable from condensation of the sun's mass, the "age of the sun's heat" would have to be very greatly extended. These are matters, however, on which further light may be thrown as research in radio-activity progresses. Lord Kelvin was engaged when seized with his last illness in discussing the changes of energy in a gaseous, or partially gaseous, globe, slowly cooling and shrinking in doing so; and a posthumous paper on the subject will shortly be published which may possibly contain further information on this question of solar physics.
But Thomson put forward a third argument in the paper on Geological Time, which has always been regarded as the most important. It is derived from the fact, established by abundant observations, that the temperature in the earth's crust increases from the surface inwards; and that therefore the earth must becontinually losing heat by conduction from within. If the earth be supposed to have been of uniform temperature at some period of past time and in a molten state, and certain assumptions as to the conductive power and melting point of its material be made, the time of cooling until the gradient of temperature at the surface acquired its present value can be calculated. This was done by Thomson in a paper published in theTransactions, R.S.E., in 1862. We propose to give here a short sketch of his argument, which has excited much interest, and been the cause of some controversy.
In order to understand this argument, the reader must bear in mind some fundamental facts of the flow of heat in a solid. Let him imagine a slab of any uniform material, say sandstone or marble, the two parallel faces of which are continually maintained at two different temperatures, uniform over each face. For example, steam may be continually blown against one face, while ice-cold water is made to flow over the other. Heat will flow across the slab from the hotter face to the colder. It will be found that the rate of flow of heat per unit area of face, that is per square centimetre, or per square inch, is proportional to the difference of the temperatures in the slab at the two faces, and inversely proportional to the thickness of the slab. In other words, it is proportional to the fall of temperature from one face to the other taken per unit of the thickness, that is, to the "gradient of temperature" from one face to the other. Moreover, comparing the flow in one substance with the flow in another, we find it different in different substances for the same gradient of temperature. Thus we get finally a flow of heat across unit area of the slab whichis equal to the gradient of temperature multiplied by a number which depends on the material: that number is called the "conductivity" of the substance.
Now, borings made in the earth show that the temperature increases inwards, and the same thing is shown by the higher temperatures found in deeper coal mines. By means of thermometers sunk to different depths, the rate of increase of temperature with depth has been determined. Similar observations show that the daily and annual variations of temperature caused by the succession of day and night, and summer and winter, penetrate to only a comparatively small depth below the surface—three or four feet in the former case, sixty or seventy in the latter. Leaving these variations out of account, since the average of their effects over a considerable interval of time must be nothing, we have in the earth a body at every point of the crust of which there is a gradient of increasing temperature inwards. The amount of this may be taken as one degree of Fahrenheit's scale for every 50 feet of descent. This gradient is not uniform, but diminishes at greater depths. Supposing the material of uniform quality as regards heat-conducting power, the mathematical theory of a cooling globe of solid material (or of a straight bar which does not lose heat from its sides) gives on certain suppositions the gradients at different depths. The surface gradient of 1° F. in 50 feet may be taken as holding for 5000 feet or 6000 feet or more.
This gradient of diminution of temperature outwards leads inevitably to the conclusion that heat must be constantly flowing from the interior of the earth towards the surface. This is as certain as that heatflows along a poker, one end of which is in the fire, from the heated end to the other. The heat which arrives at the surface of the earth is radiated to the atmosphere or carried off by convection currents; there is no doubt that it is lost from the earth. Thus the earth must be cooling at a rate which can be calculated on certain assumptions, and it is possible on these assumptions to calculate backwards, and determine the interval of time which must have elapsed since the earth was just beginning to cool from a molten condition, when of course life cannot have existed on its surface, and those geological changes which have effected so much can hardly have began.
