UNIVERSITY OF CALIFORNJA AT LOS ANGELES Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/congressofartssc04congiala CONGRESS OF ARTS AND SCIENCE UNIVERSAL EXPOSITION, ST. LOUIS, 1904 EDITED BY HOWARD J. ROGERS, A.M., LL.D. DIRECTOS OF CONOBESSES VOLUME IV PHYSICS CHEMISTRY ASTRONOMY SCIENCES OF THE EARTH BOSTON AND NEW YORK HOUGHTON, MIFFLIN AND COMPANY dbe iRitaerjerilie ptt^jiy CambrilJoe 1906 COPYRIGHT 1906 BY HOUGHTON MIKFLIN * CO. ALL RIGHTS RBSKRVED Published June 1906 ORGANIZATION OF THE CONGRESS PRESIDENT OF THE EXPOSITION: HON. DAVID R. FRANCIS, A.M., LL.D. DIRECTOR OF CONGRESSES: HOWARD J. ROGERS, A.M., LL.D. Universal Exposition, 1904. ADMINISTRATIVE BOARD NICHOLAS MURRAY BUTLER, Ph.D., LL.D. President of Columbia University, Chairman. WILLIAM R. HARPER, Ph.D., LL.D. President of the University of Chicago. R. H. JESSE, Ph.D., LL.D. • President of the University of Missouri. HENRY S. PRITCHETT, Ph.D., LL.D. President of the Massachusetts Institute of Technology. HERBERT PUTNAM, Lrrr.D., LL.D. Librarian of Congress. FREDERICK J. V. SKIFF, A.M. Director of the Field Columbian Museum. OFFICERS OF THE CONGRESS PRESIDENT: SIMON NEWCOMB, Ph.D., LL.D. Retired Professor U. S. N. VICE-PRESIDENTS: HUGO MtJNSTERBERG, Ph.D., LL.D. Professor of Psychology in Harvard University. ALBION W. SMALL, Ph.D., LL.D. Professor of Sociology in the University of Chicago. 355836 TABLE OF CONTENTS DIVISION C — PHYSICAL SCIENCE T}ie Unity of Physical Science 3 Robert Simpson Woodward DEPARTMENT IX — PHYSICS The Fundamental Concepts of Physical Science 18 Edward Leamington Nichols The Progress of Physics in the Nineteenth Century 29 Carl Barus Section A — Physics op Matter. The Relations of the Science of Physics of Matter to Other Branches of Learning 69 Arthur Lalanne Kimbali:< Present Problems in the Physics of Matter 87 Francis Eugene Nipher Section B — Physics op Ether. The Ether and Moving Matter 105 Dewitt Bristol Brace Section C — Physics op the Electron. The Relations of Physics of Electrons to Other Branches of Science . . 121 Paul Langevin Present Problems of Radioactivity . ' 157 Ernest Rutherford Short Paper 187 Bibliography: Department of Physics 188 DEPARTMENT X — CHEMISTRY On the Fundamental Conceptions Underlying the Chemistry of the Element Carbon 195 John Ulric Nef The Progress and Development of Chemistry during the Nineteenth Century 221 Frank Wigglesworth Clarke Section A — Inorganic Chemistry. Inorganic Chemistry: Its Relations with the Other Sciences , . . 243 Henri Moissan viii TABLE OF CONTENTS The Present Problems of Inorganic Chemistry 258 Sir William Ramsay Section B — Organic Chemistry. The Relations of Organic Chemistry to Other Sciences .... 276 Julius Stieglitz Present Problems of Organic Chemistry 285 William Albert Noyes Section C — Physical Chemistry. The RelcUions of Physical Chemistry to Physics and Chemistry . . . 304 Jacobus Henricus van 't Hoff The Physical Properties of Aqueous Salt Solutions in relation to the Ionic Theory 311 Arthur A. Noyes Short Papers 324 Section D — Physiological Chemistry. Problems in Nutrition - . 327 Otto Cohnheim The Present Problems of Physiological Chemistry 336 Russell Henry Chittenden Short Paper 351 Bibliography: Department of Chemistry 352 Special Works of Reference for Paper of Professor Frank W. Clarke . . 354 Special Works of Reference for Section of Physiological Chemistry . . 355 DEPARTMENT XI — ASTRONOMY Fundamental Conceptions and Methods in Astronomical Science . . 360 Lewis Boss The Light of the Stars 374 Edward Charles Pickering Section A — Astrometry. The Development of Celestial Mechanics during the Nineteenth Century . 387 OSKAR BaCKLUND Statistical Methods in Stellar Astronomy 396 Jacobus Cornelius Kapteyn Short Papers 426 Section B — Astrophysics. The Relations of Photography to Astrophysics ..,,.. 429 Herbert Hall Turner TABLE OF CONTENTS ix The Problems of Astrophysics 446 William Wallace Campbell Short Papers 470 Bibliography : Department of Astronomy 471 DEPARTMENT XII — SCIENCES OF THE EARTH The Methods of the Earth-Sciences 477 Thomas Chrowder Chamberlin The Relations of the Earth-Sciences in View of their Progress in the Nine- teenth Century 488 WILLLA.M Morris Davis Section A — Geophysics. Present Problems of Geophysics 608 George Ferdinand Becker Section B — Geology. The Problems of Geology 525 Charles Richard Van Hise Section C — Paleontology. The Relations of Paleontology to Other Branches of Science . . . 551 Arthtir Smith Woodward The Present Problems of Paleontology ' . 566 Henry Fairfield Osborn Section D — Petrology and Mineralogy. The Relations existing between Petrography and its Related Sciences . 591 Ferdinand Zirkel Short Paper 604 Section E — Physiography. The Relations of Physiography to the Other Sciences .... 607 Albrecht Penck Works of Reference to accompany Professor PencWs Paper .... 626 Physiographic Problems of To-day 627 Israel Cook Russell Section F — Geography. The Present Problems of Geography 653 Hugh Robert Mill The Relative Value of Geographical Position 671 Henry Yule Oldham X TABLE OF CONTENTS Section G — Oceanography. The Relation of Oceanography to the Other Sciences 683 Sir John Murray The CtUtivation of Marine and Fresh-Water Animals in Japan . . . 694 K. MiTSUKURI Section H — Cosmical Physics. The Relation of Meteorology to Other Sciences 733 SvANTE August Arrhenius The Present Problems of Meteorology 741 Abbott Lawrence Rotch The Present Problems of Terrestrial Magnetism 750 Louis Agricola Bauer Books of Reference on Geology and Paleontology 757 Works of Reference on Petrology and Mineralogy 760 Books of Reference on Physiography and Geography 762 Special Books of Reference on Oceanography 763 General Books of Reference relating to Meteorology 764 CONTENTS OF THE SERIES 765 DIVISION C — PHYSICAL SCIENCE DIVISION C — PHYSICAL SCIENCE (Hall 4, September 20, 10 a. m.) Speaker : Professor Robert S. Woodward, Columbia University. THE UNITY OF PHYSICAL SCIENCE BY ROBERT SIMPSON WOODWARD [Robert Simpson Woodward, Ph.D., Sc.D., LL.D., President of the Carnegie In- stitution of Washington, b. Rochester, Mich., 1849. C.E. University of Michi- gan, 1872; Ph.D. University of Michigan, 1892; Honorary LL.D. University of Wisconsin, 1904; Sc.D., University of Pennsylvania, and Columbia Univer- sity, 1905. Assistant engineer, U. S. Lake Survey, 1872-82; assistant astro- nomer, U. S. Transit of Venus Commission, 1882-84; astronomer, geographer, and chief geographer, U. S. Geological Survey, 1884-90; assistant, U. S. Coast and Geodetic Survey, 1890-93; Professor of Mechanics and Mathematical Physics, Columbia University, 1893-1905; Dean of School of Pure Science, ibid., 1895-1905; President of Carnegie Institution of Washington, 1905. Member of National Academy of Sciences; Past President and Treasurer (since 1894) of American Association for the Advancement of Science; Past President of American Mathematical Society and of New York Academy of Sciences ; mem- ber of Astronomical and Astrophysical Society of America, Geological Society of America, Physical Society of America, and Washington Academy of Sciences. Author of Smithsonian Geographical Tables ; Higher Mathematics (with Mansfield Merriman); also of many Government reports and numerous papers and ad- dresses on subjects in astronomy, geodesy, mathematics, mathematical physics, and education.] There is a tradition, still tacitly sanctioned even by men of science, that there have been epochs when the more eminent minds were able to compass the entire range of knowledge. Amongst the vanishing heroic figures of the past it seems possible, indeed, to discern, here and there, a Galileo, a Huygens, a Descartes, a Leibnitz, a Newton, a Laplace, or a Humboldt, each capable, at least, of summing up with great completeness the state of contemporary knowledge. Traditions, however, are generally more or less mythical, and the myth in this case seems to be in flat contradiction with the fact that there never was such an epoch, that the great masters of our distinguished pre- decessors were, after all, much like the masters of to-day, simply the leading specialists of their times. But however this may be, if we grant the possibility of the requisite attainments, even in a few individuals at any epoch, we shall speedily conclude that there never was an epoch so much in need of them as the immediate present, when the divisional speakers of this Congress are called upon to explain the unities which pervade the ever-widening and largely diverse fields of their several domains. 4 PHYSICAL SCIENCE The domain of physical science, concerning which I have the honor to address you to-day, presents peculiar and peculiarly for- midable difficulties in the way of a summary review. While we may not be disposed to limit the wide range of inclusion specified by our programme, we must at once disclaim any attempt to speak author- itatively with respect to most of its details. There is, in fact, such a vast array of knowledge now comprehended under any one of the six Departments of our Division, that the boldest author must hesi- tate to enter on a limited discussion with respect to any of them. But if it is thus difficult to consider any department of physical science, it appears incomparably more difficult to contemplate all of them in the bewildering complexity of their interrelations and in the bewildering diversity of their subject-matter. What, for example, could seem more appalling to the average man of science than the duty of explaining the connections of archeology and astro- physics, or those of ecology and electrons? Happily, however, the managers of the Congress have provided an adequate division of labor, whereby the technical details of the various Departments are allotted to experts, giving thus to a divis- ional speaker a degree of freedom with respect to depth in some way commensurate with the breadth of his task. Presuming, there- fore, that I may deal only with the broader outlines and salient features of the subject, I invite your attention to a summary view of the present status and the apparent trend of physical science. Whatever may be affirmed with respect to science in general, there appears to be no doubt that all of the physical sciences are characterized by three remarkable unities, — a unity of origin, a unity of growth, and a unity of purpose. Physical science originates in observation and experiment; it rises from the fact-gathering stage of unrelated qualities to the higher plane of related quantities, and passes thence on to the realm of correlation, computation, and prediction under theory; and its purpose is to interpret in consistent and verifiable terms the universe, of which we form a part. The re- cognition of these unities is of prime importance ; for it helps us to understand and to anticipate a great diversity of perfection amongst the different branches of science, and hence leads us to appreciate the desirability of hearty cooperation on the part of scientific workers in order that progress may be ever positive towards the common goal. Glancing rapidly seriatim at the different departments of physical science as specified by our programme, we come first to a consider- ation of formal physics, and we may most quickly orient ourselves aright in this department by trying to state in what respects the physics of to-day differs from the physics of a hundred years ago. In spite of the extraordinary perfection of the work of Lagrange, Laplace, Fourier, Young, Fresnel, Poisson, Green, Gauss, and others THE UNITY OF PHYSICAL SCIENCE 5 of the early part of the nineteenth century, it will be at once admitted that great progress has been made. In addition to noteworthy ad- vances and improvements along the lines laid down by these mas- ters, there have been developed the relatively new fields of elasticity, electromagnetics, thermodynamics, and astrophysics; and there has been discovered the widest of all generalizations in physical science, — the law of conservation of energy. Whereas it was easy a century ago to conceive, as in gravitational astronomy, of action at a dis- tance across empty space, the universe in the mean time has come to appear more and more plethoric not only with "gross matter," but with that most wonderful entity we call the ether. The astro- nomers have shown us, in fact, that the number of molar systems in the universe is enormously greater than was supposed possible a cen- tury ago; while the physicists have revealed to us molecular systems rivaling our solar system and its Jovian and Saturnian subsystems, and they have loaded down the ether with a burden of properties and relationships which its usual tenuity seems scarcely fitted to bear. Whereas, also, a century ago the tendency of thought, under the stimulus of the remarkable developments of the elastic solid theory of light and the fluid theories of electricity, was chiefly to- wards an ether whose continuity would have pleased Anaxagoras, the tendency to-day is chiefly towards an ether whose atomicity would have pleased Democritus. On the whole, it must be said that the advances of the past cen- tury, and especially those of the past half -century, have been mainly along the lines of molecular physics. The epoch of Laplace was dis- tinctly an epoch of molar physics; the epoch of to-day is distinctly an epoch of molecular physics. Light, heat, electricity, and magnetism have been definitely correlated as molecular and ethereal pheno- mena; while the recently discovered X-rays and the wonders of radioactivity, along with the "electrons," the "corpuscles" and the " electrions " of current investigations, all point towards a molecular constitution of the ether. Thermodynamics, likewise, large as it has grown in recent decades, is essentially a development of the mole- cular theory of gases. It would be too bold, perhaps, to assert that the trend of accumulating knowledge is towards an atomic unity of matter, but the day seems not far distant when there will be room for a new Principia and for a treatise which will accomplish for molecular systems what the Mecanique Celeste accomplished for the solar system. One of the most important advances of recent decades is found in the fixation of ideas with respect to the units of physical science, and in the great improvements which have been wrought in metro- logy by the "International Bureau of Weights and Measures." Our standards of length, mass, and time are now fixed with a degree 6 PHYSICAL SCIENCE of precision which leaves little to be desired for the present; and the capital resources of measurement and calculation are now avail- able to an extent never hitherto approached. It should be noted, however, that confidence in the stability of our standards is by no means comparable with the perfection of their current applications. Indeed, we may raise with respect to them the question so long mooted with regard to the motions of the members of the solar system: namely, are they stable? Not- withstanding the admirable precision of the intercomparisons of the prototype meters and prototype kilograms and the equally admir- able precision of Professor Michelson's determination of the length of the meter in terms of wave-lengths of cadmium light, we cannot affirm that these observed relations will hold indefinitely. Our inherited notions of mass have been rather rudely shaken, also, by the penetrating criticisms of Mach, and it appears possible even that the law of conservation of mass may need modification in the light of pending researches. But worst of all, our time-unit, the sidereal day, is so far from possessing the element of constancy that we may affirm with practical certainty that it is secularly variable. Having realized, through Professor Michelson's superb determination just referred to, the cosmic standard of length suggested by Max- well thirty years ago, we are now much more in need of an equally trustworthy cosmic standard of time. If the progress of physics during the past century has been chiefly in the direction of atomic theory, the progress of chemistry has been still more so. Chemistry is, in fact, the science of atoms and mole- cules par excellence, a distinction it has maintained for well-nigh a full century under the dominance of the fruitful atomic and mole- cular hypotheses of Dalton and of Avogadro and Ampere, and under the similarly fruitful laws of gases established by Dalton and Gay- Lussac. Perhaps the most striking feature of this progress, in a general way, is the gradual disappearance it has entailed of the imaginary lines which have been long thought to separate the fields of chemistry and physics. Through the remarkable discoveries of Faraday the two fields have been found to overlap in actual electrical contact. Through the wonderful revelations of spectrum analysis, originating with Bunsen and Kirchhoff , they have been proved to be very largely common ground. And through the broader generaliz- ations inaugurated by Willard Gibbs,Helmholtz,and others, they are now both somewhat in danger of being annexed as a sub-province of rational mechanics. To one whose work has fallen more especially in the fields of pre- cise astronomy, geodesy, or metrology, it might seem a just reproach to chemistry that it is a science whose measurements and calcul- ations demand, as a rule, no greater arithmetical resources than THE UNITY OF PHYSICAL SCIENCE 7 those of four-place tables of logarithms and anti-logarithms. The so-called "Constants of Nature " supplied by chemistry are, in fact, known with a low degree of certainty; a degree expressed, say, by three to five significant figures. A small amount of reflection, how- ever, will convince one that the phenomena with which the chemist has to deal are usually far more complex than those which have yielded the splendid precision of astronomy, geodesy, and metro- logy. Moreover, it should be observed that the certainties even of these highly perfected sciences are very unequal in their different branches. It appears more correct, therefore, as well as more just, considering the central position it occupies and the wide range of its ramifications, along with the vast aggregate of qualitative and quantitative knowledge it has massed, to assert that the precision of chemistry affords the best numerical index of the present state of physical science. That is, when reduced to the most compact form of statement, the certainties of physical science are best indicated, in a general way, by a table of the combining weights of the eighty- odd chemical elements. When one contemplates the numbers of such a table, and when one adds to its suggestions those which flow from the various peri- odic groupings of the same numbers, he can hardly avoid being in- spired by the day-dreams of those who have looked long for the atomic unity of matter. But however the grand problem which thus obtrudes itself may be resolved finally, it appears certain that this table must stand as one of the great landmarks along the path of progress in physical science. It was justly remarked by Laplace in his Systhne du Monde that "L'Astronomie, par la dignity de son objet et par la perfection de ses theories, est le plus beau monument de I'esprit humain, le titre le plus noble de son intelligence " ; and we must all admit that subse- quent progress has gone far to maintain this high position for the most ancient and interesting of the older sciences. One finds little difl&culty in accounting for the early rise of astronomical science and for the universal interest in celestial phenomena. Their im- manence and omnipresence appeal even to the dullest intellects. But it is not so easy to account for the remarkable fact that although astronomy deals chiefly with the relations of bodies separated by immense distances, progress in its development has thus far been at least equal to, if not in advance of, the progress of physics and chemistry, which have to deal with matter close at hand. Without attempting a full explanation of this fact, it may suffice to observe that the principal phenomena of astronomy thus far developed appear to be relatively simple in comparison with those of the other physical sciences; and that the immense distances which separate the celestial bodies, instead of being an obstacle to, are a fortunate 8 PHYSICAL SCIENCE circumstance directly in favor of, the triumphant advances which have distinguished astronomical science from the epoch of Galileo down to the present day. Not less noteworthy than his high estimate of the position of astronomy in his time are Laplace's anticipations of the course of future progress. Our admiration is kindled by the clearness of his vision with respect to ways and means, and by the penetration of his predictions of future discoveries. Advances in sidereal astro- nomy, he rightly thought, would depend chiefly on improvements in telescopes; while advances in dynamical astronomy were to come along with increased precision in the observed places of the members of the solar system and along with the growing perfection of analysis. It is almost needless to say that Laplace's brilliant anti- cipations have been quite surpassed by the actual developments. Observational astronomy has become one of the most delicately perfect of all the sciences; dynamical astronomy easily outstrips all competitors in the perfection of its theories and in the certainty of its predictions; while the newly developed branch of astrophysics supplies the last link in the chain of evidence of the essential unity of the material universe. The order of the dimensions and the order of the mass contents of the visible universe, at any rate, have been pretty clearly made out. In addition to the vast aggregate of direct observational evi- dence collected and recorded during the past century, numerous theoretical researches have gone far, also, to interpret the laws which reign in the apparent chaos of the stars. The solar system, with its magnificent subsystems, has been proved to exhibit the type of stellar systems in general. In a profound investigation recently published. Lord Kelvin has sought to correlate under the law of gravitation the principal observed data of the visible universe. Assuming this universe to lie within a sphere of radius equal to the distance of a star whose parallax is one thousandth of a second of arc, he concludes that there must be something like a thousand million masses of the mag- nitude of our sun within that sphere. Light traveling at the rate of 300,000 kilometers per second would require about six thousand years to traverse the diameter of this universe, and while the aver- age distance asunder of the visible stars is considerably less, it is still of the same order. It is only essential, therefore, to imagine our luminary surrounded by a thousand million such suns, most of which are, in all probability, attended by groups of planets, to get some idea of the quantity of matter within visual range of our relatively insignificant terrestrial abode. And the imposing range of the astronomer's time-scale is perhaps impressively brought home to us when we reflect that a million years is the smallest convenient THE UNITY OF PHYSICAL SCIENCE 9 unit for recording the life-history of a star, while the current events in that history are transmitted across the interstellar medium by vibrations which occur at the rate of about six hundred million million times per second. Measured by its accumulation of achieve- ments, then, the astronomy of to-day fulfills the requirements of a highly developed science. It is characterized by a vast aggregate of accurately determined facts related by theories founded on a small number of hypotheses. In the past it has called forth the two greatest of all systematic treatises, the Principia of Newton and the Mecanigue Celeste of Laplace. It has probably done more also than any other science, up to the present time, to illuminate the dark periods during which man has floundered in his struggle for advance- ment; and the indications are that its prestige will long continue. But there are spots on every sun; and lest some may infer, even humorously, as Carlyle did seventy-odd years ago, that our system of the world is •''as good as perfect," attention should be called to some noteworthy defects in astronomical data and to some singular obscurities in astronomical theory. Here, however, great caution and brevity are essential to avoid poaching on the preserves of our colleagues of the Sections. It may suffice, therefore, merely to mention, under the head of defective data, the low precision of the solar parallax, the aberration constant, the masses of the members of the solar system, and the uncertainty of our time-unit, already referred to. Two instances, likewise, which belong to the general field of physics as well, may suffice as illustrations of obscurities in astro- nomical theory. Stated in the order of their apparent complexity, these obscurities refer to the law of gravitation and to the phenome- non of stellar aberration. Probably both are related, and one may hope that any explanation of either will throw light on the other. So long as no attempt is made to reconcile the law of gravitation with other branches of physics, progress, up to a certain point, is easy; and probably great advantage has resulted from the fact that dynam- ical astronomers have not been seriously disturbed by a desire to harmonize this law with the more elementary laws of mechanics. Perhaps they have unconsciously rested on the platform that gravi- tation is one of the " primordial causes " which are impenetrable to us. There are some indications that even Laplace and Fourier did so rest. However this may be, it has grown steadily more and more imperative during the past century to explain gravitation, or to dis- cover the mechanism which provides that the force between two widely separated masses is proportional to their product directly and to the square of the distance between them inversely. All evidence seems to indicate that the ether must provide this mechanism; but, strangely enough, so far, the ether has baffled all attempts to reveal the secret. The problem has been attacked also on the purely 10 PHYSICAL SCIENCE observational