Part 58

Note.

Footnote 153:

It appears that the most accurate experimental demonstration ever made of this law was that of E. W. Morley, published in the Journal (=41=, 220, 276, 1891). He showed that 2·0002 volumes of hydrogen combine with one volume of oxygen.

XI A CENTURY’S PROGRESS IN PHYSICS

By LEIGH PAGE

Dynamics.—At the beginning of the nineteenth century mechanics was the only major branch of physical science which had attained any considerable degree of development. Two centuries earlier, Galileo’s experiments on the rate of fall of iron balls dropped from the top of the Leaning Tower of Pisa, had marked the origin of dynamics. He had easily disproved the prevalent idea that even under conditions where air resistance is negligible heavy bodies would fall more rapidly than light ones, and further experiments had led him to conclude that the increase in velocity is proportional to the time elapsed, and not to the distance traversed, as he had at first supposed. Less than a century later Newton had formulated the laws of motion in the same words in which they are given to-day. These laws of motion, coupled with his discovery of the law of universal gravitation, had enabled him to correlate at once the planetary notions which had proved so puzzling to his predecessors. His success gave a tremendous stimulus to the development and extension of the fundamental dynamical principles that he had brought to light, which culminated in the work of the great French mathematicians, Lagrange and Laplace, a little over a hundred years ago.

Newton’s laws of motion, it must be remembered, apply only to a particle, or to those bodies which can be treated as particles in the problem under consideration. In his “Mécanique Analytique” Lagrange extended these principles so as to make it possible to treat the motion of a connected system by a method almost as simple as that contained in the second law of motion. Instead of three scalar equations for each of the innumerably large number of particles involved, he showed how to reduce the ordinary dynamical equations to a number equal to that of the degrees of freedom of the system. This is made possible by a combination of d’Alembert’s principle, which eliminates the forces due to the connections between the particles, and the principle of virtual work, which confines the number of equations to the number of possible independent displacements. The aim of Lagrange was to make dynamics into a branch of analysis, and his success may be inferred from the fact that not a single diagram or geometrical figure is to be found in his great work.

Celestial Mechanics.—Almost simultaneously with the publication of the “Mécanique Analytique” appeared Laplace’s “Mécanique Celeste.” Laplace’s avowed aim was to offer a complete solution of the great dynamical problem involved in the solar system, taking into account, in addition to the effect of the sun’s gravitational field, those perturbations in the motion of each planet caused by the approach and recession of its neighbors. So successful was his analysis of planetary motions that his contemporaries believed that they were not far from a complete explanation of the world on mechanical principles. Laplace himself was undoubtedly convinced that nothing was needed beyond a knowledge of the masses, positions, and initial velocities of every material particle in the universe in order to completely predetermine all subsequent motion.

The greatest triumph of these dynamical methods was to come half a century later. The planet Uranus, discovered in 1781 by the elder Herschel, was at that time the farthest known planet from the sun. But the orbit of Uranus was subject to some puzzling variations. After sifting all the known causes of these disturbances, Leverrier in France and Adams in England independently reached the conclusion that another planet still more remote from the sun must be responsible, and computed its orbit. Leverrier communicated to Galle of Berlin the results of his calculations, and during the next few days the German astronomer discovered Neptune within one degree of its predicted position!