Considering a globe of uniform material, and of great radius, which was initially at one temperature, and at a certain instant had its surface suddenly brought to, let us say, the temperature of melting ice, at which the surface was kept ever after, we can find, by Fourier's mathematical theory of the flow of heat, the gradient of temperature at any subsequent time for a point on the surface, or at any specified distance within it. For a point on the surface this gradient is simply proportional to the initial uniform temperature, and inversely proportional to the square root of the product of the "diffusivity" of the material (the ratio of the conductivity to the specific heat) by the interval of time which has elapsed since the cooling was started. Taking a foot as the unit of length, and a year as the unit of time, we find the diffusivity of the surface strata to be 400. If we take the initial temperature as 7000 degrees F.—which is high enough for melting rock—and take the interval of time which has elapsed as 100,000,000 years, we obtain at the surface agradient approximately equal to that which now exists. A greater interval of time would give a lower gradient, a smaller interval would give a higher gradient than that which exists at present. A lower initial temperature would require a smaller interval of time, a higher initial temperature a longer interval for the present gradient.
With the initial temperature of 7,000 degrees F., an interval of 4,000,000 years would give a surface gradient of 1° F. in 10 ft. Thus, on the assumption made, the surface gradient of temperature has diminished from1⁄10to1⁄50in about 96,000,000 years. After 10,000 years from the beginning of the cooling the gradient of temperature would be 2° F. per foot. But, as Thomson showed, such a large gradient would not lead to any sensible augmentation of the surface temperature, for "the radiation from earth and atmosphere into space would almost certainly be so rapid" as to prevent this. Hence he inferred that conducted heat, even at that early period, could not sensibly affect the general climate.
Two objections (apart from the assumptions already indicated) will readily occur to any one considering this theory, and these Thomson answered by anticipation. The first is, that no natural action could possibly bring the surface of a uniformly heated globe instantaneously to a temperature 7000° lower, and keep it so ever after. In reply to this Thomson urged "that a large mass of melted rock, exposed freely to our earth and sky, will, after it once becomes crusted over, present in a few hours, or a few days, or at most a few weeks, a surface so cool that it can be walked over with impunity. Hence, after 10,000years, or indeed, I may say, after a single year, its condition will be sensibly the same as if the actual lowering of temperature experienced by the surface had been produced in an instant, and maintained constant ever after." The other objection was, that the earth was probably never a uniformly heated solid 7000° F. above the present surface temperature as assumed for the purpose of calculation. This Thomson answers by giving reasons for believing that "the earth, although once all melted, or melted all round its surface, did, in all probability, really become a solid at its melting temperature all through, or all through the outer layer which has been melted; and not until the solidification was thus complete, or nearly so, did the surface begin to cool."
Thomson was inclined to believe that a temperature of 7000° F. was probably too high, and results of experiments on the melting of basalt and other rocks led him to prefer a much reduced temperature. This, as has already been pointed out, would give a smaller value for the age of the earth. In a letter on the subject published inNature(vol. 51, 1895) he states that he "is not led to differ much" from an estimate of 24,000,000 years founded by Mr. Clarence King (American Journal of Science, January 1893) on experiments on the physical properties of rocks at high temperatures.
It is to be observed that the assumptions made above that the physical constants of the material are constant throughout the earth, and at all temperatures, are confessedly far from the truth. Nevertheless Thomson strongly held that the uncertainty of the data can at most extend the earth's age to some valuebetween 20,000,000 and 200,000,000 of years, and that the enormously long periods which were wont to be asked for by geologists and biologists for the changes of the earth's surface and the development of its flora and fauna, cannot possibly be conceded.
InNaturefor January 3, 1895, Professor John Perry suggested that very possibly the conductivity of the material composing the interior of the earth was considerably higher than that of the surface strata. If this were so, then, as can be shown without difficulty, the attainment of the present gradient would be very greatly retarded, and therefore the age of the earth correspondingly increased. The question then arose, and was discussed, as to whether the rocks and other materials at high temperatures were more or less conducting than at low temperatures, and experiments on the subject were instituted and carried out. On the whole, the evidence seemed to show that the conductivity of most substances is diminished, not increased, by the rise of temperature, and so far as it went, therefore, the evidence was against Professor Perry's suggestion. On the other hand, he contended that the inside of the earth may be a mass of great rigidity, partly solid and partly fluid, possessing a "quasi-conductivity" which might greatly increase the period of cooling. The subject is a difficult one both from a mathematical and from the physical point of view, and further investigation is necessary, especially of the behaviour of materials under the enormous stresses which they undoubtedly sustain in the interior of the earth.