side of the numerical value of the gravitation constant. But the splendid experimental researches for this purpose throw no light on the mechanism in question, and, unfortunately, they bring out values for the constant of a low order of precision. With regard to stellar aberration, it must be at once admitted that we have neither an adequate theory nor a precisely determined fact. The astronomer has generally contented himself with the elementary view that aberration is a purely kinematical phenomenon; that the earth not only slips through the ether without sensible retardation, but that the ether slips through the earth without sensible effects. This difficulty was recognized, in a way, by Young and Fresnel, and, although the subject of elaborate investigation in recent decades, it has proved equally baffling with Newtonian gravitation. As in the case of the latter also, the numerous attempts made to determine the constant of aberration by observational methods have been re- warded by results of only meagre precision. Possibly the time has arrived when one may raise the question. Within what limits is it proper to speak of a gravitation constant or of an aberration con- stant? • If we agree with Laplace that astronomy is entitled to the highest rank among the physical sciences, we can accord nothing short of second place to the sciences of the earth. Most of them are, indeed, intimately related to astronomy; and some of them are scarcely less ancient in their origins, less dignified in their objects, or less perfect in their theories. Primarily, also, it should be observed, geo- physics is not simply a part of, but is the very foundation of, astro- nomy; for the earth furnishes the orientation, the base-line, and the timepiece by means of which the astronomer explores the heavens. Geology, likewise, in the broader sense of the term, as we are now coming to see, is a fundamental science not only by reason of its interpretations of terrestrial phenomena, but also by reason of its parallel interpretations of celestial phenomena; for there is little doubt that in the evolution of the earth we may read a history which is in large degree typical of the history of celestial bodies. In any revised estimate, therefore, of the relative rank of the physical sciences, while it would be impossible to lower the science of the heavens, it would appear essential to raise the sciences of the earth to a much higher plane of importance than was thought appropriate by our predecessors of a hundred years ago. As with physics, chemistry, and astronomy, the wonderful progress of the nineteenth century in geophysical science has been along lines converging towards the more recondite properties of matter. All parts of the earth, through observation, experiment, induction, and deduction, have yielded increasing evidence of limited unities amid endless diversities. Adopting the convenient terminology of THE UNITY OF PHYSICAL SCIENCE 11 geologists for the different shells of the earth, let us glance rapidly in turn at the sciences of the atmosphere, the hydrosphere or oceans, the lithosphere or crust, and the centrosphere or nucleus. The atmosphere is the special province of meteorologists, and although they are not yet able to issue long-range predictions, like those guaranteed by our theories of tides and terrestrial magnetism, it must be admitted that they have made great progress towards a rational description of the apparently erratic phenomena of the weather. One of the peculiar anomalies of this science illustrates in a striking way the general need of additional knowledge of the properties of matter; in this case, especially, the properties of gases. It is the fact that in meteorology greater progress has been made, up to date, in the interpretation of the kinetic than in the inter- pretation of the static phenomena of the atmosphere. Considering that static properties are usually much simpler than kinetic proper- ties, it seems strange that we should know much more about cyclones, for example, than we do about the mass and the mass distribution of the atmosphere. In respect to this apparently simple question meteor- ology seems to have made no advance beyond the work of Laplace. There are indications, however, that this, along with many other questions, must await the advent of a new Principia. The geodesists, who are the closest allies of the astronomers, may be said to preside over the hydrosphere, since most of their theories as well as most of their observations are referred to the sea level. They have determined the shape and the size of the earth to a sur- prising degree of certainty; but they are now confronted by pro- blems which depend chiefly on the mass and mass distribution of the earth. The exquisite refinement of their observational methods has brought to light a minute wandering in the earth of its axis of rotation, which makes the latitude of any place a variable quantity; but the interpretation of this phenomenon is again a physical and not a mensurational problem. They have worked improvements also in all kinds of apparatus for refined measurements, as of base- lines, angles, and differences of level; but here, likewise, they appear to approach limits set by the properties of matter. The lithosphere was once thought to be the restricted province of geologists, but they now lay claim to the entire earth, from the centre of the centrosphere to the limits of the atmosphere, and they threaten to invade the region of the astronomers on their way toward the outlying domain of cosmogony. Geology illustrates better than any other science, probably, the wide ramifications and the close interrelations of physical phenomena. There is scarcely a process, a product, or a principle in the whole range of physical science, from physics and chemistry up to astronomy and astrophysics, which is not fully illustrated in its imiqueness or in its diversity by actual 12 PHYSICAL SCIENCE operations still in progress on the earth, or by actual records pre- served in her crust. The earth is thus at once the grandest of labor- atories and the grandest of museums available to man. Any summary statement, from a non-professional student, of the advances in geology during the past century, would be hopelessly in- adequate. Such a task could be fitly undertaken only by an expert, or by a corps of them. But out of the impressive array of achieve- ments of this science, two seem to be especially worthy of general attention. They are the essential determination of the properties and the role of the lithosphere, and the essential determination of the time-scale suitable for measuring the historical succession of ter- restrial events. The lithosphere is the theatre of the principal activ- ities, mechanical and biological, of our planet; and a million years is the smallest convenient unit for recording the march of those activ- ities. When one considers the intellectual as well as the physical obstacles which had to be surmounted, and when one recalls the bitter controversies between the Neptunists and the Vulcanists and between the Catastrophists and the Uniformitarians, these achieve- ments are seen to be amongst the most important in the annals of science. The centrosphere is the terra incognita whose boundaries only are accessible to physical science. It is that part of the earth con- cerning which astronomers, geologists, and physicists have written much, but concerning which, alas! we are still in doubt. Where direct observation is imattainable, speculation is generally easy, but the exclusion of inappropriate hypotheses is, in such cases, generally diffi- cult. Nevertheless, it may be affirmed that the range of possibilities for the state of the centrosphere has been sharply restricted during the past half-century. Whatever may have been the origin of our planet, whether it has evolved from nebular condensation or from meteoric accretion; and whatever may be the distribution of tem- perature within the earth's mass as a whole; it appears certain that pressure is the dominant factor within the nucleus. Pressure from above, supplied in hydrostatic measure by the plastic lithosphere, supplemented by internal pressure below, must determine, it would seem, within narrow limits, the actual distribution of density through- out the centrosphere, regardless of its material composition, of its effective rigidity, or of its potential liquidity. Here, however, we are extending the known properties of matter quite beyond the bounds of experience, or of present possible experiment; and we are again reminded of the unity of our needs by the diversity of our difficulties. In his recently published autobiography, Herbert Spencer asserts that at the time of issue of his work on biology (1864) "not one person in ten or more knew the meaning of the word . . . and THE UNITY OF PHYSICAL SCIENCE 13 among those who knew it, few cared to know anything about the subject." That the attitude of the educated public towards biolog- ical science could have been thus indifferent, if not inimical, forty years ago, seems strange enough now even to those of us who have witnessed in part the scientific progress subsequent to that epoch. But this was a memorable epoch, marked by the advent of the great intellectual awakening ushered in by the generalizations of Darwin, Wallace, Spencer, and their coadjutors. And the quarter of a cen- tury which immediately followed this epoch appears, as we look back upon it, like an heroic age of scientific achievement. It was an age during which some men of science, and more men not of science, lost their heads temporarily, if not permanently; but it was also an age during which most men of science, and thinking people in gen- eral, moved forward at a rate quite without precedent in the history of human advancement. A new, and a greatly enlarged, view of the universe was introduced in the doctrine of evolution, advanced and opposed, alike vigorously, chiefly by reason of its biological appli- cations and implications. Galileo, Newton, and Laplace had given us a system of the inorganic world; Darwin, Spencer, and their followers have foreshadowed a system which includes the organic world as well. The astonishing progress of biology in recent times furnishes the most convincing evidence of the unity and the efficiency of the methods of physical science in the interpretation of natural phe- nomena. For the biologist has followed the same methods, with changes appropriate to his subject-matter only, as those found fruitful in astronomy, chemistry, and all the rest. And whatever may be the increased complexity of the organic over the inorganic world, or however high the factor of life may seem to raise the pro- blems of biology above the plane of the other physical sciences, there has appeared no sufficient reason, as yet, to doubt either the validity or the adequacy of those methods. Moreover, the interrelations of biology with chemistry and phys- ics especially are yearly growing more and more extended and in- timate through the rapidly expanding researches of bacteriology, physiology, and physiological chemistry, plant and animal patho- logy, and so on, up through cytology to the embryology of the higher forms of life. Through the problems of these researches also we are again brought face to face, sooner or later, with the problems of molecular science. And finally, what may be said of anthropology, which is at once the most interesting and the most novel of the physical sciences, — interesting by reason of its subject-matter, novel by reason of its applications? Some of us, perhaps, might be inclined to demur from a classification which makes man, along with matter, a fit object 14 PHYSICAL SCIENCE of investigation in physical science. Granted even that he is usually a not altogether efficient thermodynamic engine, it may yet appear that he is worthy of a separate category. Fortunately, however, it is not a rule of physical science to demand immediate answers to such ulterior questions. It is enough for the present to know that man furnishes no exception, save in point of complexity, to the mani- festations of physical phenomena so widely exhibited in the animal kingdom. But whatever may be our inherited prejudices, or our philosophic judgments, we are confronted by the fact that the study of man in all his attributes is now an established domain of science. And herein we rise to a table-land of transcendent fascination; for, to adapt a phrase of an eminent master in physical science, the instru- ments of investigation are the objects of research. Herein also we find the culminating unity, not only of the physical sciences, but of all of the sciences; and it is chiefly for the promotion of these higher interests of anthropology that we are assembled in this cosmopoli- tan congress to-day. It has been our good fortune to witness in recent decades an un- paralleled series of achievements in the fields of physical science. All of them, from anthropology and astronomy up to zoology, have yielded rich harvests of results; and one is prone to raise the question whether a like degree of progress may be expected to prevail during the century on which we have now entered. No man can tell what a day may bring forth; much less may one forecast the progress of a decade or a century. But, judging from the long experience of the past, there are few reasons to doubt and many reasons to expect that the future has still greater achievements available. It would appear that we have found the right methods of investigation. Phil- osophically considered, the remarkable advances of the past afford little cause for marvel. On the contrary, they are just such results as we should anticipate from persistent pursuit of scientific investi- gation. Conscious of the adequacy of his methods, therefore, the devotee to physical science has every inducement to continue his labors with unflagging zeal and confident optimism. DEPARTMENT IX — PHYSICS DEPARTMENT IX — PHYSICS (HaU 6, September 20, 2 p. m.) Chairman: Professor Henry Crew, Northwestern University. Speakers: Professor Edward L. Nichols, Cornell University. Professor Carl Barus, Brown University. The Chairman of the Department of Physics was Professor Henry Crew, of Northwestern University, who opened the proceedings of the Department by saying: " Whatever views we may entertain con- cerning the classification of the sciences which Professor Miinster- berg has proposed for the guidance of this congress, we will, I believe, all concur in the opinion that it is full of suggestion and very instruct- ive. For my own part, I think it gives a really profound glimpse into the relationships of the various departments of human learn- ing. You will recall that the first main division is between the pure and applied sciences. We have come together this afternoon to con- sider a subject which lies in the former group. But physics is not the only pure science: it is merely one belonging to that subdivision which deals with phenomena. Again, there are two classes of phe- nomena, the mental and the physical: and physics has to do only with the latter class. Indeed, it does not cover the entire field of physical phenomena, but constitutes merely one of the six Depart- ments in this Division. Physics is, however, the most general and most fundamental of this group of six. It is properly found, there- fore, at the head of the list. Our theme this afternoon, then, is that fundamental science which deals with the general properties of matter and energy and which includes the general principles of all physical phenomena. We are fortunate in having with us men who, by wide experience gained in their own researches, and by a thor- ough study of the philosophy of the subject, are eminently fitted to treat this topic." THE FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE BY EDWARD LEAMINGTON NICHOLS [Edward Leaminston Nichols, Professor of Physics, Cornell University, and Editor-in-chief of the Physical Review, b. September 14, 1854, Leamington, England. B.S. Cornell University, 1875; Ph.D. Gottingen, 1879; Fellowship in Physics, Johns Hopkins University, 1879-80; Professor of Physics and Chem- istry, Central University, 1881-83; Professor of Physics and Astronomy, Uni- versity of Kansas, 1883-87. Member of National Academy of Science, American Academy of Arts and Sciences, American Institute of Electrical Engineers, American Philosophical Society, American Physical Society. Author of A Lab- oratory Manual of Physics and Applied Electricity; The Outlines of Physics, etc.] All algebra, as was pointed out by von Helmholtz ^ nearly fifty years ago, is based upon the three following very simple proposi- tions: Things equal to the same thing are equal to each other. If equals he added to equals the wholes are equal. If uneqvxils he added to eqvxils the wholes are uneqvul. Geometry, he adds, is founded upon a few equally obvious and simple axioms. The science of physics, similarly, has for its foundation three funda- mental conceptions: those of mass, distance, and time, in terms of which all physical quantities may be expressed. Physics, in so far as it is an exact science, deals with the relations of these so-called physical quantities; and this is true not merely of those portions of the science which are usually included under the head of physics, but also of that broader realm which consists of the entire group of the physical sciences, viz., astronomy, the physics of the heavens; chemistry, the physics of the atom; geology, the physics of the earth's crust; biology, the physics of matter im- bued with life; physics proper (mechanics, heat, electricity, sound, and light). The manner in which the three fundamental quantities L, M, and T (length, mass, and time) enter, in the case of a physical quantity, is given by its dimensional formula. Thus the dimensional formula for an acceleration is LT'^ which expresses the fact that an acceleration is a velocity (a length di- vided by a time) divided by a time. Energy has for its dimensional formula UMT-^; it is a force, LTm (an acceleration multiplied by a mass), multiplied by a distance. Not all physical quantities, in the present state of our knowledge, can be assigned a definite dimensional formula, and this indicates that not all of physics has as yet been reduced to a clearly established * Von Helmholtz, Populdre Wissenschaftliche Vortrdge, p. 136. FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 19 mechanical basis. The dimensional formula thus affords a valuable criterion of the extent and boundaries of our strictly definite know- ledge of physics. Within these boundaries we are on safe and easy ground, and are dealing, independent of all speculation, with the relations between precisely defined quantities. These relations are mathematical, and the entire superstructure is erected upon the three fundamental quantities, L, M, and T, and certain definitions; just as geometry arises from its axioms and definitions. Of many of those physical quantities, for which we are not as yet able to give the dimensional formula, our knowledge is precise and definite, but it is incomplete. In the case, for example, of one import- ant group of quantities, those used in electric and magnetic measure- ments, we have to introduce, in addition to L, M, and T, a constant factor to make the dimensional formula complete. This, the swp- pressed factor of Riicker,^ is /u,, the magnetic permeability, when the quantity is expressed in the electromagnetic system, and becomes k, the specific inductive capacity, when the quantity is expressed in terms of the electrostatic system. Here the existence of the suppressed factor is indicative of our ignorance of the mechanics involved. If we knew in what way a medium like iron increased the magnetic field, or a medium like glass the electric field, we should probably be able to express /x, and k in terms of the three selected fundamental dimensions and complete the dimensional formulae of a large number of quantities. Where direct mechanical knowledge ceases, the great realm of physical speculation begins. It is the object of such speculation to place all phenomena upon a mechanical basis; excluding as unsci- entific all occult, obscure, and mystical considerations. Whenever the mechanism by means of which phenomena are pro- duced is incapable of direct observation either because of its remote- ness in space, as in the case of physical processes occurring in the stars, or in time, as in the case of the phenomena with which the geologist has to do, or because of the minuteness of the moving parts, as in molecular physics, physical chemistry, etc., the speculative ele- ment is unavoidable. Here we are compelled to make use of analogy. We infer the unknown from the known. Though our logic be without flaw, and we violate no mathematical principle, yet are our con- clusions not absolute. They rest of necessity upon assumptions, and these are subject to modification indefinitely as our knowledge becomes more complete. A striking instance of the uncertainties of extrapolation and of the precarious nature of scientific assumptions is afforded by the various estimates of the temperature of the sun. Pouillet placed this tempera- ture between 146rC. and 1761°C.; Secchi at 5,000,000°; Ericsson * Rucker, Philos. Mag., 27, p. 104. 1889. 20 PHYSICS at 2,500,000°. The newer determinations * of the temperature of the surface are, to be sure, in better agreement. Le Chatelier finds it to be 7600° J Paschen, 5400°; Warburg, 6000°. Wilson and Gray publish as their corrected result 8000°. The estimate of the internal temper- ature is of a more speculative character. Schuster's computation gives 6,000,000° to 15,000,000°; that of Kelvin, 200,000,000°; that of Ekholm, 5,000,000°. Another interesting illustration of the dangers of extrapolation occurs in the history of electricity. Faraday, starting from data con- cerning the variation between the length of electric sparks through air with the difference of potential, made an interesting computation of the potential difference between earth and sky necessary to dis- charge a cloud at a height of one mile. He estimated the difference of potential to be about 1,000,000 volts. Later investigations of the sparking distance have, however, shown this function to possess a character quite different from that which might have been inferred from the earlier work, and it is likely that Faraday's value is scarcely nearer the truth than was the original estimate of the temperature of the sun, mentioned above. Still another notable instance of the errors to which physical re- search is subject when the attempt is made to extend results beyond the limits established by actual observation occurs in the case of the measurements of the infra-red spectrum of the sun by Langley. His beautiful and ingenious device, the bolometer, made it possible to explore the spectrum to wave-lengths beyond those for which the law of dispersion of the rock-salt prism had at that time been experi- mentally determined. Within the limits of observation the dispersion showed a curve of simple form, tending apparently to become a straight line as the wave-length increased. There was nothing in the appearance of the curve to indicate that it differed in character from the numerous empirical curves of similar type employed in experi- mental physics, or to lead even the most experienced investigator to suspect values for the wave-length derived from an extension of the curve. The wave-lengths published by Langley were accordingly ac- cepted as substantially correct by all other students of radiation; but subsequent measurements of the dispersion of rock salt at the hands of Rubens and his co-workers showed the existence of a second sudden and unlooked-for turn of the curve just beyond the point at which the earlier determinations ceased; and in consequence Langley 's wave- lengths and all work based upon them are now known to be not even approximately accurate. The history of physics is full of such ex- amples of the dangers of extrapolation, or, to speak more broadly, of the tentative character of most of our assumptions in experimental physics. * See Arrhenius, Kosmische Physik, p. 131. FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 21 We have, then, two distinct sets of physical concepts. The first of these deals with that positive portion of physics, the mechanical basis of which, being established upon direct observation, is fixed and defi- nite, and in which the relations are as absolute and certain as those of mathematics itself. Here speculation is excluded. Matter is simply one of the three factors, which enters, by virtue of its mass, into our formulae for energy, momentum, etc. Force is simply a quantity of which we need to know only its magnitude, direction, point of appli- cation, and the time during which it is applied. The Newtonian con- ception of force — the producer of motion — is adequate. All troublesome questions as to how force acts, of the mechanism by means of which its effects are produced, are held in abeyance. Speculative physics, to which the second set of concepts belongs, deals with those portions of the science for which the mechanical basis has to be imagined. Heat, light, electricity, and the science of the nature and ultimate properties of matter belong to this domain. In the history of the theory of heat we find one of the earliest manifestations of a tendency so common in speculative physics that it may be considered characteristic: the assumption of a medium. The medium in this case was the so-called imponderable caloric; and it was one of a large class, of which the two electric fluids, the mag- netic fluid, etc., were important members. The theory of heat remained entirely speculative up to the time of the establishment of the mechanical equivalent of heat by Joule. The discovery that heat could be measured in terms of work in- jected into thermal theory the conception of energy, and led to the development of thermodynamics. Generalizations of the sort expressed by Tyndall's phrase, heat a mode of motion, follow easily from the experimental evidence of the part which energy plays in thermal phenomena, but the specification of the precise mode of motion in question must always depend upon our views concerning the nature of matter, and can emerge from the speculative stage only, if ever, when our knowledge of the mechanics of the constitution of matter becomes fixed. The problem of the mechanism by which energy is stored or set free rests upon a similar speculative basis. These are proper subjects for theoretical consideration, but the dictum of Rowland ^ that we get out of mathematical formulae only what we put into them should never be lost from sight. So long as we put in only assumptions we shall take out hypotheses, and useful as these may prove, they are to be regarded as belonging to the realm of scientific speculation. They must be recognized as subject to modi- fication indefinitely as we, in consequence of increasing knowledge, are led to modify our assumptions. * Rowland, President's Address to the American Physical Society. 