We shall mention but one other achievement of the methods of celestial mechanics. Those visitors of the skies, the comets, which become so prominent only to fade away and vanish perhaps forever, had interested astronomers from the earliest times. Soon after the discovery of the law of gravitation, Newton had worked out a method by which the elements of a comet’s orbit can be computed from observations of its position. It was found that the great majority of these bodies move in nearly parabolic paths and only a few in ellipses. Of the latter the most prominent is the brilliant comet first observed by Halley in 1681. It has reappeared regularly at intervals of seventy-six years; the last appearance in the spring of 1910 is no doubt well remembered by the reader. Kant had considered comets to be formed by condensing solar nebulæ, whereas Laplace had maintained that they originate in matter which is scattered throughout stellar space and has no connection with the solar system. A study of the distribution of inclinations of comet orbits by H. A. Newton (=16=, 165, 1878) of New Haven substantiated Laplace’s hypothesis, and led to the conclusion that the periodic comets have been captured by the attraction of those planets near to which they have passed. Of these comets a number have comparatively short periods, and are found to have orbits which are in general only slightly inclined to those of the planets, and are traversed in the same direction. Moreover, the fact that the orbit of each of these comets comes very close to that of Jupiter made it seem probable that they have been attached to the solar system by the attraction of this planet. Further confirmation of this hypothesis was furnished by H. A. Newton’s (=42=, 183 and 482, 1891) explanation of the small inclination of their orbits and the scarcity of retrograde motions among them.

In 1833 occurred one of the greatest meteoric showers of history. Olmstead (=26=, 132, 1834) and Twining (=26=, 320, 1834) of New Haven noticed that these shooting stars traverse parallel paths, and were the first to suggest that they must be moving in swarms in a permanent orbit. From an examination of all accessible records, H. A. Newton (=37=, 377, 1864; =38=, 53, 1864) was able to show that meteoric showers are common in November, and of particular intensity at intervals of 33 or 34 years. He confidently predicted a great shower for Nov. 13th, 1866, which not only actually occurred but was followed by another a year later, showing that the meteoric swarm extended so far as to require two years to cross the earth’s orbit. H. A. Newton (=36=, 1, 1888) in America and Adams in England took up the study of meteoric orbits with great interest, and the former concluded that these orbits are in every sense similar to those of the periodic comets, implying that a swarm of meteors originates in the disintegration of a comet. In fact Schiaparelli actually identified the orbit of the Perseids, or August meteors, with Tuttle’s comet of 1862, and shortly after the orbit of the Leonids, or November meteors, was found to be the same as that of Tempel’s comet.

Electromagnetism.—During the eighteenth century much interest had been manifested in the study of electrostatics and magnetism. Du Fay, Cavendish, Michell and Coulomb abroad and Franklin in America had subjected to experimental investigation many of the phenomena of one or both of these sciences, and in the early years of the nineteenth century Poisson developed to a remarkable extent the analytical consequences of the law of force which experiment had revealed. Both Laplace and he made much use of the function to which Green gave the name “potential” in 1828, and which is such a powerful aid in solving problems involving magnetism or electricity at rest.

Meantime electric currents had been brought under the hand of the experimenter by the discoveries of Galvani and Volta. Large numbers of cells were connected in series, and interest seemed to lie largely in producing brilliant sparks or fusing metals by means of a heavy current. Hare (=3=, 105, 1821) of the University of Pennsylvania constructed a battery consisting of two troughs of forty cells each, so arranged that the coppers and zincs can be lowered simultaneously into the acid and large currents obtained before polarization has a chance to interfere. This “deflagrator” was used to ignite charcoal in the circuit, or melt fine wires, and was for some time the most powerful arrangement of its kind. That “galvanism” is something quite different from static electricity was the opinion of many investigators; Hare considered the heat developed to be the distinguishing mark of the electric current. He says: “It is admitted that the action of the galvanic fluid is upon or between atoms; while mechanical electricity when uncoerced, acts only upon masses. This difference has not been explained unless by my hypothesis, in which caloric, of which the influence is only exerted between atoms, is supposed to be a principal agent in galvanism.”

Questioning minds were beginning to suspect that there must be some connection between electricity and magnetism. For lightning had been known to make magnets of steel knives and forks, and Franklin had magnetized a sewing needle by the discharge from a Leyden jar. Finally Oersted of Copenhagen undertook systematic investigation of the effect of electricity on the magnetic needle. His researches were without result until during the course of a series of lectures on “Electricity, Galvanism, and Magnetism” delivered during the winter of 1819–20 it occurred to him to investigate the action of an electric current on a magnetic needle. At first he placed the wire bearing the current at right angles to the needle, with, of course, no result; then it occurred to him to place it parallel. A deflection was observed, for to his surprise the needle insisted on turning until perpendicular to the wire.