After the publication of the paper on Geological Time a reply to it was made by Professor Huxley, inan address to the Geological Society of London, delivered on February 19, 1869. He adopted therôleof an advocate retained for the defence of geology against what seems to have been regarded as an unwarranted attack, made by one who had no right to offer an opinion on a geological question. For, after a long and eloquent "pleading," he concludes his address with the words: "My functions, as your advocate, are at an end. I speak with more than the sincerity of a mere advocate when I express the belief that the case against us has entirely broken down. The cry for reform which has been raised from without is superfluous, inasmuch as we have long been reforming from within with all needful speed; and the critical examination of the grounds upon which the very grave charge of opposition to the principles of Natural Philosophy has been brought against us, rather shows that we have exercised a wise discrimination in declining to meddle with our foundations at the bidding of the first passer-by who fancies our house is not so well built as it might be." To this Thomson rejoined in an address entitled "Of Geological Dynamics," also delivered to the Geological Society of Glasgow on April 5, 1869; and to this, with Professor Huxley's address, the reader must be referred for the objection, brought against Thomson's arguments, and the replies which were immediately forthcoming. This is not the place to discuss the question, but reference may be made to an interesting paper on the subject in theGlasgow Heraldfor February 22, 1908, by Professor J. W. Gregory, in which the suggestion of Professor Perry, of a nearer approach to uniformity of temperature in the interior of the earth than Thomson hadthought possible, is welcomed as possibly extending the interval of time available to a period sufficient for all purposes. In Professor Gregory's opinion, "Lord Kelvin in one respect showed a keener insight than Huxley, who, referring to possible changes in the rate of rotation of the earth, or in the heat given forth from the sun or in the cooling of the earth, declared that geologists are Gallios, 'who care for none of these things.' An ever-increasing school of geologists now cares greatly for these questions, and reveres Lord Kelvin as one of the founders of the geology of the inner earth."
After all, the problem is not one to be dealt with by the geologist or biologist alone, but to be solved, so far as it can be solved at all, by a consideration of all relevant evidence, from whatsoever quarter it may come. It will not do in these days for scientific men to shut themselves up within their special departments and to say, with regard to branches of science which deal with other aspects of nature and other problems of the past, present and future of that same earth on which all dwell and work, that they "care for none of these things." This is an echo of an old spirit, not yet dead, that has done much harm to the progress of science. The division of science into departments is unavoidable, for specialisation is imperative; but it is all the more necessary to remember that the divisions set up are more or less arbitrary, and that there are absolutely no frontiers to be guarded and enforced. Chemistry, physiology, and physics cannot be walled off from one another without loss to all; and geology has suffered immensely through its having been regarded as essentially a branch of natural history, thedevotees of which have no concern with considerations of natural philosophy. Lord Kelvin's dignified questions were unanswerable. "Who are the occupants of 'our house,' and who is the 'passer-by'? Is geology not a branch of physical science? Are investigations, experimental and mathematical, of underground temperature not to be regarded as an integral part of geology?... For myself, I am anxious to be regarded by geologists not as a mere passer-by, but as one constantly interested in their grand subject, and anxious in any way, however slight, to assist them in their search for truth."
WhenProfessor Thomson began his work as a teacher in the University of Glasgow, there was, as has already been noticed, great vagueness of specification of physical quantities. Few of the formal definitions of units of measurement, now to be found in the pages of every elementary text book, had been framed, and there was much confusion of quantities essentially distinct, a confusion which is now, to some extent at least, guarded against by the adoption of a definite unit, with a distinctive name for each magnitude to be measured. Thus rate of working, or activity, was confused with work done; the condition for maximum activity in the circuit of a battery or dynamo was often quoted as the condition of greatest efficiency, that is of greatest economy of energy, although it was exactly that in which half the available energy was wasted.