1900. 22 PHYSICS The conditions with which the physicist has to deal in his study of optics are especially favorable to the development of the scientific imagination, and it is in this field that some of the most remarkable instances of successful speculative work are to be found. The emission theory died hard, and the early advocates of the undulatory theory of light were forced to work up, with a completeness probably without parallel in the history of science, the evidence, necessarily indirect, that in optics we have to do with a wave-motion. The standpoint of optical theory may be deemed conclusive, possibly final, so far as the general proposition is concerned that it is the science of a wave- motion. In a few cases, indeed, such as the photography of the actual nodes of a standing wave-system, by Wiener,we reach the firm ground of direct observation. Optics has nevertheless certain distinctly speculative features. Wave-motion demands a medium. The enormous velocity of light excludes known forms of matter; the transmission of radiation in vacuo and through outer space from the most remote regions of the universe, and at the same time through solids such as glass, demands that this medium shall have properties very different from that of any substance with which chemistry has made us acquainted. The assumption of a medium is, indeed, an intellectual necessity, and the attempt to specify definitely the properties which it must possess in order to fulfill the extraordinary functions assigned to it has afforded a field for the highest display of scientific acumen. While the problem of the mechanism of the luminiferous ether has not as yet met with a satisfactory solution, the ingenuity and imaginative power developed in the attack upon its difficulties command our admiration. Happily the development of what may be termed the older optics did not depend upon any complete formulation of the mechanics of the ether. Just as the whole of the older mechanics was built up from Kepler's laws, Newton's laws of motion, the law of gravitational attraction, the law of inverse squares, etc., without any necessity of describing the mechanics of gravitation or of any force, or of matter itself, so the system of geometrical relations involved in the con- sideration of reflection and refraction, diffraction, interference, and polarization was brought to virtual completion without introducing the troublesome questions of the nature of the ether and the consti- tution of matter. Underlying this field of geometrical optics, or what I have just termed the older optics, are, however, a host of fundamental questions of the utmost interest and importance, the treatment of which de- pends upon molecular mechanics and the mechanics of the ether. Our theories as to the nature and causes of radiation, of absorption, and of dispersion, for example, belong to the newer optics, and are based FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 23 upon our conceptions of the constitution of matter; and since our ideas concerning the nature of matter, like our knowledge of the ether, is purely speculative, the science of optics has a doubly specu- lative basis. One type of selective absorption, for example, is as- cribed to resonance of the particles of the absorbing substance, and our modern dispersion theories depend upon the assumption of nat- ural periods of vibration of the particles of the refracting medium of the same order of frequency as that of the light-waves. When the frequency of the waves falling upon a substance coincides with the natural period of vibration of the particles of the latter, we have selective absorption, and accompanying it, anomalous dispersion. For these and numerous other phenomena no adequate theory is possible which does not have its foundation upon some assumed conception as to the constitution of matter. The development of the modem idea of the ether forms one of the most interesting chapters in the history of physics. We find at first a tendency to assume a number of distinct media corresponding to the various effects (visual, chemical, thermal, phosphorescent, etc.) of light-waves, and later the growth of the conception of a single medium, the luminiferous ether. In the development of electricity and magnetism, meantime, the assumption of media was found to be an essential — something with- out which no definite philosophy of the phenomena was possible. At first there was the same tendency to a multiplicity of media — there were the positive and negative electric fluids, the magnetic fluid, etc. Then there grew up in the fertile mind of Faraday that wonderful fabric of the scientific imagination, the electric field; the conception upon which all later attempts to form an idea of a thinkable mechan- ism of electric and magnetic action have been established. It is the object of science, as has been pointed out by Ostwald, to reduce the number of hypotheses; the highest development would be that in which a single hypothesis served to elucidate the relations of the entire universe. Maxwell's discovery that the whole theory of optics is capable of expression in terms identical with those found most convenient and suitable in electricity, in a word, that optics may be treated simply as a branch of electromagnetics, was the first great step towards such a simplification of our fundamental conceptions. This was followed by Hertz's experimental demonstra- tion of the existence of artificially produced electromagnetic waves in every respect identical with light-waves, an achievement which served to establish upon a sure foundation the conception of a single medium. The idea of one universal medium as the mechanical basis for all physical phenomena was not altogether new to the theoretical physicist, but the unification of optics and electricity did much to strengthen this conception. 24 PHYSICS The question of the ultimate structure of matter, as has already- been pointed out, is also speculative in the sense that the mechanism upon which its properties are based is out of the range of direct observation. For the older chemistry and the older molecular physics the assumption of an absolutely simple atom and of molecules com- posed of comparatively simple groupings of such atoms sufficed. Physical chemistry and that new phase of molecular physics which has been termed the physics of the ion demand the breaking up of the atom into still smaller parts and the clothing of these with an electric charge. The extreme step in this direction is the suggestion of Larmor that the electron is a " disembodied charge " of negative electricity. Since, however, in the last analysis, the only conception having a definite and intelligible mechanical basis which physicists have been able to form of an electric charge is that which regards it as a phenomenon of the ether, this form of speculation is but a return under another name to views which had earlier proved attractive to some of the most brilliant minds in the world of science, such as Helmholtz and Kelvin. The idea of the atom, as a vortex motion of a perfect fluid (the ether), and similar speculative conceptions, whatever be the precise form of mechanism imagined, are of the same class as the moving electric charge of the later theorists. Lodge, ^ in a recent article in which he attempts to voice in a pop- ular way the views of this school of thought, says : "Electricity under strain constitutes * charge'; electricity in loco- motion constitvies light. What electricity itself is we do not know, bvi it may, perhaps, be a form or aspect of matter. . . . Now we can go one step further and say, matter is composed of electricity and of nothing else. ..." If for the word electricity in this quotation from Lodge we substi- tute ether, we have a statement which conforms quite as well to the accepted theories of light and electricity as his original statement does to the newer ideas it is intended to express. This reconstructed statement would read as follows : Ether under strain constitutes "charge "; ether in locomotion con- stitutes current and magnetism; ether in vibration constitutes light. What ether itself is we do not know, but it may, perhaps, be a form or aspect of matter. Now we can go one step further and say : "Matter is composed of ether and of nothing else." The use of the word electricity, as employed by Lodge and others, is now much in vogue, but it appears to me unfortunate. It would be distinctly conducive to clearness of thought and an avoidance of confusion to restrict the term to the only meaning which is free from criticism; that in which it is used to designate the science which deals with electrical phenomena. * Lodge, Harper's Magazine, August, 1904, p. 383. FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 25 The only way in which the noun electricity enters, in any definite and legitimate manner, into our electrical treatises is in the designa- tion of Q in the equations — Q =/Idt, C = Q\E, W = QE, etc. Here we are in the habit — whether by inheritance from the age of the electric fluid, by reason of the hydrodynamic analogy, or as a matter of convention or of convenience merely — of calling Q the quantity of electricity. Now Q is " charge " and its unit, the coulomb, is unit-charge. The alternative expression, quantity of electricity, is a purely conventional designation and without independent physical significance. It owes its prevalence among electricians to the fact that by virtue of long familiarity we prefer to think in terms of matter, which is tangible, rather than of ether. Charge is to be regarded as fimdamental, and its substitute, quantity of electricity, as merely an artificial term of convenience; because of the former we have a definite mechanical con- ception, whereas we can intelligently define a quantity of electricity only in terms of charge. In the science of heat the case differs, in that the term heat is used, if not as precisely synonymous with energy, at least for a quantity having the same dimensions as energy and having as its unit the erg. It might easily have happened, as has happened in electrical theory, that the ancient notion of a heat substance should survive. In which case we should have had for the quantity of heat not something measured in terms of energy, but, as in the case of electricity, one of the terms which enter into our expression for energy. We should then have had to struggle continually, in thermodynamics, as we now do in electrical theory, against the tendency to revert to an antiquated and abandoned view. It would, I cannot but think, have been fortunate had the word electricity been used for what we now call electrical energy; using charge, or some other convenient designation, for the quantity Q. That aspect of the science in accordance with which we regard it as a branch of energetics in which movements of the ether are pri- marily involved would have been duly emphasized. We should have been quit forever of the bad notion of electricity as a medium, just as we are already freed from the incubus of heat as a medium. We should have had electricity — a mode of motion (or stress), ether, as we have heat — a mode of motion of matter. When our friends asked us: "What is electricity?" we should have had a ready answer for them instead of a puzzled smile. One real advance which has been attained by means of the theory of ionization, and it is of extreme significance and of far-reaching importance, consists in the discovery that electrification, or the pos- session of charge, instead of being a casual or accidental property. 26 PHYSICS temporarily imparted by friction or other process, is a fundamental property of matter. According to this newer conception of matter, the fruit of the ionic theory, the ultimate parts of matter are elec- trically charged particles. In the language of Rutherford: ^ "It must then be supposed that the process of ionization in gases consists in a removal of a negative corpuscle or electron from the molecule of gas. At atmospheric pressure this corpuscle immediately becomes the centre of an aggregation of molecules which moves with it and is the negative ion. After removal of the negative ion the molecule retains a positive charge and probably also becomes the centre of a cluster of new molecules. " The electron or corjmscle is the body of smallest mass yet known to science. It carries a negative charge of 3.4 X 10~^" electrostatic units. Its presence has only been detected when in rapid motion, when it has for speeds up to about 10^° cms. a second, an apparent mass m given by e/m — 1.86 X 10^. electromagnetic units. This apparent mass increases with the speed as the velocity of light is approached." At low pressures the electron appears to lose its load of cluster- ing molecules, so that finally the negative ion becomes identical with the electron or corpuscle, and has a mass, according to the estimates of J. J. Thomson, about one thousandth of that of the hydrogen atom. The positive ion is, however, supposed to remain of atomic size even at low pressures. The ionic theory and the related hypothesis of electrolytic dis- sociation afford a key to numerous phenomena concerning which no adequate or plausible theories had hitherto been formed. By means of them explanations have been found, for example, of such widely divergent matters as the positive electric charge known to exist in the upper atmosphere, and the perplexing phenomena of fluorescence. The evidence obtained by J. J. Thomson and other students of ionization, that electrons from different substances are identical, has greatly strengthened the conviction which for a long time has been in process of formation in the minds of physicists, that all matter is in its ultimate nature identical. This conception, neces- sarily speculative, has been held in abeyance by the facts, regarded as established, and lying at the foundation of the accepted system of chemistry, of the conservation of matter and the intransmut- ability of the elements. The phenomena observed in recent investi- gations of radioactive substances have, however, begun to shake our faith in this principle. If matter is to be regarded as a product of certain operations performed upon the ether, there is no theoretical difficulty about ^ Rutherford, Radioactivity, p. 53. 1904. FUNDAMENTAL CONCEPTS OF PHYSICAL SCIENCE 27 transmutation of elements, variation of mass, or even the complete disappearance or creation of matter. The absence of such phe- nomena in our experience has been the real difficulty, and if the views of students of radioactivity concerning the transformations undergone by uranium, thorium, and radium are substantiated, the doctrines of the conservation of mass and matter which lie at the foundation of the science of chemistry will have to be modified. There has been talk of late of violations of the principle of the con- servation of energy in connection with the phenomena of radio- activity, but the conservation of matter is far more likely to lose its place among our fundamental conceptions. The development of physics on the speculative side has led, then, to the idea, gradually become more definite and fixed, of a universal medium, the existence of which is a matter of inference. To this medium properties have been assigned which are such as to enable us to form an intelligible, consistent conception of the mechanism by means of which phenomena, the mechanics of which is not capable of direct observation, may be logically considered to be produced. The great step in this speculation has been the discovery that a single medium may be made to serve for the numerous phenomena of optics, and that, without ascribing to it any characteristics incompatible with a luminiferous ether, it is equally available for the description and explanation of electric and magnetic fields, and finally may be made the basis for intelligible theories of the structure of matter. To many minds this seemingly universal adaptability of the ether to the needs of physics almost removes it from the field of specu- lation; but it should not be forgotten that a system, entirely imagin- ary, may be devised, which fits all the known phenomena and appears to offer the only satisfactory explanation of the facts, and which subsequently is abandoned in favor of other views. The history of physics is full of instances where a theory is for a time regarded as final on account of its seeming completeness, only to give way to something entirely different. In this consideration of the fundamental concepts I have attempted to distinguish between those which have the positive character of mathematical laws and which are entirely independent of all theories of the ultimate nature of matter, and those which deal with the latter questions and which are essentially speculative. I have purposely refrained from taking that further step which plunges us from the heights of physics into the depths of philosophy. With the statement that science in the ultimate analysis is nothing more than an attempt to classify and correlate our sensations the physicist has no quarrel. It is, indeed, a wholesome discipline for him to formulate for himself his own relations to his science in terms such as those which, to paraphrase and translate very freely the 28 PHYSICS opening passages of his recent Treatise on Physics, Chwolson * has employed. "For every one there exist two worlds, an inner and an outer, and our senses are the medium of communication between the two. The outer world has the property of acting upon our senses, to bring about certain changes, or, as we say, to exert certain stimuli. "The inner world, for any individual, consists of all those phe- nomena which are absolutely inaccessible (so far as direct observa- tion goes) to other individuals. The stimulus from the outer world produces in our inner world a subjective perception which is de- pendent upon our consciousness. The subjective perception is made objective, viz., is assigned time and place in the outer world and given a name. The investigation of the processes by which this objectiv- ication is performed is a function of philosophy." Some such confession of faith is good for the man of science, — lest he forget; but once it is made he is free to turn his face to the light once more, thankful that the investigation of ohjectivication is, indeed, a function of philosophy, and that the only speculations in which he, as a physicist, is entitled to engage are those which are amenable at every step to mathematics and to the equally definite axioms and laws of mechanics. ' Chwolson, Physik, vol. i, Introduction. THE PROGRESS OF PHYSICS IN THE NINETEENTH CENTURY BT CABL BARUS [Carl Barus, Dean of the Graduate Department, Brown University, b. Febniary 19, 1856, Cincinnati, Ohio. Ph.D. Columbia University, University of Wiirzburg, Ba- varia. Physicist, U. S. Geological Survey; Professor of Meteorology, U. S. Weather Bureau; Professor of Physics, Smithsonian Institution; Member of the National Academy of Science of the United States; Vice-President of American Association for the Advancement of Science; Corresponding Member of the British Association for the Advancement of Science; Honorary Member of the Royal Institution of Great Britain; President of American Physical Society; Rumford Medalist. Author of The Laws of Gases; The Physical Properties of the Iron Carburets; and many other books; contributor to the standard magazines.] You have honored me by requesting at my hands an account of the advances made in physics during the nineteenth century. I have endeavored, in so far as I have been able, to meet the grave respon- sibilities implied in your invitation; yet had I but thought of the overwhelmingly vast territory to be surveyed, I well might have hesitated to embark on so hazardous an undertaking. To mention merely the names of men whose efforts are linked with splendid accomplishments in the history of modern physics would far exceed the time allotted to this address. To bear solely on certain subjects, those, for instance, with which I am more familiar, would be to de- velop an unsymmetrical picture. As this is to be avoided, it will be necessary to present a straightforward compilation of all work above a certain somewhat vague and arbitrary lower limit of importance. Physics is, as a rule, making vigorous though partial progress along independent parallel lines of investigation, a discrimination between which is not possible until some cataclysm in the history of thought ushers in a new era. It will be essential to abstain from entering into either explanation or criticism, and to assume that all present are familiar with the details of the subjects to be treated. I can neither popularize nor can I endeavor to entertain, except in so far as a rapid review of the glorious conquests of the century may be stimulating. In spite of all this simplicity of aim, there is bound to be distortion. In any brief account, the men working at the beginning of the cen- tury, when investigations were few and the principles evolved neces- sarily fundamental, will be given greater consideration than equally able and abler investigations near the close, when workers (let us be thankful) were many, and the subjects lengthening into detail. Again, the higher order of genius will usually be additionally exalted at the expense of the less gifted thinker. I can but regret that these are the inevitable limitations of the cursory treatment prescribed. 