Oersted’s discovery that an electric current exerts a couple on a magnetic needle was followed a few months later by Ampère’s demonstration before the French Academy that two currents flowing in the same direction attract each other, while two in opposite directions repel. The story goes that a critic attempted to belittle this discovery by remarking that as it was known that two currents act on one and the same magnet, it was obvious that they would act upon each other. Whereupon Arago arose to defend his friend. Drawing two keys out of his pocket he said, “Each of these keys attracts a magnet; do you believe that they therefore attract each other?”

A few years later Ampère showed how to express quantitatively the force between current elements, and indeed developed to a considerable degree the equivalence between a closed circuit carrying a current and a magnetic shell. So convincing was his analysis and so thorough his discussion of the subject, that Maxwell said of this memoir half a century later, “The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the ‘Newton of electricity.’ It is perfect in form and unassailable in accuracy; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electrodynamics.”

Shortly afterwards the dependence of a current on the conductivity of the wire used and the grouping of cells employed, was made clear by the work of Ohm. Many of his results were obtained independently by Joseph Henry (=19=, 400, 1831) of the Albany Academy, who described in 1831 a powerful electromagnet in which a great many coils of wire insulated with silk were wound around an iron core and connected in parallel with a single cell. He remarks in this paper that with long wires, as in the telegraph, many cells arranged in series should be used, whereas for several short wires connected in parallel a single cell with large plates is more efficient.

Current Induction.—Impressed by the fact that electric charges have the power of inducing other charges on neighboring conductors without coming into contact with them, Faraday was engaged in investigating the possibility of an analogous phenomenon in the case of electric currents. His idea at first seems to have been that a current should induce another current in any closed conducting circuit which happens to be in its vicinity. Experiment readily showed the falsity of this conception, but a brief deflection of the galvanometer in the secondary circuit was noticed at the instant of making and breaking the current in the primary. Further experiments showed that thrusting a permanent steel magnet into a coil connected to a galvanometer caused the needle to deflect. In fact Faraday’s report to the Royal Society on November 24th, 1831, contains a complete account of all experimental methods available for inducing a current in a closed circuit.

While Faraday is entitled to credit for the discovery of current induction by virtue of the priority of his publication, it must not pass unnoticed that Henry obtained many of the same experimental results independently and some even earlier. Henry was at this time instructor in mathematics at the Albany Academy, and seven hours of teaching a day made it well nigh impossible to carry on original research except during the vacation month of August. As early as the summer of 1830 he had wound 30 feet of copper wire around the armature of a horseshoe electromagnet and connected it to a galvanometer. When the magnet was excited, a momentary deflection was observed. “I was, however, much surprised,” he says, “to see the needle suddenly deflected from a state of rest to about 20° to the east, or in a contrary direction, when the battery was withdrawn from the acid, and again deflected to the west when it was re-immersed.” In addition a deflection was obtained by detaching the armature from the magnet, or by bringing it again into contact. Had the results of these experiments been published promptly, America would have been entitled to credit for the most important discovery of the greatest of England’s many great experimenters. But Henry desired first to repeat his experiments on a larger scale, and while new magnets were being constructed, the news of Faraday’s discovery arrived. This occasioned hasty publication of the work already done in an appendix to volume =22=, 1832, of the Journal.

At almost the same time Henry made another important discovery and this time he was anticipated by no other investigator in making public his results. In the paper already referred to be describes the phenomenon known to-day as self-induction. “When a small battery is moderately excited by diluted acid and its poles, which must be terminated by cups of mercury, are connected by a copper wire not more than a foot in length, no spark is perceived when the connection is either formed or broken; but if a wire thirty or forty feet long be used, instead of the short wire, though no spark will be perceptible when the connection is made, yet when it is broken by drawing one end of the wire from its cup of mercury a vivid spark is produced.... The effect appears somewhat increased by coiling the wire into a helix; it seems to depend in some measure on the length and thickness of the wire; I can account for these phenomena only by supposing the long wire to become charged with electricity which by its reaction on itself projects a spark when the connection is broken.”