Partly as a consequence of this vagueness of specification, there was a great want of knowledge of the values of physical constants; for without exact definitions of quantities to be determined, such definitions as would indicate units for their measurement, related to ordinary dynamical units according to a consistent scheme, it was impossible to devise satisfactory experimental methodsto do for electricity and magnetism what had been done by Regnault and others for heat.
The first steps towards the construction of a complete system of units for the quantitative measurement of magnetic and electric quantities were taken by Gauss, in his celebrated paper entitledIntensitas vis magneticæ terrestris ad mensuram absolutam revocata, published in 1832. In this he showed how magnetic forces could be expressed in absolute units, and thus be connected with the absolute dynamical units which Gauss, in the same paper, based on chosen fundamental units of length, mass, and time. Thus the modern system of absolute units of dynamical quantities, and its extension to magnetism, are due to the practical insight of a great mathematician, not to the experimentalists or "practicians" of the time.
Methods of measuring electric quantities in absolute units were described by W. Weber, in Parts II and III of hisElecktrodynamische Maassbestimmungen, published in 1852. These were great steps in advance, and rendered further progress in the science of absolute measurement comparatively easy. But they remained the only steps taken until the British Association Committee began their work. We have already (pp.74-76) referred to the great importance of that work, not only for practical applications but also for the advancement of science. But it was not a task which struck the imagination or excited the wonder of the multitude. For the realisation of standards of resistance, for example, involved long and tedious investigations of the effects of impurities on the resistance of metals, and the variation of resistance caused by change of temperature and lapse of time. Then alloys had tobe sought which would have a temperature effect of small amount, and which were stable and durable in all their properties.
The discoveries of the experimentalist who finds a new element of hitherto undreamed-of properties attract world-wide attention, and the glory of the achievement is deservedly great. But the patient, plodding work which gives a universal system of units and related standards, and which enables a great physical subject like electricity and magnetism to rise from a mere enumeration of qualitative results to a science of the most delicate and exact measurement, and to find its practical applications in all the affairs of daily life and commerce, is equally deserving of the admiration and gratitude of mankind. Yet it receives little or no recognition.
The construction of a standard of resistance was the first task undertaken by the committee; but other units, for example of quantity of electricity, intensity of electric field and difference of potential, had also to be defined, and methods of employing them in experimental work devised. It would be out of place to endeavour to discuss these units here, but some idea of the manner in which their definitions are founded on dynamical conceptions may be obtained from one or two examples. Therefore we shall describe two simple experiments, which will illustrate this dynamical foundation. An account has been given in Chapter XI of the series of electrometers which Thomson invented for the measurement of differences of electric potential. These all act by the evaluation in terms of ordinary dynamical units of the force urging an electrified body from a place of higher towards a place of lower potential.
Some indication of the meaning of electrical quantities has been given in Chapter IV. Difference of electric potential between two points in an electric field was there defined as the dynamical work done in carrying a unit of positive electricity against the forces of the field from the point of lower to the point of higher potential. Now by the definition of unit quantity of electricity given in electrical theory—that quantity which, concentrated at a point at unit distance from an equal quantity also concentrated at a point, is repelled with unit force—we can find, by the simple experiment of hanging two pith balls (or, better, two hollow, gilded beads of equal size) by two fine fibres of quartz, a metre long, say, electrifying the two balls as they hang in contact, and observing the distance at which they then hang, the numerical magnitude in absolute units of a charge of electricity, and apply that to finding the charge on a large spherical conductor and the potential at points in its field also in absolute units. Ifmbe the mass of a ball,ggravity in cm. sec. units,dthe distance in cms. of the centres of the balls apart, andlthe length in cms. of a thread, the chargeq, say, on each ball is easily found to beThus the charge is got in absolute centimetre-gramme-second units in terms of the massmobtained by ordinary weighing, andlanddobtained by easy and exact measurements.