30 PHYSICS As time rolls on, the greatest names more and more fully absorb the activity of a whole epoch. Metrology Finally, it will hardly be possible to consider the great advances made in physics except on the theoretical side. Of renowned experi- mental researches, in particular of the investigations of the con- stants of nature to a degree of ever-increasing accuracy, it is not prac- ticable to give any adequate account. Indeed, the refinement and precision now demanded have placed many subjects beyond the reach of individual experimental research, and have culminated in the establishment of the great national or international laboratories of investigation at Sevres (1872), at Berlin (1887, 1890), at London (1900), at Washington (1901). The introduction of uniform inter- national units in cases of the arts and sciences of more recent develop- ment is gradually, but inexorably, urging the same advantages on all. Finally, the access to adequate instruments of research has everywhere become an easier possibility for those duly qualified, and the institutions and academies which are systematically undertaking the distribution of the means of research are continually increasing in strength and in number. Classification In the present paper it will be advisable to follow the usual pro- cedure in physics, taking in order the advances made in dynamics, acoustics, heat, light, and electricity. The plan pursued will, there- fore, specifically consider the progress in elastics, crystallography, capillarity, solution, diffusion, dynamics, viscosity, hydrodynamics, acoustics; in thermometry, calorimetry, thermodynamics, kinetic theory, thermal radiation; in geometric optics, dispersion, photo- metry, fluorescence, photochemistry, interference, diffraction, polar- ization, optical media; in electrostatics, Volta contacts, Seebeck contacts, electrolysis, electric current, magnetism, electromagnetism, electrodynamics, induction, electriQ oscillation, electric field, radio- activity. Surely this is too extensive a field for any one man! Few who are not physicists realize that each of these divisions has a splendid and voluminous history of development, its own heroes, its sublime class- ics, often culled from the activity of several hundred years. I repeat that few understand the unmitigatedly fundamental character, the scope, the vast and profound intellectual possessions, of pure physics; few think of it as the one science into which all other sciences must ultimately converge — or a separate representation would have been given to most of the great divisions which I have named. PROGRESS IN NINETEENTH CENTURY 31 Hence even if the literary references may be given in print with some fullness, it is impossible to refer verbally to more than the chief actors, and quite impossible to delineate sharply the real significance and the relations of what has been done. Moreover, the dates will in most instances have to be omitted from the reading. It has been my aim, however, to collect the greater papers in the history of physics, and the suggestion is implied that science would gain if by some august tribunal researches of commanding importance were formally canonized for the benefit of posterity. Elastics To begin with elasticity, whose development has been of such marked influence throughout the whole of physics, we note that the theory is virtually a creation of the nineteenth century. Antedating Thomas Young, who in 1807 gave to the subject the useful concep- tion of a modulus, and who seems to have definitely recognized the shear, there were merely the experimental contribution of Galileo (1638), Hooke (1660), Mariotte (1680), the elastic curve of J. Ber- noulli (1705), the elementary treatment of vibrating bars of Euler and Bernoulli (1742), and an attempted analysis of flexure and tor- sion by Coulomb (1776). The establishment of a theory of elasticity on broad lines begins almost at a bound with Navier (1821), reasoning from a molecular hypothesis to the equation of elastic displacement and of elastic po- tential energy (1822-1827); yet this startling advance was destined to be soon discredited, in the light of the brilliant generalizations of Cauchy (1827). To him we owe the six component stresses and the six component strains, the stress quadric and the strain quadric, the reduction of the components to three principal stresses and three principal strains, the ellipsoids, and other of the indispensable con- ceptions of the present day. Cauchy reached his equations both by the molecular hypothesis and by an analysis of the oblique stress across an interface, — methods which predicate fifteen constants of elasticity in the most general case, reducing to but one in the case of isotropy. Contemporaneous with Cauchy's results are certain in- dependent researches by Lam6 and Clapeyron (1828) and by Poisson (1829). Another independent and fundamental method in elastics was introduced by Green (1837), who took as his point of departure the potential energy of a conservative system in connection with the Lagrangian principle of virtual displacements. This method, which has been fruitful in the hands of Kelvin (1856), of Kirchhoff (1876), of Neumann (1885), leads to equations with twenty-one constants for the seolotropic medium reducing to two in the simplest case. 32 PHYSICS The wave-motion in an isotropic medium was first deduced by Poisson in 1828, showing the occurrence of longitudinal and trans- verse waves of different velocities; the general problem of wave- motion in aeolotropic media, though treated by Green (1842), was attacked with requisite power by Blanchet (1840-1842) and by Christoffel (1877). Poisson also treated the case of radial vibrations of a sphere (1828), a problem which, without this restriction, awaited the solutions of Jaerisch (1879) and of Lamb (1882). The theory of the free vibra- tions of solids, however, is a generalization due to Clebsch (1857-58, Vorlesungen, 1862). Elasticity received a final phenomenal advance through the long- continued labors of de St. Venant (1839-55), which in the course of his editions of the work of Moigno, of Navier (1863), and of Clebsch (1864), effectually overhauled the whole subject. He was the first to assert adequately the fundamental importance of the shear. The pro- found researches of de St. Venant on the torsion of prisms and on the flexure of prisms appeared in their complete form in 1855 and 1856. In both cases the right sections of the stressed solids are shown to be curved, and the curvature is succinctly specified; in the former Coulomb's inadequate torsion formula is superseded, and in the latter flexural stress is reduced to a transverse force and a couple. But these mere statements convey no impression of the magnitude of the work. Among other notable creations with a special bearing on the theory of elasticity there is only time to mention the invention and applica- tion of curvilinear coordinates by Lam6 (1852) ; the reciprocal the- orem of Betti (1872), applied by Cerruti (1882) to solids with a plane boundary — problems to which Lam6 and Clapeyron (1828) and Boussinesq (1879-85) contributed by other methods; the case of the strained sphere studied by Lam6 (1854) and others; Kirchhoff's flexed plate (1850); Rayleigh's treatment of the oscillations of systems of finite freedom (1873); the thermo-elastic equations of Duhamel (1838), of F. Neumann (1841), of Kelvin (1878); Kelvin's analogy of the torsion of prisms with the supposed rotation of an incompressible fluid within (1878); his splendid investigations (1863) of the dynamics of elastic spheroids and the geophysical applications to which they were put. Finally, the battle royal of the molecular school following Navier, Poisson, Cauchy, and championed by de St. Venant, with the disciples of Green, headed by Kelvin and Kirchhoff , — the struggle of the fif- teen constants with the twenty-one constants, in other words, — seems to have temporarily subsided with a victory for the latter through the researches of Voigt (1887-89). PROGRESS IN NINETEENTH CENTURY 33 Crystallogra'phy Theoretical crystallography, approached by Steno (1669), but formally founded by Haiiy (1781, Traits, 1801), has limited its development during the century to systematic classifications of form. Thus the thirty-two type sets of Hessel (1830) and of Bravais (1850) have expanded into the more extensive point series involving 230 types due to Jordan (1868), Sohncke (1876), Federow (1890), and Schoenfliess (1891). Physical theories of crystalline form have scarcely been unfolded. Capillarity Capillarity antedated the century in little more than the provi- sional, though brilliant, treatment due to Clairaut (1743). The theory arose in almost its present state of perfection in the great memoir of Laplace (1805), one of the most beautiful examples of the Newton-Boscovichian (1758) molecular dynamics. Capillary pressure was here shown to vary with the principal radii of curva- ture of the exposed surface, in an equation involving two constants, one dependent on the liquid only, the other doubly specific for the bodies in contact. Integrations for special conditions include the cases of tubes, plates, drops, contact angle, and similar instances. Gauss (1829), dissatisfied with Laplace's method, virtually repro- duced the whole theory from a new basis, avoiding molecular forces in favor of Lagrangian displacements, while Poisson (1831) obtained Laplace's equations by actually accentuating the molecular hypo- thesis; but his demonstration has since been discredited. Young in 1805 explained capillary phenomena by postulating a constant surface tension, a method which has since been popularized by Max- well (Heat, 1872). With these magnificent theories propounded for guidance at the very threshold of the century, one is prepared to anticipate the wealth of experimental and detailed theoretical research which has been devoted to capillarity. Among these the fascinating mono- graph of Plateau (1873), in which the consequences of theory are tested by the behavior both of liquid lamellse and by suspended masses, Savart's (1833), and particularly Rayleigh's, researches with jets (1879-83), Kelvin's ripples (1871), may be cited as typ- ical. Of peculiar importance, quite apart from its meteorological bearing, is Kelvin's deduction (1870) of the interdependence of sur- face tension and vapor pressure when varying with the curvature of a droplet. 34 PHYSICS Diffusion Diffusion was formally introduced into physics by Graham (1850). Fick (1855), appreciating the analogy of diffusion and heat conduc- tion, placed the phenomenon on a satisfactory theoretical basis, and Fick's law has since been rigorously tested, in particular by H. F. Weber (1879). The development of diffusion from a physical point of view fol- lowed Pfeffer's discovery (1877) of osmotic pressure, soon after to be interpreted by van 't Hoff (1887) in terms of Boyle's and Avogadro's laws. A molecular theory of diffusion was thereupon given by Nernst (1887). Dynamics In pure dynamics the nineteenth century inherited from the eighteenth that unrivaled feat of reasoning called by Lagrange the Mecanique analytique (1788), and the great master was present as far as 1813 to point out its resources and to watch over the legit- imacy of its applications. Throughout the whole century each new advance has but vindicated the preeminent power and safety of its methods. It triumphed with Maxwell (1864), when he deduced the concealed kinetics of the electromagnetic field, and with Gibbs (1876-78), when he adapted it to the equilibrium of chemical sys- tems. It will triumph again in the electromagnetic dynamics of the future. Naturally there were reactions against the tyranny of the method of "liaisons." The most outspoken of these, propounded under the protection of Laplace himself, was the celebrated Mecanique phy- sique of Poisson (1828), an accentuation of Boscovich's (1758) dynamics, which permeates the work of Navier, Cauchy, de St. Venant, Boussinesq, even Fresnel, Ampere, and a host of others. Cauchy in particular spent much time to reconcile the molecular method with the Lagrangian abstractions. But Poisson's method, though sustained by such splendid genius, has, nevertheless, on more than one occasion — in capillarity, in elastics — shown itself to be untrustworthy. It was rudely shaken when, with the rise of modern electricity, the influence of the medium was more and more pushed to the front. Another complete reconstruction of dynamics is due to Thomson and Tait (1867), in their endeavor to gain clearness and uniformity of design, by referring the whole subject logically back to Newton. This great work is the first to make systematic use of the doctrine of the conservation of energy. Finally, Hertz (1894), imbued with the general trend of con- temporaneous thought, made a powerful effort to exclude force PROGRESS IN NINETEENTH CENTURY 35 and potential energy from dynamics altogether — postulating a uni- verse of concealed motions such as Helmholtz (1884) had treated in his theory of cyclic systems, and Kelvin had conceived in his adynamic gyrostatic ether (1890). In fact, the introduction of con- cealed systems and of ordered molecular motions by Helmholtz and Boltzmann has proved most potent in justifying the Lagrangian dynamics in its application to the actual motions of nature. The specific contributions of the first rank which dynamics owes to the last century, engrossed as it was with the applications of the subject, or with its mathematical difiiculties, are not numerous. In chronological order we recall naturally the statics (1804) and the rotational dynamics (1834) of Poinsot, all in their geometrical character so surprisingly distinct from the contemporary dynamics of Lagrange and Laplace. We further recall Gauss's principle of least constraint (1829), but little used, though often in its appli- cations superior to the method of displacement; Hamilton's prin- ciple of varying action (1834) and his characteristic function (1834, 1835), the former obtainable by an easy transition from D'Alem- bert's principle and by contrast with Gauss's principle, of such exceptional utility in the development of modern physics; finally the development of the Leibnitzian doctrine of work and vis viva into the law of the conservation of energy, which more than any other principle has consciously pervaded the progress of the nine- teenth century. Clausius's theorem of the Virial (1870) and Jacobi's (1866) contributions should be added among others. The potential, though contained explicitly in the writings of Lagrange (1777), may well be claimed by the last century. The differential equation underlying the doctrine had already been given by Laplace in 1782, but it was subsequently to be completed by Poisson (1827). Gauss (1813, 1839) contributed his invaluable theorems relative to the surface integrals and force flux, and Stokes (1854) his equally important relation of the line and the surface integral. Legendre (published 1785) and Laplace (1782) were the first to apply spherical harmonics in expansions. The detailed devel- opment of volume surface and line potential has enlisted many of the ablest writers, among whom Chasles (1837, 1839, 1842), Helmholtz (1853), C. Neumann (1877, 1880),Lejeune-Dirichlet (1876), Murphy (1833), and others are prominent. The gradual growth of the doctrine of the potential would have been accelerated, had not science to its own loss overlooked the famous essay of Green (1828), in which many of the important theorems were anticipated, and of which Green's theorem and Green's function are to-day familiar reminders. Recent dynamists incline to the uses of the methods of modem geometry and to the vector calculus with continually increasing 36 PHYSICS favor. Noteworthy progress was first made in this direction by Moebius (1837-43, Statik, 1838), but the power of these methods to be fully appreciated required the invention of the Ausdehnungs- lehre, by Grassmann (1844), and of quaternions, by Hamilton (1853). Finally the profound investigations of Sir Robert Ball (1871, et seq., Treatise) on the theory of screws with its immediate dynamical applications, though as yet but little cultivated except by the author, must be reckoned among the promising heritages of the twentieth century. On the experimental side it is possible to refer only to researches of a strikingly original character, like Foucault's pendulum (1851) and Fizeau's gyrostat; or like Boys's (1887, et seq.) remarkable quartz-fibre torsion-balance, by which the Newtonian constant of gravitation and the mean density of the earth originally deter- mined by Maskelyne (1775-78) and by Cavendish (1798) were evalu- ated with a precision probably superior to that of the other recent measurements, the pendulum work of Airy (1856) and Wilsing (1885-87), or the balance methods of Jolly (1881), Konig, and Richarz (1884). Extensive transcontinental gravitational surveys like that of Mendenhall (1895) have but begun. Hydrodynamics The theory of the equilibrium of liquids was well understood prior to the century, even in the case of rotating fluids, thanks to the labors of Maclaurin (1742), Clairaut (1743), and Lagrange (1788). The generalizations of Jacobi (1834) contributed the triaxial ellip- soid of revolution, and the case has been extended to two rotating attracting masses by Poincar6 (1885) and Darwin (1887). The astonishing revelations contained in the recent work of Poincar6 are particularly noteworthy. Unlike elastics, theoretical hydrodynamics passed into the nine- teenth century in a relatively well-developed state. Both types of the Eulerian equations of motion (1755, 1759) had left the hands of Lagrange (1788) in their present form. In relatively recent times H. Weber (1868) transformed them in a way combining certain advantages of both, and another transformation was undertaken by Clebsch (1859). Hankel (1861) modified the equation of con- tinuity, and Svanberg and Edlund (1847) the surface conditions. Helmholtz in his epoch-making paper of 1858 divided the subject into those classes of motion (flow in tubes, streams, jets, waves) for which a velocity potential exists and the vortex motions for which it does not exist. This classification was carried even into higher orders of motion by Craig and by Rowland (1881). For cases with a velocity potential, much progress has been made during PROGRESS IN NINETEENTH CENTURY 37 the century in the treatment of waves, of discontinuous fluid motion, and in the dynamics of solids suspended in frictionless liquids. Kelland (1844), Scott Russel (1844), and Green (1837) dealt with the motion of progressive waves in relatively shallow vessels, Ger- ster (1804) and Rankine (1863) with progressive waves in deep water, while Stokes (1846, 1847, 1880), after digesting the contemporaneous advances in hydrodynamics, brought his powerful mind to bear on most of the outstanding difiiculties. Kelvin introduced the case of ripples (1871), afterwards treated by Rayleigh (1883). The soli- tary wave of Russel occupied Boussinesq (1872, 1882), Rayleigh (1876), and others; group-waves were treated by Reynolds (1877) and Rayleigh (1879). Finally the theory of stationary waves re- ceived extended attention in the writings of de St. Venant (1871), Kirchhoff (1879), and Greenhill (1887). Early experimental guid- ance was given by the classic researches of C. H. and W. Weber (1825). The occurrence of discontinuous variation of velocity within the liquid was first fully appreciated by Helmholtz (1868), later by Kirchhoff (1869), Rayleigh (1876), Voigt (1885), and others. It lends itself well to conformal representations. The motions of solids within a liquid have fascinated many inves- tigators, and it is chiefly in connection with this subject that the method of sources and sinks was developed by English mathema- ticians, following Kelvin's method (1856) for the flow of heat. The problem of the sphere was solved more or less completely by Poisson (1832), Stokes (1843), Dirichlet (1852); the problem of the ellip- soid by Green (1833),Clebsch (1858), generalized by Kirchhoff (1869). Rankine treated the translatory motion of cylinders and ellipsoids in a way bearing on the resistance of ships. Stokes (1843) and Kirch- hoff entertain the question of more than one body. The motion of rings has occupied Kirchhoff (1869), Boltzmann (1871), Kelvin (1871), Bjerknes (1879), and others. The results of C. A. Bjerknes (1868) on the fields of hydrodynamic force surrounding spheres, pulsating or oscillating, in translatory or rotational motion, accent- uate the remarkable similarity of these fields with the corresponding cases in electricity and magnetism, and have been edited in a unique monograph (1900) by his son. In a special category belong certain powerful researches with a practical bearing, such as the modern treatment of ballistics by Greenhill and of the ship propeller of Ressel (1826), summarized by Gerlach (1885, 1886). The numerous contributions of Kelvin (1888, 1889) in particular have thrown new light on the difficult but exceedingly important question of the stability of fluid motion. The century, moreover, has extended the working theory of the 355938 38 PHYSICS tides due to Newton (1687) and Laplace (1774), through the labors of Airy, Kelvin, and Darwin. Finally the forbidding subject of vortex motion was gradually approached more and more fully by Lagrange, Cauchy (1815, 1827), Svanberg (1839), Stokes (1845); but the epoch-making integrations of the dififerential equations, together with singularly clear-cut inter- pretations of the whole subject, are due to Helmholtz (1858). Kelvin (1867, 1883) soon recognized the importance of Helmholtz's work and extended it, and further advance came in particular from J. J. Thomson (1883) and Beltrami (1875). The conditions of stability in vortex motion were considered by Kelvin (1880), Lamb (1878), J. J. Thomson, and others, and the cases of one or more columnar vortices, of cylindrical vortex sheets, of one or more vortex rings, simple or linked, have all yielded to treatment. The indestructibility of vortex motion in a frictionless fluid, its open structure, the occurrence of reciprocal forces, were compared by Kelvin (1867) with the essential properties of the atom. Others like Fitzgerald in his cobwebbed ether, and Hicks (1885) in his vortex sponge, have found in the properties of vortices a clue to the pos- sible structure of the ether. Yet it has not been possible to deduce the principles of dynamics from the vortex hypothesis, neither is the property which typifies the mass of an atom clearly discernible. Kelvin invokes the corpuscular hypothesis of Lesage (1818). Viscosity The development of viscous flow is largely on the experimental side, particularly for solids, where Weber (1835), Kohlrausch (1863, et seq.), and others have worked out the main laws. Stokes (1845) deduced the full equations for liquids. Poiseiulle's law (1847), the motion of small solids in viscous liquids, of vibrating plates, and other important special cases, has yielded to treatment. The coefficients of viscosity defined by Poisson (1831), Maxwell (1868), Hagenbach (1860), O. E. Meyer (1863), are exhaustively investigated for gases and for liquids. Maxwell (1877) has given the most suggestive and Boltzmann (1876) the most carefully formulated theory for solids, but the investigation of absolute data has but begun. The difficulty of reconciling viscous flow with Lagrange's dynamics seems first to have been adjusted by Navier. Aeromechanics Aerostatics is indissolubly linked with thermodynamics. Aero- dynamics has not marked out for itself any very definite line of progress. Though the resistance of oblique planes has engaged the PROGRESS IN NINETEENTH CENTURY 39 attention of Rayleigh, it is chiefly on the experimental side that the subject has been enriched, as, for instance, by the labors of Langley (1891) and Lilienthal. Langley (1897) has, indeed, constructed a steam-propelled aeroplane which flew successfully; but man himself has not yet flown. Moreover, the meteorological applications of aerodynamics con^ tained in the profound researches of Guldberg and Mohn (1877), Ferrel (1877), Oberbeck (1882, 1886), Helmholtz (1888, 1889), and others, as well as in such investigations as Sprung's (1880) on the in- ertia path, are as yet rather qualitative in their bearing on the actual motions of the atmosphere. The marked progress of meteorology is observational in character. Acoustics Early in the century the velocity of sound given in a famous equa- tion of Newton was corrected to agree with observation by Laplace (1816). The great problems in acoustics are addressed in part to the elas- tician, in part to the physiologist. In the former case the work of Rayleigh (1877) has described the present stage of development, interpreting and enriching almost every part discussed. In the latter case Helmholtz (1863) has devoted his immense powers to a like purpose and with like success. Konig has been prominently con- cerned with the construction of accurate acoustic apparatus. It is interesting to note that the differential equation representing the vibration of strings was the first to be integrated; that it passed from D'Alembert (1747) successively to Euler (1779), Bernoulli (1753) and Lagrange (1759). With the introduction of Fourier's series (1807) and of spherical harmonics at the very beginning of the cen- tury, D'Alembert's and the other corresponding equations in acous- tics readily yielded to rigorous analysis. Rayleigh's first six chapters summarize the results for one and for two degrees of freedom. Flexural vibration in rods, membranes, and plates become pro- minent in the unique investigations of Chladni (1787, 1796, Akustik, 1802). The behavior of vibrating rods has been developed by Euler (1779), Cauchy (1827), Poisson (1833), Strehlke (1833), Lissajous (1833), Seebeck (1849), and is summarized in the seventh and eighth chapters of Rayleigh's book. The transverse vibration of membranes engaged the attention of Poisson (1829). Round membranes were rigorously treated by Kirchhoff (1850) and by Clebsch (1862); elUp- tic membranes by Mathieu (1868). The problem of vibrating plates presents formidable difficulties resulting not only from the edge con- ditions, but from the underlying differential equation of the fourth degree due to Sophie Germain (1810) and to Lagrange (1811). The 40 PHYSICS solutions have taxed the powers of Poisson (1812, 1829), Cauchy (1829), Kirchhoff (1850), Boussinesq (1871-79), and others. For the circular plate Kirchhoff gave the complete theory. Rayleigh system- atized the results for the quadratic plate, and the general account makes up his ninth and tenth chapters. Longitudinal vibrations, which are of particular importance in case of the organ-pipe, were considered in succession by Poisson (1817), Hopkins (1838), Quet (1855); but Helmholtz in his famous paper of 1860 gave the first adequate theory of the open organ -pipe, involv- ing viscosity. Further extension was then added by Kirchhoff (1868), and by Rayleigh (1870, et seq.), including particularly powerful analysis of resonance. The subject in its entirety, including the allied treatment of the resonator, completes the second volume of Ray- leigh's Sound. On the other hand, the whole subject of tone-quality, of combin- ation and difference tones, of speech, of harmony, in its physical, physiological, and sesthetic relations, has been reconstructed, using all the work of earlier investigators, by Helmholtz (1862), in his mas- terly Tonempfindungen. With rare skill and devotion Konig contrib- uted a wealth of siren-like experimental appurtenances. Acousticians have been fertile in devising ingenious methods and apparatus, among which the tuning-fork with resonator of Marloye, the siren of Cagniard de la Tour (1819), the Lissajous curves (1857), the stroboscope of Plateau (1832), the manometric flames of Konig (1862, 1872), the dust methods of Chladni (1787) and of Kundt (1865-68), Melde's vibrating strings (1860, 1864), the phonograph of Edison and of Bell (1877), are among the more famous. Heat: Thermometry The invention of the air thermometer dates back at least to Amon- tons (1699), but it was not until Rudberg (1837), and more thor- oughly Regnault (1841, et seq.) and Magnus (1842), had completed their work on the thermal expansion and compressibility of air, that air thermometry became adequately rigorous. On the theoret- ical side Clapeyron (1834), Helmholtz (1847), Joule (1848), had in various ways proposed the use of the Carnot function (1894) for temperature measurement, but the subject was finally disposed of by Kelvin (1849, et seq.) in his series of papers on temperature and temperature measurement. Practical thermometry gained much from the measurement of the expansion of mercury by Dulong and Petit (1818), repeated by Regnault. It also profited by the determination of the viscous behavior of glass, due to Pernet (1876) and others, but more from the elimination of these errors by the invention of the Jena glass. PROGRESS IN NINETEENTH CENTURY 41 It is significant to note that the broad question of thermal expan- sion has yet no adequate equation, though much has been done experimentally for fluids by the magnificent work of Amagat (1869, 1873, et seq.). Heat Conduction The subject of heat conduction from a theoretical point of view was virtually created by the great memoir of Fourier (1822), which shed its first light here, but subsequently illumined almost the whole of physics. The treatment passed successively through the hands of many of the foremost thinkers, notably of Poisson (1835, 1837), Lame (1836, 1839, 1843), Kelvin (1841-44), and others. With the latter (1856) the ingenious method of sources and sinks originated. The character of the conduction is now well known for continuous media, isotropic or not, bounded by the more simple geometrical forms, in particular for the sphere under all reasonable initial and surface conditions. Much attention has been given to the heat con- duction of the earth, following Fourier, by Kelvin (1862, 1878), King (1893), and others. Experimentally, Wiedemann and Franz (1853) determined the relative heat conduction of metals and showed that for simple bodies a parallel gradation exists for the cases of heat and of electrical con- ductivity. Noteworthy absolute methods for measuring heat conduc- tion were devised in particular by Forbes (1842), F. Neumann (1862), Angstrom (1861-64), and a lamellar method applying to fluids by H. F. Weber (1880). Calorimetry Practical calorimetry was virtually completed by the researches of Black in 1763. A rich harvest of experimental results, therefore, has since accrued to the subjects of specific, latent, and chemical heats, due in particularly important cases to the indefatigable Reg- nault (1840, 1845, et seq.). Dulong and Petit (1819) discovered the remarkable fact of the approximate constancy of the atomic heats of the elements. The apparently exceptional cases were interpreted for carbon silicon and boron by H. F. Weber (1875), and for sulphur by Regnault (1840). F. Neumann (1831) extended the law to com- pound bodies, and Joule (1844) showed that in many cases specific heat could be treated as additively related to the component specific heats. Among recent apparatus the invention of Bunsen's ice calorimeter (1870) deserves particular mention. 