Soon after, Henry went to Princeton and there continued his experiments in electromagnetism. No difficulty was experienced in inducing currents of the third, fourth and fifth orders by using the first secondary as primary for yet another secondary circuit, and so on (=38=, 209, 1840). The directions of these currents of higher orders when the primary is made or broken proved puzzling at first, but were satisfactorily explained a year later (=41=, 117, 1841). In addition induced currents were obtained from a Leyden jar discharge. Faraday failed to find any screening effect of a conducting cylinder placed around the primary and inside the secondary. Henry examined the matter, and found that the screening effect exists only when the induced current is due to a make or break of the primary circuit, and not when it is caused by motion of the primary.

Henry’s work was mainly descriptive; it remained for Faraday to develop a theory to account for the phenomena discovered and to prepare the way for quantitative formulation of the laws of current induction. This he did in his representation of a magnetic field by means of lines of force; a conception which he found afterwards to be equally valuable when applied to electrostatic problems. Every magnet and every current gives rise to these closed curves; in the case of a magnet they thread it from south pole to north, while a straight wire bearing a current is surrounded by concentric rings. The connection between lines of force and the induction of currents is contained in the rule that a current is induced in a closed circuit only when a change takes place in the number of lines of force passing through it. Furthermore the dependence of the current strength on the conductivity of the wire employed has led to recognition of the fact that it is the electromotive force and not the current itself which is conditioned by the change in magnetic flux.

Great interest was attached to the utilization of the newly discovered forces of electromagnetism. In 1831 Henry (=20=, 340, 1831) described a reciprocating engine depending on magnetic attraction and repulsion, and C. G. Page (=33=, 118, 1838; =49=, 131, 1845) devised many others. The latter’s most important work, however, was the invention of the Ruhmkorff coil. In 1836 (=31=, 137, 1837) he found the strongest shocks to be obtained, from a secondary coil of many windings forming a continuation of a primary of half the number of turns. His perfection of the self-acting circuit breaker (=35=, 252, 1839) widened the usefulness of the induction coil, and his substitution of a bundle of iron wires for a solid iron core (=34=, 163, 1838) greatly increased its efficiency.

Conservation of Energy.—Perhaps the most important advance of the nineteenth century has been the establishment of the principle of conservation of energy. Despite the fact that the “principe de la conservation des force vives” had been recognized by the French mathematicians of the early part of the century, the application of this principle even to purely mechanical problems was contested by some scientists. Through the early numbers of the Journal runs a lively controversy as to whether there is not a loss of power involved in imparting momentum to the reciprocating parts of a steam engine only to check the motion later on in the stroke. Finally Isaac Doolittle (=14=, 60, 1828), of the Bennington Iron Works, ends the discussion by the pertinent remark: “If there be, as is contended by one of your correspondents, a loss of more than one third of the power, in transforming an alternating rectilinear movement into a continuous circular one by means of a crank, I should like to be informed what would be the effect if the proposition were reversed, as in the case of the common saw mill, and in many other instances in practical mechanics.”