If one of the balls be now taken away without discharging the other, and the latter be placed in the field of a large electrified spherical conductor, the fibre will be deflected from the vertical by the force on the ball. Let the two centres be now on the same level. That force is got at once from the angle of deflection (which iseasily observed), the charge on the ball, and the value ofm. The electric field-intensity is obtained by dividing the value of the force byq. The field intensity multiplied byD, the distance apart in cms. of the centres of the ball and the conductor, gives the potential at the centre of the ball in C.G.S. units. Multiplication again byDgives the charge on the conductor.
When it made its first Report in 1862 (to the meeting at Cambridge) the committee consisted of Professors A. Williamson, C. Wheatstone, W. Thomson, W. H. Miller, Dr. A. Matthiessen, and Mr. F. Jenkin. At the next meeting, at Newcastle, it had been augmented by the addition of Messrs. Balfour Stewart, C. W. Siemens, Professor Clerk Maxwell, Dr. Joule, Dr. Esselbach, and Sir Charles Bright. The duty with which the committee had been charged was that of constructing a suitable standard of resistance. A reference to the account given in Chapter X above, of the derivation of what came to be called the electromagnetic unit of difference of potential, or electromotive force, by means of a simple magneto-electric machine—a disk turning on a uniform magnetic field, or the simple rails and slider and magnetic field arrangement there described—will show how from this unit and the electromagnetic unit of current (there also defined) the unit of resistance is defined. It is the resistance of the circuit of slider, rails, and connecting wire, when with this electromagnetic unit of electromotive force the unit of current is made to flow.
This was one clear and definite way of defining the unit of current, and of attaining the important object of connecting the units in such a way that the rate of working in a circuit, or the energy expended in any time, should be expressed at once in ordinary dynamicalunits of activity or energy. A considerable number of proposals were discussed by the committee; but it was finally determined to take the basis here indicated, and to realise a standard of resistance in material of constant and durable properties, which should have some simple multiple of the unit of resistance, in the system of dynamical units based on the centimetre as unit of length, the gramme as unit of mass, and the second as unit of time—the so-called C.G.S. system. The comparison of the different metals and alloys available was a most important but exceedingly laborious series of investigations, carried out mainly by Dr. Matthiessen and Professor Williamson.
Professor Thomson suggested to the committee the celebrated method of determining the resistance of a circuit by revolving a coil, which formed the main part of the circuit about a vertical axis in the earth's magnetic field. An account of the experiments made with this method is contained in the Report of 1863. They were carried out at King's College, London, where Maxwell was then Professor of Experimental Physics, by Maxwell, Balfour Stewart, and Fleeming Jenkin. The theoretical discussion and the description of the experiments was written by Maxwell, the details of the apparatus were described by Jenkin.
The principle of the method is essentially the same as that of the simple magneto-electric machine, to which reference has just been made. Two parallel coils of wire were wound in channels cut round rings of brass, which, however, were cut across by slots filled with vulcanite, to prevent induced currents from circulating in the brass. These coils were mounted in a vertical position and could be driven as a rigid system, at a constant measured speed, about a verticalaxis passing through the centre of the system. Between the coils at this centre was hung, from a steady support, a small magnetic needle by a single fibre of silk; and a surrounding screen prevented the needle and suspension from being affected by currents of air.
The ends of the coil were connected together so that the whole revolved as a closed circuit about the vertical axis. When the coil system was at right angles to the magnetic meridian there was a magnetic induction through it of amountAH, whereAdenotes the effective area of the coils, andHthe horizontal component of the earth's magnetic field. By one half-turn the coil was reversed with reference to this magnetic induction, and as the coil turned an induced current was generated, which depended at any instant on the rate at which the magnetic induction was varying at the instant, on the inductive electromotive force due to the varying of the current in the coil itself, and on the resistance of the circuit. A periodic current thus flowed in one directionrelatively to the coilin one half-turn from a position perpendicular to the magnetic meridian, and in the opposite direction in the next half-turn. But as the position of the coil was reversed in every half-turn as well as the current in it, the current flowed on the whole in the same average direction relatively to the needle, and but for self-induction would have had its maximum value always when the plane of the coil was in the magnetic meridian.