42 PHYSICS Thermodynamics Thermodynamics, as has been stated, in a singularly fruitful way interpreted and broadened the old Leibnitzian principle of vis viva of 1686. Beginning with the incidental experiments of Rumford (1798) and of Davy (1799) just antedating the century, the new conception almost leaped into being when J. R. Mayer (1842, 1845) defined and computed the mechanical equivalent of heat, and when Joule (1843, 1845, et seq.) made that series of precise and judiciously varied measurements which mark an epoch. Shortly after Helmholtz (1847), transcending the mere bounds of heat, carried the doctrine of the conservation of energy throughout the whole of physics. Earlier in the century Carnot (1824), stimulated by the growing importance of the steam engine of Watt (1763, et seq.), which Fulton (1806) had already applied to transportation by water and which Stephenson (1829) soon after applied to transportation by land, invented the reversible thermodynamic cycle. This cycle or sequence of states of equilibrium of two bodies in mutual action is, perhaps, without a parallel in the prolific fruitfulness of its contributions to modern physics. Its continued use in fifty years of research has but sharpened its logical edge. Carnot deduced the startling doc- trine of a temperature criterion for the efficiency of engines. Clapey- ron (1834) then gave the geometrical method of representation universally used in thermodynamic discussions to-day, though often made more flexible by new coordinates as suggested by Gibbs (1873). To bring the ideas of Carnot into harmony with the first law of thermodynamics it is necessary to define the value of a transform- ation, and this was the great work of Clausius (1850), followed very closely by Kelvin (1851) and more hypothetically by Rankine (1851). The latter's broad treatment of energetics (1855) antedates many recent discussions. As early as 1858 Kirchhoff investigated the solution of solids and of gases thermodynamically, introducing at the same time an original method of treatment. The second law was not generally accepted without grave mis- giving. Clausius, indeed, succeeded in surmounting most of the objections, even those contained in theoretically delicate problems associated with radiation. Nevertheless, the confusion raised by the invocation of Maxwell's " demon " has never quite been calmed; and while Boltzmann (1877, 1878) refers to the second law as a case of probability, Helmholtz (1882) admits that the law is an expression of our inability to deal with the individual atom. Irreversible pro- cesses as yet lie quite beyond the pale of thermodynamics. For these the famous inequality of Clausius is the only refuge. The value of an uncompensated transformation is always positive. The invention of mechanical systems which more or less fully PROGRESS IN NINETEENTH CENTURY 43 conform to the second law has not been infrequent. Ideas of this nature have been put forward by Boltzmann (1866, 1872), by Clau- sius (1870, 1871), and more powerfully by Helmholtz (1884) in his theory of cyclic systems, which in a measure suggested the hidden mechanism at the root of Hertz's dynamics. Gibbs's (1902) element- ary principles of statistical mechanics seem, however, to contain the nearest approach to a logical justification of the second law — an approach which is more than a dynamical illustration. The applications of the first and second laws of thermodynamics are ubiquitous. As interesting instances we may mention the con- ception of an ideal gas and its properties; the departure of physical gases from ideality as shown in Kelvin and Joule's plug experiment (1854, 1862); the corrected temperature scale resulting on the one hand, and the possibility of the modern liquid air refrigerator of Linde and Hampson (1895) on the other. Difficulties encoimtered in the liquefaction of incoercible gases by Cailletet and Pictet (1877) have vanished even from the hydrogen coercions of Olezewski (1895) and of Dewar and Travers. Again, the broad treatment of fusion and evaporation, beginning with James Thomson's (1849) computation of the melting point of ice under pressure, Kirchhoff's (1858) treatment of sublimation, the extensive chapter of thermo-elastics set on foot by Kelvin's (1883) equation, are further examples. To these must be added Andrews's (1869) discovery of the continu- ity of the liquid and the gaseous states foreshadowed by Cagniard de la Tour (1822, 1823) ; the deep insight into the laws of physical gases furnished by the experimental prowess of Amagat (1881, 1893, 1896), and the remarkably close approximation amounting almost to a prediction of the facts observed which is given by the great work of van der Waals (1873). The further development of thermodynamics, remarkable for the breadth, not to say audacity, of its generalizations, was to take place in connection with chemical systems. The analytical power of the conception of a thermodynamic potential was recognized nearly at the same time by many thinkers:^ by Gibbs (1876), who discovered both the isothermal and the adiabatic potential; by Massieu (1877), independently in his Fonctions characteristiques ; by Helmholtz (1882), in his Freie Energie; by Duhem (1886) and by Planck (1887, 1891), in their respective thermodynamic potentials. The transformation of Lagrange's doctrine of virtual displacements of infinitely more complicated systems than those originally contem- plated, in other words the introduction of a virtual thermodynamic modification in complete analogy with the virtual displacement of the mecanique analytique, marked a new possibility of research of ^ Maxwell's available energy is accidentally overlooked in the text. 44 PHYSICS which Gibbs made the profoundest use. Unaware of this marshaling of powerful mathematical forces, van 't HofE (1886, 1888) consum- mated his marvelously simple application of the second law; and from interpretations of the experiments of Pfeffer (1877) and of Raoult (1883, 1887) propounded a new theory of solution, indeed, a basis for chemical physics, in a form at once available for experi- mental investigation. The highly generalized treatment of chemical statics by Gibbs bore early fruit in its application to Deville's phenomenon of disso- ciation (1857), and in succession Gibbs (1878, 1879), Duhem (1886), Planck (1887), have deduced adequate equations, while the latter in case of dilute solutions gave a theoretical basis for Guldberg and Waage's law of mass action (1879). An earlier independent treat- ment of dissociation is due to Horstmann (1869, 1873). In comparison with the brilliant advance of chemical statics which followed Gibbs, the progress of chemical dynamics has been less obvious; but the outlines of the subject have, nevertheless, been suc- cinctly drawn in a profound paper by Helmholtz (1886), followed with much skill by Duhem (1894, 1896) and Natanson (1896). Kinetic Theory of Gases The kinetic theory of gases at the outset, and as suggested by Herapath (1821), Joule (1851, 1857), Kronig (1856), virtually re- affirmed the classic treatise of Bernoulli (1738). Clausius in 1857-62 gave to the theory a modern aspect in his derivation of Boyle's law in its thermal relations, of molecular velocity and of the ratio of translational to total energy. He also introduced the mean free path (1858). Closely after followed Maxwell (1860), adducing the law for the distribution of velocity among molecules, later critically and elaborately examined by Boltzmann (1868-81). Nevertheless, the difficulties relating to the partition of energy have not yet been surmounted. The subject is still under vigorous discussion, as the papers of Burbury (1899) and others testify. To Maxwell (1860, 1868) is due the specifically kinetic interpret- ation of viscosity, of diffusion, of heat conduction, subjects which also engaged the attention of Boltzmann (1872-87). Rigorous data for molecular velocity and mean free path have thus become avail- able, and van der Waals (1873) added a final allowance for the size of the molecules. Less satisfactory has been the exploration of the character of molecular force for which Maxwell, Boltzmann (1872, et seq.), Sutherland (1886, 1893), and others have put forward tenta- tive investigations. The intrinsic equation of fluids discovered and treated in the great paper of van der Waals (1873), though partaking of the charac- PROGRESS IN NINETEENTH CENTURY 45 ter of a first approximation, has greatly promoted the coordination of most of the known facts. Corresponding states, the thermal coefficients, the vapor pressure relation, the minimum of pressure- volume products, and even molecular diameters, are reasonably in- ferred by van der Waals from very simple premises. Many of the results have been tested by Amagat (1896). The data for molecular diameter furnished by the kinetic theory as a whole, viz., the original values of Loschmidt (1865), of van der Waals (1873), and others, are of the same order of values as Kelvin's estimates (1883) from capillarity and contact electricity. Many converging lines of evidence show that an approximation to the truth has surely been reached. Radiation Our knowledge of the radiation of heat, diathermacy, thermo- crosis, was promoted by the perfection which the thermopyle reached in the hands of Melloni (1835-53). These and other researches set at rest forever all questions relating to the identity of heat and light. The subject was, however, destined to attain a much higher order of precision with the invention of Langley's bolometer (1881). The survey of heat spectra, beginning with the laborious attempts of Herschel (1840), of E. Becquerel (1843, 1870), H. Becquerel (1883), and others, has thus culminated in the magnificent development shown in Langley's charts (1883, 1884, et seq.). Kirchhoff's law (1860), to some extent anticipated by Stewart (1857, 1858), pervades the whole subject. The radiation of the black body, tentatively formulated in relation to temperature by Stefan (1879) and more rigorously by Boltzmann (1884), has furnished the savants of the Reichsanstalt with means for the development of a new pyrometry whose upper limit is not in sight. Among curious inventions Crooke's radiometer (1874) and Bell's photophone may be cited. The adaptation of the former in case of high exhaustion to the actual measurement of Maxwell's (1873) light pressure by Lebedew (1901) and Nichols and Hull (1903) is of quite recent history. The first estimate of the important constant of solar radiation at the earth was made by Pouillet (1838); but other pyrheliometric methods have since been devised by Langley (1884) and more re- cently by Angstrom (1886, et seq.). Velocity of light Data for the velocity of light, verified by independent astronom- ical observations, were well known prior to the century; for Romer 46 PHYSICS had worked as long ago as 1675, and Bradley in 1727. It remained to actually measure this enormous velocity in the laboratory, appar- ently an extraordinary feat, but accomplished simultaneously by Fizeau (1849) and by the aid of Wheatstone's revolving mirror (1834) by Foucault (1849, 1850, 1862). Since that time precision has been given to this important constant by Comu (1871, 1873, 1874), Forbes and Young (1882), Michelson (1878, et seq.), and Newcomb (1885). Foucault (1850), and more accurately Michelson (1884), deter- mined the variation of velocity with the medium and wave-length, thus assuring to the undulatory theory its ultimate triumph. Grave concern, however, still exists, inasmuch as Michelson and Morley (1886) by the most refined measurement, and differing from the older observations of Fizeau (1851, 1859), were unable to detect the optical effect of the relative motion of the atmosphere and the luminiferous ether predicted by theory. Romer's observation may in some degree be considered as an anticipation of the principle first clearly stated by Doppler (1842), which has since become invaluable in spectroscopy. Estimates of the density of the luminiferous ether have been published, in par- ticular by Kelvin (1854). Geometric optics Prior to the nineteenth century geometric optics, having been mustered before Huyghens (1690), Newton (1704), Malus (1808), Lagrange (1778, 1803), and others, had naturally attained a high order of development. It was, nevertheless, remodeled by the great paper of Gauss (1841), and was thereafter generalized step by step by Listing, Mobius (1855), and particularly by Abbe (1872), post- ulating that in character, the cardinal elements are independent of the physical reasons by which one region is imaged in another. So many able thinkers, like Airy (1827), Maxwell (1856, et seq.), Bessel (1840, 1841), Helmholtz (1856, 1867), Ferraris (1877, 1880), and others have contributed to the furtherance of geometric optics, that definite mention is impossible. In other cases, again, profound methods like those of Hamilton (1828, et seq.), Kummer (1859), do not seem to have borne correspondingly obvious fruit. The fun- damental bearing of diffraction on geometric optics was first pointed out by Airy (1838), but developed by Abbe (1873), and after him by Rayleigh (1879). An adequate theory of the rainbow, due to Airy and others, is one of its picturesque accomplishments (1838). The so-called astronomical refraction of a medium of continu- ously varying index, successively treated by Bouguer (1739, 1749), Simpson (1743), Bradley (1750, 1762), owes its recent refined de- velopment to Bessel (1823, 1826, 1842), Ivory (1822, 1823, et seq.), PROGRESS IN NINETEENTH CENTURY 47 Radau (1884), and others. Tait (1883) gave much attention to the allied treatment of mirage. In relation to instruments the conditions of aplantism were exam- ined by Clausius (1864), by Helmholtz (1874), by Abbe (1873, et seq.), by Hockin (1884), and others, and the apochromatic lens was introduced by Abbe (1879). The microscope is still well subserved by either the Huyghens or the Ramsden (1873) eye-piece, but the objective has undergone successive stages of improvement, begin- ning with Lister's discovery in 1830. Amici (1840) introduced the principle of immersion; Stephenson (1878) and Abbe (1879), homo- geneous immersion; and the Abbe-Zeiss apochromatic objective (188B), the outcome of the Jena-glass experiments, marks, perhaps, the high-water mark of the art for the microscope. Steinheil (1865, 1866) introduced the guiding principle for photographic objectives. Alvan Clark carried the difficult technique of telescope lens con- struction to a degree of astonishing excellence. Spectrum — Dispersion Curiously, the acumen of Newton (1666, 1704) stopped short of the ultimate conditions of purity of spectrum. It was left to WoUas- ton (1802), about one hundred years later, to introduce the slit and observe the dark lines of the solar spectrum. Fraunhofer (1814, 1815, 1823) mapped them out carefully and insisted on their solar origin. Brewster (1833, 1834), who afterwards (1860) published a map of 3000 lines, was the first to lay stress on the occurrence of absorption, believing it to be atmospheric. Forbes (1836) gave even greater definiteness to absorption by referring it to solar origin. Foucault (1849) pointed out the coincidence of the sodium lines with the D group of Fraunhofer, and discovered the reversing effect of sodium vapor. A statement of the parallelism of emission and absorption came from Angstrom (1855) and with greater defin- iteness and ingenious experiments from Stewart (1860). Never- theless, it was reserved to Kirchhoff and Bunsen (1860, 1861) to give the clear-cut distinctions between the continuous spectra and the characteristically fixed bright-line or dark-line spectra upon which spectrum analysis depends. Kirchhoff 's law was annoimced in 1861, and the same year brought his map of the solar spectrum and a discussion of the chemical composition of the sun. Huggins (1864, et seq.), Angstrom (1868), Thal6n (1875), followed with im- proved observations on the distribution and wave-length of the solar lines; but the work of these and other observers was suddenly over- shadowed by the marvelous possibilities of the Rowland concave grating (1882, et seq.). Rowland's maps and tables of the solar spec- trum as they appeared in 1887, 1889, et seq., his summary of the 48 PHYSICS elements contained in the sun (1891), each marked a definite stage of advance of the subject. Mitscherlich (1862, 1863) probably was the first to recognize the banded or channeled spectra of compound bodies. Balmer (1885) constructed a valuable equation for recog- nizing the distribution of single types of lines. Kayser and Runge (1887, et seq.) successfully analyzed the structure of the spectra of alkaline and other elements. The modernized theory of the grating had been given by Rayleigh in 1874 and was extended to the concave grating by Rowland (1892, 1893) and others. A general theory of the resolving power of pris- matic systems is also due to Rayleigh (1879, 1880), and another to Thollon (1881). The work of Rowland for the visible spectrum was ably paral- leled by Langley's investigations (1883 et seq.) of the infra-red, dating from the invention of the bolometer (1881). Superseding the work of earlier investigators like Fizeau and Foucault (1878) and others, Langley extended the spectrum with detailed accuracy to over eight times its visible length. The solar and the lunar spectrum, the radiations of incandescent and of hot bodies, were all specified abso- lutely and with precision. With artificial spectra Rubens (1892, 1899) has since gone further, reaching the longest heat-waves known. A similarly remarkable extension was added for the ultra-violet by Schumann (1890, 1892), contending successfully with the grad- ually increasing opacity of all known media. Experimentally the suggestion of the spectroheliograph by Lock- yer (1868) and by Janssen (1868) and its brilliant achievement by Hale (1892) promise notable additions to our knowledge of solar activity. Finally, the refractions of absorbing media have been of great importance in their bearing on theory. The peculiarities of metallic reflection were announced from his earlier experiments (1811) by Arago in 1817 and more fully investigated by Brewster (1815, 1830, 1831). F. Neumann (1832) and MacCullagh (1837) gave sharper statements to these phenomena. Equations were advanced by Cauchy (1836, et seq.) for isotropic bodies, and later with greater detail by Rayleigh (1872), Ketteler (1875, et seq.), Drude (1887, et seq.), and others. Jamin (1847, 1848) devised the first experiments of requisite precision and found them in close agreement with Cauchy 's theory. Kundt (1888) more recently investigated the refraction of metallic prisms. Anomalous dispersion was discovered by Christiansen in 1870, and studied by Kundt (1871, et seq.). Sellmeyer's (1872) powerful and flexible theory of dispersion was extended to include absorp- tion effects by Helmholtz (1874), with greater detail by Ketteler (1879, et aeq.), and from a different point of view by Kelvin (1885). PROGRESS IN NINETEENTH CENTURY 49 The electromagnetic theory lends itself particularly well to the same phenomena, and Kolazek (1887, 1888), Goldhammer (1892), Helm- holtz (1892), Drude (1893), and others instanced its adaptation with success. Photometry, Fluorescence, Photochemistry The cosine law of Lambert (1760) has since been interpreted in a way satisfying modern requirements by Fourier (1817, 1824) and by Lommel (1880). Among new resources for the experimentalist the spectrophotometer, the Lummer-Brodhun photometer (1889), and Rood's flicker photometer (1893, 1899), should be mentioned. Fluorescence, though ingeniously treated by Herschel (1845, 1853) and Brewster (1846, et seq.), was virtually created in its philo- sophical aspects by Stokes in his great papers (1852, et seq.) on the subject. In recent years Lommel (1877) made noteworthy contribu- tions. Phosphorescence has engaged the attention of E. Becquerel (1859), among others. The laws of photochemistry are in large measure due to Bunsen and Roscoe (1857, 1862). The practical development of photography from its beginnings with Daguerre (1829, 1838) and Ni^pce and Fox-Talbot (1839), to its final improvement by Maddox (1871) with the introduction of the dry plate, is familiar to all. Vogel's (1873) discovery of appropriate sensitizers for different colors has added new resources to the already invaluable application of photo- graphy to spectroscopy. Interference The colors of thin plates treated successively by Boyle (1663), Hooke (1665), and more particularly by Newton (1672, Optiks, 1704), became in the hands of Young (1802) the means of framing an adequate theory of light. Young also discovered the colors of mixed plates and was cognizant of loss of half a wave-length on reflection from the denser medium. Fresnel (1815) gave an inde- pendent explanation of Newton's colors in terms of interference, devising for further evidence his double mirrors (1816), his biprism (1819), and eventually the triple mirror (1820). Billet's plates and split lens (1858) belong to the same classical order, as do also Lloyd's (1837) and Haidinger's (1849) interferences. Brewster's (1817) observation of interference in case of thick plates culminated in the hands of Jamin (1856, 1857) in the useful interferometer. The scope of this apparatus was immensely advanced by the famous device of Michelson (1881, 1882), which has now become a funda- mental instrument of research. Michelson's determination of the length of the meter in terms of the wave-length of light with as- tounding accuracy is a mere example of its accomplishments. 