A realization of the equivalence of heat and mechanical work did not come until the middle of the century, in spite of the conclusive experiments of the American Count Rumford and the English Davy before the year 1800. So firmly enthroned was the caloric theory, according to which heat is an indestructible fluid, that evidence against it was given scant consideration. In fact the success of the analytical method introduced by Fourier in 1822 for the solution of problems in conduction of heat only added to the difficulties of the adherents of the kinetic theory. But recognition of heat as a form of energy was on the way, and when it came it made its appearance almost simultaneously in half a dozen different places. Perhaps Robert Mayer of Heilbronn was the first to state explicitly the new principle. His paper “On the Forces of Inorganic Nature” was refused publication in Poggendorff’s Annalen, but fared better at the hands of another editor. During the next few years Joule determined the mechanical equivalent of heat experimentally by a number of different methods, some of which had already been devised by Carnot. Of those he used, the most familiar consists in churning up a measured mass of water by means of paddles actuated by falling weights and calculating the heat developed from the rise in temperature. However, the work of the young Manchester brewer received little attention from the members of the British Association before whom it was reported until Kelvin showed them its significance and attracted their interest to it. Meanwhile Helmholtz had completed a very thorough disquisition on the conservation of energy not only in dynamics and heat but in other departments of physics as well. His paper on “Die Erhaltung der Kraft” was frowned upon by the members of the Physical Society of Berlin before whom he read it, and received the same treatment as Mayer’s from the editor of Poggendorff’s Annalen. Helmholtz’s “Kraft,” like the “vis viva” of other writers, is the quantity which Young had already christened energy. Not many years elapsed, however, until the convictions of Mayer, Joule, Kelvin and Helmholtz became the most clearly recognized of all physical principles. As early as 1850 Jeremiah Day (=10=, 174, 1850), late president of Yale College, admitted the improbability of constructing a machine capable of perpetual motion, even though the “imponderable agents” of electricity, galvanism and magnetism be utilized.

Thermodynamics.—The importance of the principle of conservation of energy lies in the fact that it unites under one rule such diverse phenomena as gravitation, electromagnetism, heat and chemical action. Another principle as universal in its scope, although depending upon the coarseness of human observations for its validity rather than upon the immutable laws of nature, was foreshadowed even before the first law of thermodynamics, or principle of conservation of energy, was clearly recognized. This second law was the consequence of efforts to improve the efficiency of heat engines. In 1824 Carnot introduced the conception of cyclic operations into the theory of such engines. Assuming the impossibility of perpetual motion, he showed that no engine can have an efficiency greater than that of a reversible engine. Finally Clausius expressed concisely the principle toward which Carnot’s work had been leading, when he asserted that “it is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.” Kelvin’s formulation of the same law states that “it is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.”

The consequences of the second law were rapidly developed by Kelvin, Clausius, Rankine, Barnard (=16=, 218, 1853, et seq.) and others. Kelvin introduced the thermodynamic scale of temperature, which he showed to be independent of such properties of matter as condition the size of the degree indicated by the mercury thermometer. This scale, which is equivalent to that of the ideal gas thermometer, was used subsequently by Rowland in his exhaustive determination of the mechanical equivalent of heat by an improved form of Joule’s method. He found different values for different ranges in temperature, showing that the specific heat of water is by no means constant. Since then electrical methods of measuring this important quantity have been used to confirm the results of purely mechanical determinations.

The definition of a new quantity, entropy, was found necessary for a mathematical formulation of the second law of thermodynamics. This quantity, which acts as a measure of the unavailability of heat energy, was given a new significance when Boltzmann showed its connection with the probability of the thermodynamic state of the substance under consideration. If two bodies have widely different temperatures, a large amount of the heat energy of the system is available for conversion into mechanical work. From the macroscopic point of view this is expressed by saying that the entropy is small, or if the motions of the individual molecules are taken into account, the probability of the state is low. The interpretation of entropy as the logarithm of the thermodynamic probability has thrown much light on the meaning of this rather abstruse quantity. Gibbs’s “Elementary Principles in Statistical Mechanics” treats in detail the fundamental assumptions involved in this point of view, its limitations and its consequences. In his “Equilibrium of Heterogeneous Substances” he had already extended the principle of thermal equilibrium to include substances which are no longer homogeneous. The value of the chemical potential he introduced determines whether one phase is to gain at the expense of another or lose to it. It is unfortunate that the analytical rigor and austerity of his reasoning combined with lack of mathematical training on the part of the average chemist, delayed true appreciation of his work and full utilization of the new field which he opened up.