The needle was deflected as it would have been by a certain average current, and the deflection was opposed by the action of the earth's horizontal magnetic fieldH. But this was the field cut by the coil as it turned, and therefore (except for a small termdepending on the turning of the coil in the field of the needle) the value ofHdid not appear in the result, and did not require to be known.
Full details of the theory of this method and of the experiments carried out to test it will be found in various memoirs and treatises23; but it must suffice here to state that the resistance of the coil was determined in this way, by a large series of experiments, before and after every one of which the resistance was compared with that of a German-silver standard. The resistance of this standard therefore became known in absolute units, and copies of it, or multiples or sub-multiples of it, could be made.
A unit called the B.A. unit, which was intended to contain 109C.G.S. electromagnetic units of resistance, was constructed from these experiments, and copies of it were soon after to be found in nearly all the physical laboratories of the world. Resistance boxes were constructed by various makers, in which the coils were various multiples of the B.A. unit, so that any resistance within a certain range could be obtained by connecting these coils in series (which was easily done by removing short circuiting plugs), and thus the absolute units of current electromotive force and resistance came into general use.
In 1881 Lord Rayleigh and Professor Schuster carried out a very careful repetition of the British Association experiments with the same apparatus at the Cavendish Laboratory, and obtained a somewhat different result. They found that the former resultwas about 1.17 per cent. too small. Lord Rayleigh next carried out an independent set of experiments by the same method with improved apparatus, and found that this percentage error must be increased to about 1.35.
It may be noticed here that the simple disk machine, of Thomson's illustration of the absolute unit of electromotive force, has been used by Lorenz to give a method of determining resistance which is now recognised as the best of all. It is sketched here that the reader may obtain some idea of later work on this very important subject; work which is a continuation of that of the original British Association Committee by their successors. A circuit is made up of a standard coil of wire, the ends of which are made to touch at the circumference and near the centre of the disk, which is placed symmetrically with respect to a cylindrical coil, and within it. A current is sent round this coil from a battery, and produces a magnetic field within the coil, the lines of magnetic force of which pass across the plane of the disk. This current, or a measured fraction of it, is also made to flow through the standard coil. The disk is now turned at a measured speed about its axis, so that the electromotive force due to the cutting of the field tends to produce a current in the standard coil of wire. The electromotive force of the disk is made to oppose the potential difference between the ends of this coil due to the current, so that no current flows along the disk or the wires connecting it with the standard coil. The magnetic field within the coil can be calculated from the form and dimensions of the coil and the current in it (supposed for the moment to be known), and the electromotive force of the disk is obtained in terms of its dimensionsand its speed and the field intensity. But this electromotive force, which is proportional to the current in the coil, is equal to the product of the resistance of the wire and the same current, or a known fraction of it. Thus the current appears on both sides of the equation and goes out, and the value of the resistance is found in absolute units.
Lord Rayleigh obtained, by this method, a result which showed that the B.A. unit was 1.323 per cent. too small; and exact experiments have been made by others with concordant results. Values of the units have been agreed on by International Congresses as exact enough for general work, and with these units all electrical researches, wherever made, are available for use by other experimenters.
A vast amount of work has been done on this subject during the last forty years, and though the value of the practical unit of resistance—109C.G.S. units, now called the "ohm"—is taken as settled, and copies can now be had in resistance boxes, or separately, adjusted with all needful accuracy, at the National Physical Laboratory and at the Bureau of Standards at Washington, and elsewhere, experiments are being made on the exact measurement of currents; while a careful watch is kept on the standards laid up at these places to see whether any perceptible variation of their resistance takes place with lapse of time.
The British Association Committee also worked out a complete system of units for all electrical and magnetic quantities, and gave the first systematic statement of their relations, that is, of the so-called dimensional equations of the quantities. This will be found in the works to which reference has already been made (p.251).