50 PHYSICS Wiener (1890) in his discovery of the stationary light-wave intro- duced an entirely new interference phenomenon. The method was successfully applied to color photography by Lippmann (1891, 1892), showing that the electric and not the magnetic vector is photographically active. The theory of interferences from a broader point of view, and including the occurrence of multiple reflections, was successively perfected by Poisson (1823), Fresnel (1823), Airy (1831). It has recently been further advanced by Feussner (1880, et seq.), Sohncke and Wangerin (1881, 1883), Rayleigh (1889), and others. The inter- ferences along a caustic were treated by Airy (1836), but the endeavor to reconstruct geometric optics on a diffraction basis has as yet only succeeded in certain important instances, as already mentioned. Diffraction Though diffraction dates back to Grimaldi (1665) and was well known to Newton (1704), the first correct though crude interpret- ation of the phenomenon is due to Young (1802, 1804). Independ- ently Fresnel (1815) in his original work devised similar explanations, but later (1818, 1819, 1826) gave a more rational theory in terms of Huyghens's principle, which he was the first adequately to inter- pret. Fresnel showed that all points of a wave-front are concerned in producing diffraction, though the ultimate critical analysis was left to Stokes (1849). ' In 1822 Fraunhofer published his remarkable paper, in which, among other inventions, he introduced the grating into science. Zone plates were studied by Cornu (1875) and by Soret (1875). Rowland's concave grating appeared in 1881 ; Michelson's echelon spectrometer in 1899. The theory of gratings and other diffraction phenomena was exhaustively treated by Schwerd (1837). Babinet established the principle bearing his name in 1837. Subsequent developments were in part concerned with the improvement of Fresnel's method of computation, in part with a more rigorous treatment of the theory of diffraction. Stokes (1850, 1852) gave the first account of the polarization accompanying diffraction, and thereafter Rayleigh (1871) and many others, including Kirchhoff (1882, 1883), profoundly modified the classic treatment. Airy (1834, 1838) and others elabor- ately examined the diffraction due to a point source in view of its important bearing on the efficiency of optical instruments. A unique development of diffraction is the phenomenon of scat- tering propounded by Rayleigh (1871) in his dynamics of the blue sky. This great theory which Rayleigh has repeatedly improved (1881, et seq.) has since superseded all other relevant explanations. PROGRESS IN NINETEENTH CENTURY 51 Polarization An infinite variety of polarization phenomena grew out of Bar- tholinus's (1670) discovery. Sound beginnings of a theory were laid by Huyghens (Traite, 1690), whose wavelet principle and ele- mentary wave-front have persisted as an invaluable acquisition, to be generalized by Fresnel in 1821, Fresh foundations in this department of optics were laid by Malus (1810) in his discovery of the cosine law and the further discovery of the polarization of reflected light. Later (1815) Brewster adduced the conditions of maximum polarization for this case. In 1811 Arago announced the occurrence of interferences in con- nection with parallel plane-polarized light, phenomena which under the observations of Arago and Fresnel (1816, 1819), Biot (1816), Brewster (1813, 1814, 1818), and others grew immensely in variety, and in the importance of their bearing on the imdulatory theory. It is on the basis of these phenomena that Fresnel in 1819 insisted on the transversality of light-waves, offering proof which was sub- sequently made rigorous by Verdet (1850). Though a tentative explanation was here again given by Young (1814), the first ade- quate theory of the behavior of thin plates of SBolotropic media with polarized light came from Fresnel (1821). Airy (1833) elucidated a special case of the gorgeously compli- cated interferences obtained with convergent pencils; Neumann in 1834 gave the general theory. The forbidding equations resulting were geometrically interpreted by Bertin (1861, 1884), and Lommel (1883) and Neumann (1841) added a theory for stressed media, afterwards improved by Pockels (1889). The peculiarly undulatory character of natural light owes its explanation largely to Stokes (1852), and his views were verified by many physicists, notably by Fizeau (1862) showing interferences for path differences of 50,000 wave-lengths, and by Michelson for much larger path differences. The occurrence of double refraction in all non-regular crystals was recognized by Haiiy (1788) and studied by Brewster (1818). In 1821, largely by a feat of intuition, Fresnel introduced his gen- eralized elementary wave-surface, and the correctness of his explan- ation has since been substantiated by a host of observers. Stokes (1862, et seq.) was unremittingly active in pointing out the theoret- ical bearing of the results obtained. Hamilton (1832) supplied a remarkable criterion of the truth of Fresnel's theory deductively, in the prediction of both types of conic refraction. The phenomena were detected experimentally by Lloyd (1833). The domain of natural rotary polarization, discovered by Arago (1811) and enlarged by Biot (1815), has recently been placed in 52 PHYSICS close relation to non-symmetrical chemical structure by LeBel (1874) and van 't Hoff (1875), and a tentative molecular theory was ad- vanced by Sohncke (1876). Boussinesq (1868) adapted Cauchy's theory (1842) to these phe- nomena. Independent elastic theories were propounded by Mac- Cullagh (1837), Briot, Sarrau (1868); but there is naturally no diffi- culty in accounting for rotary polarization by the electromagnetic theory of light, as was shown by Drude (1892), Among investigational apparatus of great importance the Soleil (1846, 1847) saccharimeter may be mentioned. Theories In conclusion, a brief summary may be given of the chief mechan- isms proposed to account for the undulations of light. Fresnel sug- gested the first adequate optical theory in 1821, which, though singularly correct in its bearing on reflection and refraction in the widest sense, was merely tentative in construction. Cauchy (1829) proposed a specifically elastic theory for the motion of relatively long waves of light in continuous media, based on a reasonable hypothesis of molecular force, and deduced therefrom Fresnel's reflection and refraction equations. Green (1838), ignoring molecular forces and proceeding in accordance with his own method in elastics, published a different theory, which did not, however, lead to Fresnel's equations. Kelvin (1888) found the conditions implied in Cauchy's theory compatible with stability if the ether were considered as bound by a rigid medium. The ether implied throughout is to have the same elasticity everywhere, but to vary in density from medium to medium, and vibration to be normal to the plane of polariza- tion. Neumann (1835), whose work has been reconstructed by Kirchhoff (1876), and MacCullagh (1837), with the counter-hypothesis of an ether of fixed density but varying in elasticity from medium to medium, also deduced Fresnel's equations, obtaining at the same time better surface conditions in the case of seolotropic media. The vibrations are in the plane of polarization. Ail the elastic theories essentially predict a longitudinal light-wave. It was not until Kelvin in 1889-90 proposed his remarkable gyro- static theory of light, in which force and displacement become torque and twist, that these objections to the elastic theory were wholly removed. MacCullagh, without recognizing their bearing, seems actually to have anticipated Kelvin's equation. With the purpose of accounting for dispersion, Cauchy in 1835 gave greater breadth to his theory by postulating a sphere of action of ether particles commensurate with wave-length, and in this direction PROGRESS IN NINETEENTH CENTURY 53 he was followed by F. Neumann (1841), Briot (1864), Rayleigh (1871), and others, treating an ether variously loaded with material particles. Among theories beginning with the phenomena observed, that of Boussinesq (1867, et seq.) has received the most extensive development. The difficult surface conditions met with when light passes from one medium to another, including such subjects as ellipticity, total reflection, etc., have been critically discussed, among others, by Neu- mann (1835) and Rayleigh (1888); but the discrimination between the Fresnel and the Neumann vector was not accomplished without misgiving before the advent of the work of Hertz. It appears, therefore, that the elastic theories of light, if Kelvin's gyrostatic adynamic ether be admitted, have not been wholly routed. Nevertheless, the great electromagnetic theory of light propounded by Maxwell (1864, Treatise, 1873) has been singularly apt not only in explaining all the phenomena reached by the older theories and in predicting entirely novel results, but in harmoniously uniting, as parts of a unique doctrine, both the electric or photographic light vector of Fresnel and Cauchy and the magnetic vector of Neumann and MacCullagh, Its predictions have, moreover, been astonishingly verified by the work of Hertz (1890), and it is to-day acquiring added power in the convection theories of Lorentz (1895) and others. Electrostatics Coulomb's (1785) law antedates the century; indeed, it was known to Cavendish (1771, 1781). Problems of electric distribution were not seriously approached, however, until Poisson (1811) solved the case for spheres in contact. Afterwards Clausius (1852), Helmholtz (1868), and Kirchhoff (1877) examined the conditions for discs, the last giving the first rigorous theory of the experimentally important plate-condenser. In 1845-48 the investigation of electric distribu- tion received new incentive as an application of Kelvin's beautiful method of images. Maxwell {Treatise, 1873) systematized the treat- ment of capacity and induction coefficients. Riess (1837), in a classic series of experiments on the heat produced by electrostatic discharge, virtually deduced the potential energy of a conductor and in a measure anticipated Joule's law (1841). In 1860 appeared Kelvin's great paper on the electromotive force needed to produce a spark. As early as 1855, however, he had shown that the spark discharge is liable to be of the character of a damped vibra- tion and the theory of electric oscillation was subsequently extended by Kirchhoff (1867). The first adequate experimental verification was due to Feddersen (1858, 1861). The specific inductive capacity of a medium with its fundamental 54 PHYSICS bearing on the character of electric force was discovered by Far- aday in 1837. Of the theories propounded to account for this pro- perty the most far-reaching is Maxwell's (1865), which culminates in the unique result showing that the refraction index of a medium is the square root of its specific inductive capacity. With regard to Maxwell's theory of the Faraday stress in the ether as compared with the subsequent development of electrostriction in other media by many authors, notably by Boltzmann (1880) and by Kirchhoff (1885), it is observable that the tendency of the former to assign concrete physical properties to the tube of force is growing, partic- ularly in connection with radioactivity. Duhem (1892, 1895) in- sists, however, on the greater trustworthiness of the thermt)dynamic potential. The seemingly trivial subject of pyroelectricity interpreted by iEpinus (1756) and studied by Brewster (1825), has none the less elicited much discussion and curiosity, a vast number of data by Hankel (1839-93) and others, and a succinct explanation by Kelvin (1860, 1878). Similarly piezoelectricity, discovered by the brothers Curie (1880), has been made the subject of a searching investigation by Voigt (1890). Finally Kerr (1875, et seq.) observed the occurrence of double refraction in an electrically polarized medium. Recent researches, among which those of Lemoine (1896) are most accurate, have determined the phase difference corresponding to the Kerr effect under normal conditions, while Voigt (1899) has adduced an adequate theory. Certain electrostatic inventions have had a marked bearing on the development of electricity. We may mention in particular Kelvin's quadrant electrometer (1867) and Lippmann's capillary electrometer (1873). Moreover, among apparatus originating in Nicholson's dupli- cator (1788) and Volta's electrophorus, the Topler-Holtz machine (1865-67), with the recent improvement due to Wimshurst, has replaced all others. Atmospheric electricity, after the memorable experiment of Franklin (1751), made little progress until Kelvin (1860) organized a systematic attack. More recently a revival of interest began with Exner (1886), but more particularly with Linss (1887), who insisted on the fundamental importance of a detailed knowledge of atmospheric conduction. It is in this direction that the recent vigorous treatment of the atmosphere as an ionized medium has progressed, owing chiefly to the indefatigable devotion of Elster and Geitel (1899, et seq.) and of C. T. R. Wilson (1897, et seq.). Quali- tatively the main phenomena of atmospheric electricity are now plausibly accounted for; quantitatively there is as yet very little specific information. PROGRESS IN NINETEENTH CENTURY 55 Volta Contacts Volta's epoch-making experiment of 1797 may well be added to the century which made such prolific use of it; indeed, the Voltaic pile (1800-02) and Volta's law of series (1802) come just within it. Among the innumerable relevant experiments Kelvin's dropping electrodes (1859) and his funnel experiment (1867) are among the more interesting, while the Spannungsreihe of R. Kohlrausch (1851, 1853) is the first adequate investigation. Nevertheless, the phenomenon has remained without a universally acceptable explana- tion until the present day, when it is reluctantly yielding to electronic theory, although ingenious suggestions like Helmholtz's Doppel- schicht (1879), the interpretations of physical chemistry and the discovery of the concentration cell (Helmholtz; Nernst, 1888, 1889; Planck, 1890) have thrown light upon it. Among the earliest theories of the galvanic cell is Kelvin's (1851, 1860), which, like Helmholtz's, is incomplete. The most satisfactory theory is Nernst's (1889). Gibbs (1878) and Helmholtz (1882) have made searching critical contributions, chiefly in relation to the thermal phenomena. Volta's invention was made practically efficient in certain famous galvanic cells, among which Daniell's (1836), Grove's (1839), Clarke's (1878), deserve mention, and the purposes of measurement have been subserved by the potentiometers of Poggendorff (1841), Bosscha (1855), Clarke (1873). Seebeck Contacts Thermoelectricity, destined to advance many departments of physics, was discovered by Seebeck in 1821. The Peltier effect fol- lowed in 1834, subsequently to be interpreted by Icilius (1853). A thermodynamic theory of the phenomena came from Clausius (1853) and with greater elaboration, together with the discovery of the Thomson effect, from Kelvin (1854, 1856), to whom the thermo- electric diagram is due. This was subsequently developed by Tait (1872, et seq.) and his pupils. Avenarius (1863), however, first observed the thermoelectric parabola. The modern platinum-iridium or platinum-rhodium thermo- electric pyrometer dates from about 1885 and has recently been perfected at the Reichsanstalt. Melloni (1835, et seq.) made the most efficient use of the thermopyle in detecting minute temperature differences. Electrolysis Though recognized by Nichols and Carlisle (1800) early in the century, the laws of electrolysis awaited the discovery of Faraday 66 PHYSICS (1834). Again, it was not till 1853 that further marked advances were made by Hittorf's (1853-59) strikingly original researches on the motions of the ions. Later Clausius (1857) suggested an ade- quate theory of electrolysis, which was subsequently to be specialized in the dissociation hypothesis of Arrhenius (1881, 1884). To the elaborate investigations of F. Kohlrausch (1879, et seq.), however, science owes the fundamental law of the independent velocities of migra£ion of the ions. Polarization discovered by Ritter in 1803 became in the hands of Plants (1859-1879) an invaluable means for the storage of energy, an application which was further improved by Faure (1880). Steady Flow The fundamental law of the steady flow of electricity, in spite of its simplicity, proved to be peculiarly elusive. True, Cavendish (1771-81) had definite notions of electrostatic resistance as depend- ent on length section and potential, but his intuitions were lost to the world. Davy (1820), from his experiments on the resistances of conductors, seems to have arrived at the law of sections, though he obscured it in a misleading statement. Barlow (1825) and Becquerel (1825-26), the latter operating with the ingenious differential gal- vanometer of his own invention, were not more definite. Surface effects were frequently suspected. Ohm himself, in his first paper (1825), confused resistance with the polarization of his battery, and it was not till the next year (1826) that he discovered the true law, eventually promulgated in his epoch-making Die galvanische Kette (1827). It is well known that Ohm's mathematical deductions were un- fortunate, and would have left a gap between electrostatics and voltaic electricity. But after Ohm's law had been further experi- mentally established by Fechner (1830), the correct theory was given by Kirchhoff (1849) in a way to bridge over the gap specified. Kirchhoff approached the question gradually, considering first the distribution of current in a plane conductor (1845-46), from which he passed to the laws of distribution in branched conductors (1847- 48) — laws which now find such universal application. In his great paper, moreover, Kirchhoff gives the general equation for the act- ivity of the circuit and from this Clausius (1852) soon after deduced the Joule effect theoretically. The law, though virtually implied in Riess's results (1837), was experimentally discovered by Joule (1841). As bearing critically or otherwise on Ohm's law we may mention the researches of Helmholtz (1852), of Maxwell (1876), the solution of difficult problems in regard to terminals or of the resistance of PROGRESS IN NINETEENTH CENTURY 57 special forms of conductors, by Rayleigh (1871, 1879), Hicks (1883), and others, the discussion of the refraction of lines of flow by Kirch- hoff (1845), and many researches on the limits of accuracy of the law. Finally, in regard to the evolution of the modern galvanometer from its invention by Schweigger (1820), we may enumerate in suc- cession Nobili's astatic system (1834), Poggendorff's (1826) and Gauss's (1833) mirror device, the aperiodic systems, Weber's (1862) and Kelvin's critical study of the best condition for galvanometry, so cleverly applied in the instruments of the latter. Kelvin's siphon recorder (1867), reproduced in the Depretz-D'Arsonval system (1882), has adapted the galvanometer to modern conditions in cities. For absolute measurement Pouillet's tangent galvanometer (1837), treated for absolute measurement by Weber (1840), and Weber's dynamometer (1846) have lost little of their original importance. Magnetism Magnetism, definitely founded by Gilbert (1600) and put on a quantitative basis by Coulomb (1785), was first made the subject of recondite theoretical treatment by Poisson (1824-27). The inter- pretation thus given to the mechanism of two conditionally separable magnetic fluids facilitated discussion and was very generally used in argument, as for instance by Gauss (1833) and others, although Ampere had suggested the permanent molecular current as early as 1820. Weber (1852) introduced the revolvable molecular magnet, a theory which Ewing (1890) afterwards generalized in a way to include magnetic hysteresis. The phenomenon itself was independ- ently discovered by Warburg (1881) and by Ewing (1882), and has since become of special practical importance. Faraday in 1852 introduced his invaluable conception of lines of magnetic force, a geometric embodiment of Gauss's (1813, 1839) theorem of force flux, and Maxwell (1855, 1862, et seq.) thereafter gave the rigorous scientific meaning to this conception which per- vades the whole of contemporaneous electromagnetics. The phenomenon of magnetic induction, treated hypothetically by Poisson (1824-27) and even by Barlow (1820), has since been attacked by many great thinkers, like F. Neumann (1848), Kirchhoff (1854); but the predominating and most highly elaborated theory is due to Kelvin (1849, et seq.). This theory is broad enough to be applicable to seolotropic media and to it the greater part of the not- ation in current use throughout the world is due. A new method of attack of great promise has, however, been introduced by Duhem (1888, 1895, et seq.) in his application of the thermodynamic potential to magnetic phenomena. 58 PHYSICS Magneticians have succeeded in expressing the magnetic distri- bution induced in certain simple geometrical figures like the sphere, the spherical shell, the ellipsoid, the infinite cylinder, the ring. Green in 1828 gave an original but untrustworthy treatment for the finite cylinder. Lamellar and solenoidal distributions are defined by Kelvin (1850), to whom the similarity theorems (1856) are also due. Kirchhofif 's results for the ring were practically utilized in the absolute measurements of Stoletow (1872) and of Rowland (1878). Diamagnetism, though known since Brugmans (1778), first chal- lenged the permanent interest of science in the researches of Becquerel (1827) and of Faraday (1845). It is naturally included harmoniously in Kelvin's great theory (1847, et seq.). Independent explanations of diamagnetism, however, have by no means abandoned the field; one may instance Weber's (1852) ingenious generalization of Ampere's molecular currents (1820) and the broad critical deductions of Duhem (1889) from the thermodynamic potential. For the treatment of aeolotropic magnetic media, Kelvin's (1850, 1851) theory seems to be peculiarly applicable. Weber's theory would seem to lend itself well to electronic treatment. The extremely complicated subject of magnetostriction, originally observed by Matteuci (1847) and by Joule (1849) in different cases, and elaborately studied by Wiedemann (1858, et seq.), has been repeatedly attacked by theoretical physicists, among whom Helm- holtz (1881), Kirchhoff (1885), Boltzmann (1879), and Duhem (1891) may be mentioned. Noneof the carefully elaborated theories accoun s in detail for the facts observed. The relations of magnetism to light have increased in importance since the fundamental discoveries of Faraday (1845) and of Verdet (1854), and they have been specially enriched by the magneto-optic discoveries of Kerr (1876, et seq.), of Kundt (1884, et seq.), and more recently by the Zeemann effect (1897, et seq.). Among the theorie put forth for the latter, the electronic explanation of Lorentz (1898 1899) and that of Voigt (1899) are supplementary or at least not con tradictory. The treatment of the Kerr effect has been systematized by Drude (1892, 1893). The instantaneity of the rotational effect was first shown by Bichat and Blondlot (1882), and this result has since been found useful in chronography. Sheldon demonstrated the possibility of reversing the Faraday effect. Finally terrestrial magnetism was revolutionized and made accessible to absolute meas- urement by Gauss (1833), and his method served Weber (1840, et seq.) aad his successors as a model for the definition of absolute units throughout physics. Another equally important contribution from the same great thinker (1840) is the elaborate treatment of the dis- tribution of terrestrial magnetism, the computations of which have PROGRESS IN NINETEENTH CENTURY 59 been twice modernized, in the last instance by Neumeyer * (1880). Magnetometric methods have advanced but little since the time of Gauss (1833), and Weber's (1853) earth inductor remains a standard instrument of research. Observationally, the development of cycles of variation in the earth's constants is looked forward to with eager- ness, and will probably bear on an adequate theory of terrestrial magnetism, yet to be framed. Arrhenius (1903) accentuates the importance of the solar cathode torrent in its bearing on the earth's magnetic phenomena. Electromagnetism Electromagnetism, considered either in theory or in its applica^ tions, is, perhaps, the most conspicuous creation of the nineteenth century. Beginning with Oersted's great discovery of 1820, the quantitative measurements of Biot and Savart (1820) and Laplace's (1821) law followed in quick succession. Ampere (1820) without delay propounded his famous theory of magnetism. For many years the science was conveniently subserved by Ampere's swimmer (1820), though his functions have since advantageously yielded to Fleming's hand rule for moving current elements. The induction produced by ellipsoidal coils or the derivative cases is fully understood. In prac- tice the rule for the magnetic circuit devised by the Hopkinsons (1886) is in general use. It may be regarded as a terse summary of the theories of Euler (1780), Faraday, Maxwell, and particularly Kelvin (1872), who already made explicit use of it. Nevertheless, the clear-cut practical interpretation of the present day had to be gradually worked out by Rowland (1873, 1884), Bosanquet (1883- 85), Kapp (1885), and Pisati (1890). The construction of elementary motors was taken up by Faraday (1821), Ampere (1822), Barlow (1822), and others, and they were treated rather as laboratory curiosities; for it was not until 1857 that Siemens devised his shuttle-wound armature, and the development of the motor thereafter went pari passu with the dynamo, to be pre- sently considered. It culminated in a new principle in 1888, when Ferraris, and somewhat later Tesla (1888) and Borel (1888), intro- duced polyphase transmission and the more practical realization of Arago's rotating magnetic field (1824). Theoretical electromagnetics, after a period of quiescence, was again enriched by the discovery of the Hall effect (1879, et seq.), which at once elicited wide and vigorous discussion, and for which Row- land (1880), Lorentz (1883), Boltzmann (1886), and others put for- ward theories of continually increasing finish. Nernst and v. Ettings- hausen (1886, 1887) afterwards added the thermomagnetic effect. ' Dr. L. A. Bauer kindly called my attention to the more recent work of A. Schmidt sunomarized in Dr. Bauer's own admirable paper. 60 PHYSICS Electrodynamics The discovery and interpretation of electrodynamic phenomena were the burden of the unique researches of Ampere (1820, et seq., Memoir, 1826). Not until 1846, however, were Ampere's results critically tested. This examination came with great originality from Weber using the bifilar dynamometer of his own invention. Grass- mann (1845), Maxwell (1873), and others have invented elementary laws differing from Ampere's; but as Stefan (1869) showed that an indefinite number of such laws might be constructed to meet the given integral conditions, the original law is naturally preferred. Induction Faraday (1831, 1832) did not put forward the epoch-making dis- covery of electrokinetic induction in quantitative form, as the great physicist was insufficiently familiar with Ohm's law. Lentz, how- ever, soon supplied the requisite interpretation in a series of papers (1833, 1835) which contain his well-known law both for the mutual inductions of circuits and of magnets and circuits. Lentz clearly announced that the induced quantity is an electromotive force, in- dependent of the diameter and metal and varying, caeteris paribus, with the number of spires. The mutual induction of circuits was first carefully studied by Weber (1846), later by Filici (1852), using a zero method, and Faraday's self-induction by Edlund (1849), while Matteuci (1854) attested the independence of induction of the interposed non-magnetic medium. Henry (1842) demonstrated the successive induction of induced currents. Curiously enough the occurrence of eddy currents in massive con- ductors moving in the magnetic field was announced from a differ- ent point of view by Arago (1824-26) long before Faraday's great discovery. They were but vaguely understood, however, until Fou- cault (1855) made his investigation. The general problem of the induction to be anticipated in massive conductor is one of great interest, and Helmholtz (1870), Kirchhoff (1891), Maxwell (1873), Hertz (1880), and others have treated it for different geometrical figures. The rigorous expression of the law of induction was first ob- tained by F. Neumann (1845, 1847) on the basis of Lentz's law, both for circuits and for magnets. W. Weber (1846) deduced the law of induction from his generalized law of attraction. More acceptably, however, Helmholtz (1847), and shortly after him Kelvin (1848), showed the law of induction to be a necessary consequence of the law of the conservation of energy, of Ohm's and Joule's law. In 1851 Helmholtz treated the induction in branched circuits. Finally PROGRESS IN NINETEENTH CENTURY 61 Faraday's " electrotonic state " was mathematically interpreted thirty years later, by Maxwell, and to-day, under the name of elec- tromagnetic momentum, it is being translated into the notation of the electronic theory. Many physicists, following the fundamental equation of Neumann (1845, 1847), have developed the treatment of mutual and self in- duction with special reference to experimental measurement. On the practical side the magneto-inductor may be traced back to d'al Negro (1832) and to Pixii (1832). The tremendous devel- opment of induction electric machinery which followed the intro- duction of Siemens's (1857) armature can only be instanced. In 1867 Siemens, improving upon Wilde (1866), designed electric generators without permanent magnets. Pacinotti (1860) and later Gramme (1871) invented the ring armature, while von Hefner-Alteneck (1872) and others improved the drum armatiu-e. Thereafter further progress was rapid. It took a different direction in connection with the Ferraris (1888) motor by the development of the induction coil of the laboratory (Faraday, 1831; Neef, 1839; Ruhmkoff, 1853) into the transformer (Gaulard and Gibbs, 1882-84) of the arts. Among special apparatus Hughes (1879) contributed the induction balance, and Tesla (1891) the high frequency transformer. The Elihu Thompson effect (1887) has also been variously used. In 1860 Reiss devised a telephone, in a form, however, not at once capable of practical development. Bell in 1875 invented a different instrument which needed only the microphone (1878) of Hughes and others to introduce it permanently into the arts. Of particu- lar importance in its bearing on telegraphy, long associated with the names of Gauss and Weber (1833) or practically with Morse and Vail (1837), is the theory of conduction with distributed capac- ity and inductance established by Kelvin (1856) and extended by Kirchhoff (1857). The working success of the Atlantic cable demon- strated the acumen of the guiding physicist. Electric Oscillation The subject of electric oscillation announced in a remarkable paper of Henry in 1842 and threshed out in its main features by Kelvin in 1856, followed by Kirchhoff 's treatment of the transmission of oscillations along a wire (1857), has become of discriminating im- portance between Maxwell's theory of the electric field and the other equally profound theories of an earlier date. These crucial experiments contributed by Hertz (1887, et seq.) showed that elec- tromagnetic waves move with the velocity of light, and like it are capable of being reflected, refracted, brought to interference, and 62 PHYSICS polarized. A year later Hertz (1888) worked out the distribution of the vectors in the space surrounding the oscillatory source. Lecher (1890) using an ingenious device of parallel wires, Blondlot (1891) with a special oscillator, and with greater accuracy Trowbridge and Duane (1895) and Saunders (1896), further identified the veloc- ity of the electric wave with that of the wave of light. Simultan- eously the reasons for the discrepancies in the strikingly original method for the velocity of electricity due to Wheatstone (1834), and the American and other longitude observations (Walker, 1894; Mitchell, 1850; Gould, 1851), became apparent, though the nature of the difficulties had already appeared in the work of Fizeau and Gounelle (1850). Some doubt was thrown on the details of Hertz's results by Sarasin and de la Rive's phenomenon of multiple resonance (1890), but this was soon explained away as the necessary result of the occurrence of damped oscillations by Poincar6 (1891), by Bjerknes (1891), and others. J. J. Thomson (1891) contributed interesting results for electrodeless discharges, and on the value of the dielectric constant for slow oscillations (1889); Boltzmann (1893) examined the inter- ■ferences due to thin plates; but it is hardly practicable to summarize the voluminous history of the subject. On the practical side, we are to-day witnessing the astoundingly rapid growth of Hertzian wave wireless telegraphy, due to the successive inventions of Branly (1890, 1891), Popoff, Braun (1899), and the engineering prowess of Marconi. In 1901 these efforts were crowned by the incredible feat of Mar- coni's first message from Poldhu to Cape Breton, placing the Old World within electric earshot of the New. Maxwell's equations of the electromagnetic field were put for- ward as early as 1864, but the whole subject is presented in its broad- est relations in his famous treatise of 1873. The fundamental feature of Maxwell's work is the recognition of the displacement current, a conception by which Maxwell was able to annex the. phenomena of light to electricity. The methods by which Maxwell arrived at his great discoveries are not generally admitted as logically binding. Most physicists prefer to regard them as an invaluable possession as yet unliquidated in logical coin ; but of the truth of his equations there is no doubt. Maxwell's theory has been frequently expounded by other great thinkers, by Rayleigh (1881), by Poincar^ (1890), by Boltzmann (1890), by Heaviside (1889), by Hertz (1890), by Lorentz, and others. Hertz and Heaviside, in particular, have con- densed the equations into the symmetrical form now commonly used. Poynting (1884) contributed his remarkable theorem on the energy path. Prior to 1870 the famous law of Weber (1846) had gained wide recognition, containing as it did Coulomb's law. Ampere's law, PROGRESS IN NINETEENTH CENTURY 63 Laplace's law, Neumann's law of induction, the conditions of electric oscillation and of electric convection. Every phenomenon in electric- ity was deducible from it compatibly with the doctrine of the con- servation of energy. Clausius (1878), moreover, by a logical effort of extraordinary vigor, established a similar law. Moreover, the early confirmation of Maxwell's theory in terms of the dielectric constant and refractive index of the medium was complex and partial. Row- land's (1876, 1889) famous experiment of electric convection, which has recently been repeatedly verified by Pender and Cremieu and others, though deduced from Maxwell's theory, is not incompatible with Weber's view. Again the ratio between the electrostatic and the electromagnetic system of units, repeatedly determined from the early measurement of Maxwell (1868) to the recent elaborate determinations of Abraham (1892) and Margaret Maltby (1897), with an ever closer approach to the velocity of light, was at its incep- tion one of the great original feats of measurement of Weber himself associated with Kohlrausch (1856). The older theories, however, are based on the so-called action at a distance or on the instantane- ous transmission of electromagnetic force. Maxwell's equations, while equally universal with the preceding, predicate not merely a finite time of transmission, but transmission at the rate of the velocity of light. The triumph of this prediction in the work of Hertz has left no further room for reasonable discrimination. As a consequence of the resulting enthusiasm, perhaps, there has been but little reference in recent years to the great investigation of Helmholtz (1870, 1874), which includes Maxwell's equations as a special case; nor to his later deduction (1886, 1893) of Hertz's equations from the principle of least action. Nevertheless, Helm- holtz's electromagnetic potential is deduced rigorously from funda- mental principles, and contains, as Duhem (1901) showed, the electro- magnetic theory of light. Maxwell's own vortex theory of physical lines of force (1861, 1862) probably suggested his equations. In recent years, however, the efforts to deduce them directly from apparently simpler proper- ties of a continuous medium, as for instance from its ideal elastics, or again from a specialized ether, have not been infrequent. Kelvin (1890), with his quasi-rigid ether, Boltzmann (1893), Sommerfeld (1892), and others have worked efficiently in this direction. On the other hand, J. J. Thomson (1891, et seq.), with remarkable intuition, affirms the concrete physical existence of Faraday tubes of force, and from this hypothesis reaches many of his brilliant predictions on the nature of matter. As a final commentary on all these divers interpretations, the important dictum of Poincar^ should not be forgotten: If, says Poincar^, compatibly with the principle of the conservation of energy 64 PHYSICS and of least action, any single ether mechanism is possible, there must at the same time be an infinity of others. The Electronic Theory The splendid triumph of the electronic theory is of quite recent date, although Davy discovered the electric arc in 1821, and although many experiments were made on the conduction of gases by Faraday (1838), Reiss, Gassiot (1858, et seq.), and others. The marvelous progress which the subject has made begins with the observations of the properties of the cathode ray by Pliicker and Hittorf (1868), brilliantly substantiated and extended later by Crookes (1879). Hertz (1892) and more specifically Lenard (1894) observed the pass- age of the cathode rays into the atmosphere. Perrin (1895) showed them to be negatively charged. Rontgen (1895) shattered them against a solid obstacle, generating the X-ray, Goldstein (1886) discovered the anodal rays. Schuster's (1890) original determination of the charge carried by the ion per gram was soon followed by others utilizing both the elec- trostatic and the magnetic deviation of the cathode torrent, and by Lorentz (1895) using the Zeeman effect. J. J. Thomson (1898) suc- ceeded in measuring the charge per corpuscle and its mass, and the velocities following Thomson (1897) and Wiechert (1899), are known under most varied conditions. But all this rapid advance, remarkable in itself, became startlingly so when viewed correlatively with the new phenomena of radio- activity, discovered by Becquerel (1896), wonderfully developed by M. and Madame Curie (1898, et seq.), by J. J. Thomson and his pupils, particularly by Rutherford (1899, et seq.). From the Curies came radium (1898) and the thermal effect of radioactivity (1903), from Thomson much of the philosophical prevision which revealed the lines of simplicity and order in a bewildering chaos of facts, and from Rutherford the brilliant demonstration of atomic disintegra- tion (1903) which has become the immediate trust of the twentieth century. Even if the ultimate significance of such profound re- searches as Larmor's (1891) Ether and Matter cannot yet be dis- cerned, the evidences of the transmutation of matter are assured, and it is with these that the century will immediately have to reckon. The physical manifestations accompanying the breakdown of atomic structure, astoundingly varied as these prove to be, assume fundamental importance when it appears that the ultimate issue involved is nothing less than a complete reconstruction of dynamics on an electromagnetic basis. It is now confidently affirmed that the mass of the electron is wholly of the nature of electromagnetic inertia, and hence, as Abraham (1902), utilizing Kaufmann's data PROGRESS IN NINETEENTH CENTURY 65 (1902) on the increase of electromagnetic mass with the velocity of the corpuscle, has shown, the Lagrangian equations of motion may be recast in an electromagnetic form. This profound question has been approached independently by two lines of argument, one beginning with Heaviside (1889), who seems to have been the first to compute the magnetic energy of the electron, J. J. Thomson (1891, 1893), Morton (1896), Searle (1896), Sutherland (1899); the other with H. A. Lorentz (1895), Wiechert (1898, 1899), Des Coudres (1900), Drude (1900), Poincare (1900), Kaufmann (1901), Abraham (1902). Not only does this new electronic tendency in physics give an accept- able account of heat, light, the X-ray, etc., but of the Lagrangian function and of Newton's laws. Thus it appears, even in the present necessarily superficial sum- mary of the progress of physics within one hundred years, that, curi- ously enough, just as the nineteenth century began with dynamics and closed with electricity, so the twentieth century begins anew with dynamics, to reach a goal the magnitude of which the human mind can only await with awe. If no Lagrange stands toweringly at the threshold of the era now fully begun, superior workmen abound in continually increasing numbers, endowed with insight, adroit- ness, audacity, and resources, in a way far transcending the early visions of the wonderful century which has just closed. SECTION A — PHYSICS OF MATTER SECTION A — PHYSICS OF MATTER {Hall 11, September 23, 10 a. m.) Chairman: Professor Samuel W. Stratton, Director of the National Bureau of Standards, Washington. Speakers: Professor Arthur L. Kimball, Amherst College. Professor Francis E. Nipher, Washington University. Secretary: Professor R. A. Millikan, University of Chicago. THE RELATIONS OF THE SCIENCE OF PHYSICS OF MATTER TO OTHER BRANCHES OF LEARNING BY ARTHUR LALANNE KIMBALL [Arthur Lalanne Eamball. Professor of Physics, Amherst College, b. October 16, 1856, Succasunna Plains, N. J. A.B. Princeton, 1881; Ph.D. Johns Hopkins University, 1884; post-graduate, Johns Hopkins University; Associate Pro- fessor of Physics, Johns Hopkins University, 1888-91; FeUow of American Association for the Advancement of Science, and American Physical Society. Author of Physical Properties of Gases.] It is evident at the outset that it is quite out of the question, in the time at our disposal, to discuss adequately the relation of the physics of matter to the other sciences, even if the speaker were endowed with the requisite omniscience. For matter is the very stuff in which the phenomena of all the natural sciences are manifested, the chemist finds himself con- fronted at every turn with physical relations which must be taken into account, the astronomer finds his greatest triumph in exhibit- ing the universe that he explores with the telescope as an harmonious illustration of physical principles, the geologist also hardly faces a single question that does not demand the aid of physics or chemistry in its solution, and even in the biological sciences the laws of matter still condition the phenomena of life. Perhaps a brief consideration of the interrelations of these sciences may aid us in a clearer perception of their dependence on the physics of matter. There are three sciences that may be said to be especially funda- mental, in that they deal with the elements of the universe of phe- nomena. These are physics, which, if we define it somewhat narrowly, deals with all the phenomena that can be exhibited by and through the means of any one kind of matter, as well as all interactions between different kinds of matter in which each preserves its separate iden- tity; chemistry, which has for its province those special phenomena in which one kind of matter is broken up into two or more kinds, 70 PHYSICS OF MATTER or in which the interactions between different kinds of matter result in the formation of a substance different from either of the constitu- ents; and that phase of biology which is concerned with the study of the living cell and of the simplest conditions under which matter exhibits the phenomena of life. It might have been said that physics deals with those phenomena exhibited by and through matter when molecular groupings of atoms are not disturbed, while chemistry deals with the phenomena of the formation and breaking-up of the molecules. But such a statement is based upon a theory of the structure of matter which in itself calls for explanation, and therefore the previous statement is preferred as being more general and avoiding the theoretical assumptions that are involved in those just given. If it is asked what constitutes a particular kind of matter, why, for instance, water-vapor is said to be the same substance as water in the liquid form, it may be said that it is because one can be wholly transformed into the other, each is homogeneous, and remains un- changed in its properties during the transforming, and the trans- formation is unique. Professor Ostwald has recently given a most interesting statement of the criterion by which a substance or chemical individual may be recognized without the need of any atomic hypothesis. We may summarize his presentation thus: Where two substances are com- bined as in solution, there will be one and only one proportion be- tween the quantities of the substances for which, on change of state, such as evaporation or crystallization, the vapor or crystals will have the same composition as the remaining substance, while with a greater or less proportion of either ingredient, there will be a change of concentration with change of state. When such a combination retains this property under widely different conditions of tempera- ture and pressure, it is known as a chemical individual or definite compound. If under no circumstances it can be broken up into two phases which differ in constitution, it is called an element. Ostwald remarks, "The possibility of being changed from one phase into another without variation of the properties of the residue and of the new phase is indeed the most characteristic property of a substance or chemical individual, and all our methods of testing the purity of a substance, or of preparing a pure one, can be reduced to this one property." But returning to our classification, it is seen that physics, chemis- try, and biology are the three fundamental natural sciences, each having as its primary object not the mere arrangement and classi- fication of phenomena, but the formation of such a concept of matter in those relations with which it deals, that the varied facts of obser- vation appear as natural and inevitable consequences. RELATIONS TO OTHER SCIENCES 71 The other sciences are in a certain sense secondary to the three that have been mentioned. Each is concerned with the investigation of some system that is built up out of matter, and involves the same fundamental relations which are the objects of study for the primary sciences, but the secondary science finds its interest not in the ma- terials of which the structure is made, but in the study of the result- ing structure itself. Thus astronomy seeks to describe and make out the past history and future development of the universe of sun and star and planet. The sciences of the earth are concerned with the history of the devel- opment of our planet, with the present phenomena of its interior, of its crust, of its surface, and of its atmosphere, while the secondary biological sciences have as their aim to trace the relations of the various forms of life and to follow out the developments of each. But while each secondary science thus has an aim of its own quite distinct from that of the primary sciences, nevertheless it must be controlled and to some extent guided by the sciences of matter. Thus in almost every science chemical phenomena play a part which must be reckoned with, while physics, dealing as it does with the most universal phenomena of matter, underlies and conditions all the sciences without exception. Therefore it is to be expected that with the development of physics both in discovery and theory there should be a greater or less reaction on the other sciences, for in so far as they depend for their development on the laws of matter they are dependent on the labors of the physicist. We might therefore expect to find in every science, if we only knew it well enough, a response to every considerable advance in physics. For the advances in a science result not from discovery alone, but from new points of view taken by those who are thinking on its problems; and the ideas of physics, bearing as they may be said to do on the raw material of the other sciences, must in a preeminent degree influence the thinking of workers in all fields. It deserves to be emphasized that every science is an intellectual structure. Only as this is conceded will science be yielded the lofty and dignified position which is its due. Experiments may be multi- plied, facts and data may be accumulated in bewildering numbers, but there is no science without the clear intellectual vision that sees the parts in their dependencies and relations one to another and catches glimpses of the larger unities that run through all. They are mistaken who think the true scientist less an idealist than is the artist or student of literature, or who think the path of experiment mere drudgery in the accumulation of insignificant facts. The investigator lives in a world of ideas, and in every step of a dif- ficult inquiry he has the buoyant consciousness that he is getting a deeper, truer insight into his science. 72 PHYSICS OF MATTER This intellectual character of scientific research is well illustrated in the enthusiasm which marked the news of Hertz's discovery of electromagnetic waves. The facts observed might easily have been thought to be in themselves insignificant : a slight spark observed between the ends of a bent wire near a discharging electrified system. There was no thought of a practical application, and yet a wave of almost unprecedented excitement spread among physicists the world over. Nor was it alone admiration for the skill, the insight and grasp of the great experimenter that won the victory, though this had its effect. It was mainly an exultant enthusiasm over the triumph of an idea, the unification of science in the confirmation of Maxwell's great theory. It is clear, then, that physics may react on the other sciences in a variety of ways, in its methods and appliances, in its discoveries, and in its ideas and generalizations; and it is evident, therefore, that we must limit ourselves to a brief consideration of certain phases of the subject. I have, therefore, chosen to present very briefly some con- siderations relative to theories of matter, for here physics and chem- istry come into the closest contact; also to touch upon some other relations of chemistry and geology to physics, that are of particular interest at this present time. The fundamental problem in the physics of matter is the nature of matter itself. Of course we recognize at the outset the limitations that bound our attempts at a solution. We may hope to reach event- ually some conclusion as to the structure of matter, whether homo- geneous or molecular or grained, also as to the relative motions of the parts of the molecule and the law of variation of force between them with the distance. But if we seek to go farther and explain the forces acting in and between molecules in terms of what appear to be more simple and general laws, it seems inevitable that a medium must be assumed, the properties of which will depend on what is assumed as a primary postulate. If we accept, as is usually done, the postulate that forces in their last analysis can only be explained when referred to pressures exerted between contiguous portions of some underlying medium, it seems probable that a theory must be adopted something like the vortex atom theory of Lord Kelvin, with its continuous, incompressible, perfectly fluid medium in which vortically moving portions constitute the atoms, or Osborne Rey- nolds's theory of space as filled with fine hard spherical grains, in which, regions with nonconformity in arrangement, are the atoms of ordinary matter. Though it must be said that the assumed hard- ness of the ultimate spherules in the latter theory is a property which in itself needs explanation. Perhaps, however, in laying down the postulate mentioned above we are pushing too far inferences from our superficial experience. RELATIONS TO OTHER SCIENCES 73 The idea that force must be a pressure between contiguous portion^ of substance is derived directly from the notion of the impenetra- bility of matter. This is why the incompressible medium of Lord Kelvin's theory seems so simple a conception; it is the naked em- bodiment of the idea of impenetrability associated with inertia. It is entirely natural that such ideas as impenetrability and inertia, borne in upon us as they are by our experience of matter in bulk, should affect our theorizing, but it should never be forgotten that as fundamental postulates they have no more authority than any others that might be assumed that will coordinate the same facts of observation. But passing from this more speculative region we find a pretty general agreement on the rough outlines of the structure of matter. With one notable exception most physicists and chemists agree in the idea that matter is atomic or molecular in structure, and that these molecules are in a state of more or less energetic translatory motion, bounding and rebounding from each other. This seems to be the mechanical hypothesis which coordinates the largest number of facts. A portion of matter is conceived as in a condition of equilibrium under three pressures: the cohesive pressure due to mutual attrac- tion between all molecules which are not farther apart than 50 to 100 millionths of a millimeter; the external pressure, which also acts to cause contraction; and the internal pressure, which balances the two former, and is due to a repulsive force called the force of impact, which is usually supposed to be exerted only between contiguous molecules. In the solid and liquid states the cohesive pressure is usually very great compared with the external pressure. In case of gases it nearly vanishes. The force between molecules is thus conceived as an attrac- tion which increases rapidly as they approach, until at a certain dis-- tance it is balanced by a repulsive force which, increasing still more rapidly, is the controlling force at all less distances. Lord Kelvin has recently followed out a study of equilibrium con- ditions in a group of atoms which are assumed to have no mutual influence until within a certain distance, then to attract each other with a force that increases as they approach still nearer, rising to a maximum and then diminishing, and finally becoming a repulsion when the atoms are very near. He remarks, "It is wonderful how much toward explaining the crystallography and elasticity of solids, and the thermo-elastic properties of solids, liquids, and gases, we find without assuming in the Boscovitchian law of force more than one transition from attraction to repulsion." The fundamental soundness of the conception of matter as having a grained structure of some sort seems to be established by the re- 74 PHYSICS OF MATTER markable degree of agreement in the estimates by various physicists of the size of these ultimate particles, meaning by that the smallest distance between their centres as they rebound from each other, especially when it is considered that these results have been reached from so many different points of view, and are based on such a variety of physical data. As to the structure of the atom itself a most remarkable theory has been recently developed. J. J. Thomson has marshaled the evi- dence in favor of the theory proposed by Larmor that matter has an electrical basis, and the theory has already been considerably devel- oped by Lorentz and others. There appears to be reason for believing that the corpuscles of the Kathode rays are simply moving charges of negative electricity, their whole apparent mass being due to their relation to the ether, in consequence of which there is a magnetic field around the moving charge having energy dependent on the square of its velocity. The corpuscle, therefore, effectively has mass in consequence of this reaction between it and the ether. The corpuscles are found always to carry the same charge, what- ever the nature of the gas in which the Kathode rays are formed, and whatever the nature of the electrodes — the charge being the same as that given up by the hydrogen atom in electrolysis, while the mass of the corpuscle is about one one-thousandth that of the hydrogen atom. The energy in the ether associated with the moving corpuscle depends on the size of the corpuscle as well as upon its charge, and it is found that to account for its apparent mass it must be of ex- tremely small size relative to ordinary atomic dimensions. Professor Thomson suggests that the primordial element of matter is such a negative electron combined with an equal positive charge, the latter being of nearly atomic dimension. An atom of hydrogen may be thought of as made up of nearly a thousand such pairs, the positive charge being distributed throughout a spherical region giving rise to a field of force within it in which the force on a nega- tive corpuscle will be towards the centre and proportional to its distance from the centre. In this field of force the corpuscles are conceived as describing closed orbits with great velocities. The internal energy of such an atom is conceived as enormous. In case of the atoms contained in a gram of hydrogen Thomson reckons about 10^^ ergs as the energy received from mutual attrac- tions in the formation of the atoms, an amount of work that would lift a hundred million kilograms, one thousand meters. The whole mass of the atom is supposed to be due to the negative electrons or corpuscles which it contains. As to the positive charge, although it determines the apparent size of the atom, it appears to make no contribution to its mass. RELATIONS TO OTHER SCIENCES 75 When such an atom impacts against another, the corpuscles in each will be disturbed by the jar in their orbital motion, and there will be superposed oscillations which will cause radiation of energy. If a corpuscle escapes from such an atom, the latter will be left with a positive charge, while if an additional free corpuscle is en- trapped, the atom will have a negative charge. The conditions of stability of motion of the corpuscles in the atom would thus deter- mine whether in case of electrolysis the substance would appear electro-positive or electro-negative. J. J. Thomson, Drude, and others have discussed the electric conduction of metals from the standpoint of this theory. Drude states that in non-conductors only bound electrons are present, that is, positive and negative in combination; and that it is these that determine the dielectric constant of the medium and consequently its index of refraction and optical dispersion; while Langevin ex- plains magnetism and diamagnetism. Thus we have a theory already surprisingly developed which appears to be applicable to explain many of the properties of matter, though it is not clear that it can give an explanation of cohesion and gravitation. A theory of matter, to be accepted as final, must offer some explanation of the relation between the various elements. Many thinkers have been led to look for some primordial element from which the others are derived, influenced on the one hand by the present evolutionary ideas of biology, and on the other by com- parison of spectra and by the remarkable tendency towards whole numbers observed in the atomic weights of the elements which Strutt has discussed from the standpoint of the theory of probabili- ties. Professor Thomson has accordingly shown how atoms of matter containing great numbers of corpuscles may have been evolved from a simpler primordial form containing fewer corpuscles. But though he has made clear how the hydrogen atom with its thousand cor- puscles might be the surviving atom having the least number of corpuscles, it is not so clear why there might not be atoms having any number of corpuscles greater than that of hydrogen, within certain limits; why none should be found between hydrogen and helium for example. Some kind of natural selection seems to be needed to explain why some atoms having special numbers of cor- puscles survive while intermediate ones are eliminated, though prob- ably the answer is to be sought in the conditions of stability of the motions of the corpuscles. It is an interesting question what would be the effect of change of temperature of the substance on the motions of the corpuscles in this theory. If the corpuscles in the atom were very numerous, all moving in the same orbit at equal distances apart, they would produce almost the effect of a circular current of electricity, — a steady 76 PHYSICS OF MATTER magnetic field and no radiation; and it seems probable that in the actual case the radiation of internal energy is extremely small, and the total internal energy may be supposed to be so enormous com- pared with the energy of translation of the atom due to temperature that we may expect no appreciable change in the radiation of internal energy of the atom, whatever the temperature may be. That component of the vibration of a corpuscle which is radial within the atom, and is set up by the impact of one atom against another, seems to furnish the great mass of radiated energy. This radiation must also react on the motion of the atom as a whole, taking away from the translatory energy of the atom. The question how the Boltzmann law of partition of energy be- tween the various degrees of freedom will apply to molecules made up of such atoms as are here conceived is an interesting and im- portant one. Is it possible that the cloud, as Lord Kelvin calls it, resting on the kinetic theory of gases may be dissipated by the new theory? This theory of the atom seems also to explain the possibility of the production of spectra of great complexity. It is to be hoped that Balmer's formula and Rydberg's laws of the grouping of lines in spectra may be shown to be the natural outcome of the system of vibration possible in such an atom. We are startled at first by the very audacity of this theory, seeming as it does to upset the old point of view, and seek the explanation of matter and its laws in terms of the properties of ether and elec- tricity, instead of trying to unravel the secrets of electricity and ether in terms of matter and motion. Only a few years ago it was thought that the electromagnetic theory of light must be rationalized by giving a mechanical explan- ation of the various phenomena of the ether, or by showing at least that such an explanation was possible. Witness Maxwell's won- derfully ingenious mechanical model illustrating the phenomena of magnetism, induced currents, and the propagation of electro- magnetic waves. But is it necessary to regard the mechanical explanation as the only sound one ? If electricity and ether are fundamental entities underlying all matter and material phenomena, is it not more logical to find a basis for the mechanical laws in some more fundamental laws of ether and electricity which must be accepted as the primary postulates? In all this development of the atomic view of matter, chemistry and physics have gone hand in hand. The atomic theory of Dalton has been the basis on which both sciences have worked. Avogadro's law for gases has been reached not only by chemical evidence, but has been raised to the rank of a mechanical deduction from the kinetic RELATIONS TO OTHER SCIENCES 77 theory. The significance of the arrangement of atoms in the molecule in determining chemical reaction was emphasized and developed by Kekule, but it was not until 1874 that the space diagrams of mole- cules of van't Hoff and Le Bel marked a full appreciation of the possibilities of structure in explaining the differences of isomeric forms. All of these physical and chemical developments of the atomic theory have been in accordance with a general method of scientific procedure which may be called the method of mechanical models. According to this method, an attempt is made to conceive a certain mechanism by which the various phenomena sought to be explained may be imagined to be brought about. Such a theory of atoms, for example, if perfect, would exhibit all the properties of atoms as direct consequences of the assumed struc- ture. This cannot, however, be taken as proof that the assumption is real, though for the purpose of our thinking such a theory would have all the value of reality, since all consequences deduced from it would conform to the facts of observation. And this suggests wherein the great value of such a theory lies, not alone in the large number of observations which it correlates and brings under a few general principles, but in that it suggests the application of experiments and tests of its sufficiency, thereby enlarging and making more pre- cise our knowledge. Perhaps the most remarkable instance of the application of this method was Maxwell's development of a mechanical model to illus- trate the reactions in the electromagnetic field. Working from this model he developed the equations of the field, which later he deduced in a more general way. And Hertz speaking of them says, "We can- not study this wonderful theory without at times feeling as if an independent life and a reason of its own dwelt in these mathematical formulae; as if they were wiser than we were, wiser even than their discoverer; as if they gave out more than had been put into them." On which Boltzmann's comment is, "I should like to add to these words of Hertz only this, that Maxwell's formulae are simple conse- quences from his mechanical models; and Hertz's enthusiastic praise is due in the first place, not to Maxwell's analysis, but to his acute penetration in the discovery of mechanical analogies." Such an example well illustrates the importance of the method. But of recent years, the influence of quite a different method has been strongly marked in chemical research. A method in which certain general laws are established and then applied to particular cases by a process of mathematical reasoning, deducing conclusions quite independently of the particular details of the operation by which they are brought about. This method is well illustrated in Professor J. J. Thomson's work on the application of dynamics to 78 PHYSICS OF MATTER problems in physics and chemistry, and in the deductions based on the laws of thermodynamics that have marked the development of the new physical chemistry. It is under the influence of this method that Professor Ostwald has been led to propose a theory of matter which does not recognize the necessity of any atomic structure whatever. In a recent address, he says, "It is possible to deduce from the principles of chemical dynamics all the stoichiometrical laws; the law of constant proportion, the law of multiple proportion, and the law of combining weights." And he continues, "You all know that up to this time it has only been possible to deduce these laws by the help of the atomic hypothesis. Chemical dynamics has, therefore, made the atomic hypothesis un- necessary for this purpose and has put the theory of the stoichio- metrical laws on more secure ground than that furnished by a mere hypothesis." And then farther on he continues, " What we call matter is only a complex of energies which we find together in the same place. We are still perfectly free if we like to suppose either that the energy fills the space homogeneously, or in a periodic or grained way; the latter assumption would be a substitute for the atomic hypothesis." And then he adds, "Evidently there exists a great number of facts — and I count. the chemical facts among them — which can be com- pletely described by a homogeneous or non-periodic distribution of energy in space. Whether there exist facts which cannot be de- Scribed without the periodic assumption, I dare not decide for want of knowledge; only I am bound to say that I know of none." It is interesting and remarkable that this challenge to the atomic theories of matter should come from the side of chemistry, the very science for which the atomic theory of Dalton was conceived. Espe- cially is it remarkable, in view of the measure of success that has attended the explanation of the differences between such forms as right and left rotating tartaric acids on the basis of molecular struc- ture. And it is difficult to see how it is possible to give any satisfac- tory explanation of these differences, simply on the basis of the laws of energetics applied to a conception of matter as homogeneous. With reference to the view that " What we call matter is only a com- plex of energies which we find together in the same place," it may be said that we recognize different forms of energy only in association with matter or ether; as heat, light, chemical energy, kinetical energy, etc. Hence the term, "a complex of energies," can only mean the total energy in a given region, unless we recognize some vehicle, as matter or ether, in which the special manifestations of energy may exist. This seems to be admitted tacitly by Ostwald himself, for a little farther on he says, " The reason why it is possible to isolate a substance from a solution is that the available energy of the sub- stance is at a minimum." He thus distinguishes between the avail- RELATIONS TO OTHER SCIENCES 79 able and the total energy of a portion of matter. But this discrimi- nation can have no meaning unless it is granted that a portion of the energy of a substance is not available. If we ask why it is not avail- able, the answer may be that when a substance passes from one state to another at constant temperature the work that it can do is less than its total intrinsic energy as a consequence of the laws of thermodynamics. The case must therefore be one to which the second law of thermodynamics can apply. That is, it must involve flow of energy by some such process as heat conduction. It might perhaps be successfully argued that the very existence of such a process implies grained structure of some sort to which a statistical law may apply. However this may be, it is certainly diffi- cult to conceive of energy as existing apart from some vehicle, matter or ether or both as you will ; but to conceive of this sublimated energy as in part available and in part non-available is surely quite beyond attainment. It is with great diffidence that we dissent from the expressed views of one who has done so much for the advance of physical chemistry, and our excuse for entering on the discussion must be that as the latest utterance with regard to matter, and coming from one who has won the right to have his views given a respectful consideration, it seemed more fitting to present this brief and imperfect discussion than to pass them by wdthout comment. One of the most important reactions of physics upon the other sciences has resulted from the extension of the thermodynamic laws to chemical problems which has marked the new physical chemistry, a science which has sprung into being within the last seventeen years and has already, under the leadership of van't Hoff,Ostwald, Arrhe- nius, and Nernst, attained a surprising development, and is making itself felt in many other lines of scientific activity, notably in electro- chemistry, geology, and biology. The starting-point in this devel- opment was the idea conceived by van't Hoff that Avogadro's law might be so extended as to apply to the case of substances in solu- tion. Just as a gas expands and fills the containing vessel exerting a pressure against its walls, so a salt dissolved in a liquid diffuses uniformly throughout the liquid and exerts a pressure within the liquid tending to expand it. This osmotic pressure, so called, had been measured in certain cases by Pfeffer and de Vries, but it re- mained for van 't Hoff to show that, as in case of a gas, the pressure was proportional to the absolute temperature and to the number of molecules of the dissolved substance contained in unit volume. As has so often happened before, the study of the apparent ex- ceptions to the rule led to a second great advance, the theory of electrolytic dissociation proposed by Arrhenius, to account for the observation that in solutions of electrolytes the osmotic pressure was 80 PHYSICS OF MATTER greater than that reckoned on the basis of the number of molecules present, but was to be explained by their dissociation into ions; thus reaching the same conclusion which Clausius had announced in 1857, but affording a method by which the precise amount of the dissociation might be measured. Additional evidence in favor of this theory was afforded by the studies of the electrical conductivity of dilute solutions of electrolytes made by Kohlrausch. All this was accompanied by an increasing realization of the important relations that might be established by an application of the laws of thermodynamics to chemical problems. Thus van 't Hoff showed in his paper of 1887 that the depression of the freezing-point of a liquid due to a substance in solution depended directly on the osmotic pressure and could be used to measure it; a result which had already been experimentally reached by Raoul. In this field, Professor J. Willard Gibbs, in whose recent death the world of science has lost a most profound thinker, was a pioneer. His most important contributions to the subject were in two ex- traordinary papers, On the Equilibrium of Heterogeneous Substances. The first of these related to chemical phenomena, while the second was concerned especially with capillarity and electricity. To quote from a recent writer, "The most essential feature of Gibbs 's discoveries consisted in the extension of the notion of thermo- dynamical potential to mixtures consisting of a number of com- ponents, and the establishment of the properties that the potential is a linear function of certain quantities which Gibbs has called the potentials of the components, and that where the same component is present in different phases, which remain in equilibrium with each other, its potential is the same in all the phases, besides which the temperatures and pressures are equal. The importance of these re- sults was not realized for a considerable time. It was difficult for the experimentalist to appreciate a memoir in which the treatment is highly mathematical and theoretical, and in which but little at- tempt is made to reduce conclusions to the language of the chemist ; moreover it is not unnatural to find the pioneer dwelling at consid- erable length on comparatively infertile regions of the newly explored territory, while fields that were to prove the most productive were dismissed very briefly." "It was largely due to Professor van der Waals that two new and important fundamental laws were discovered in Gibbs 's paper, namely, the phase rule and the law of critical states." The phase rule has been the guiding principle in some most import- ant studies of chemical equilibrium. It furnishes a clue by which the polymorphism of such substances as sulphur and tin may be scien- tifically investigated and the conditions of equilibrium between the different polymorphic forms determined. The studies of the case RELATIONS TO OTHER SCIENCES 81 of ferric chloride by Roozeboom, and of the crystallization out of sea-water of the contained salts by van't Hoff and Meyerhoffer indicates the great value of the phase rule in bringing scientific order out of the complicated relations of the various components and phases involved. Speaking of this department of physical chemistry, van 't Hoff re- marked, "Since the study of chemical equilibrium has been related to thermodynamics, and so has steadily gained a broader and safer foundation, it has come into the foreground of the chemical system, and seems more and more to belong there." And Ostwald says in answer to the question, " What are the most important achievements of the chemistry of our day? I do not hesitate to answer: chemical dynamics, or the theory of the progress of chemical reaction, and the theory of chemical equilibrium." These statements, coming from two masters in the field, are most significant of the importance of the introduction of these ideas into chemistry. The conceptions and methods of physical chemistry have also been most strongly felt in the field of electrochemical theory. To the question what is the nature of electrolysis, Faraday and Hittorf and Clausius had each contributed important elements of the final answer, then came Arrhenius with the theory of electrolytic dissocia- tion, which has proved so fruitful of consequences, not only in the domain of chemistry, but also in biology and in physics. One of the most interesting scientific questions connected with electrochemistry is the relation between electromotive force and electrolytic separation, and the development of the theory of the voltaic cell. The question of the seat of electromotive force in the cell was for many years the very storm-centre of physical discussion; but from the standpoint of electrolytic dissociation Nernst has sup- plemented the work of Helmholtz and Gibbs, and out of all has come a theory which, while not perfect, seems to be in its main features on the solid foundation of the conservation of energy and the laws of thermodynamics. Another important service for which the world of science is indebted to physics is the determination of the absolute zero of temperature in terms of degrees of the ordinary centigrade scale. About a century ago, Dalton, in his new chemical philosophy, adopts — 3000° C. as the probable zero of temperature. While Lavoisier and Laplace make various estimates of the zero ranging from 1500 to 3000 degrees below the freezing-point of water. But when the doctrine of energy became firmly established together with the kinetic theory of gases, it was natural that the condition of a gas in which the particles had no energy of motion, and hence no pressure, should have been taken as indicating the absolute zero. But it was Clausius and Lord Kelvin who 82 PHYSICS OF MATTER based firmly on the laws of thermodynamics the absolute scale of temperature, as we know it to-day. The absolute zero of temperature has to the physicist all the fasci- nation that the North Pole has to Arctic explorers, and is probably even more difficult to attain. Yet steady progress has been made in conquering the difficult territory that lies toward this goal. The experimental efforts to liquefy the more refractory gases showed that far lower temperatures than had previously been reached must be employed; and step by step, following the suggestions of thermo- dynamics, the means of attaining low temperatures have been im- proved, at first cooling by adiabatic expansion of more compressible gases, then aided by the sudden expansion of the gas itself which had been compressed and cooled, and then by a continuous self- intensive action, in which the cold produced by the expansion of one portion of the compressed gas was made use of to cool the still unex- panded gas as it approached the point of expansion. The mere record of the temperatures reached marks a series of triumphs of ingenuity and perseverance. Thus Faraday, in 1845, reached a temperature of — 110 by the use of solid carbon dioxide and ether evaporated at low pressure. Pictet in 1877 reached — 140, and liquefied oxygen under pressure. Olszewski in 1885 obtained a temperature of — 225 by the evaporation of a mass of solid nitrogen. In 1898 Dewar obtained liquid hydrogen boiling at — 252, or only 20.5 above the absolute zero, and later by boiling at reduced pres- sures he was able to obtain —259.5 or 13.5 degrees absolute scale, at which point hydrogen is frozen solid. The attainment of these low temperatures has not alone made possible investigations of the greatest interest to the physicist, such as studies of the magnetic and electric properties of bodies as they approach the absolute zero, but has enabled the effect of extreme cold on chemical actions to be determined, and has led to the inter- esting conclusion that "The great majority of chemical interactions are entirely suspended." Though it has been shown by Dewar and Moissan that in case of solid hydrogen and liquid fluorine, violent reaction still takes place even at that small remove from the absolute zero. A very interesting field has also been opened to biological research, in the effect of extreme cold on the vitality of seeds and micro- organisms. It was found, for example, that barley, pea, and mustard seeds steeped for six hours in liquid hydrogen and thus kept at a tem- perature of minus 252 degrees, showed no loss of vitality. So, also, certain micro-organisms, among others the bacilli of typhoid fever, Asiatic cholera, and diphtheria, were kept by MacFadyen for seven days at the temperature of liquid air without appreciable loss of vitality. It has been suggested by Professor Travers that, "It is RELATIONS TO OTHER SCIENCES 83 quite possible that if a living organism were cooled only to temper- atures at which physical changes, such as crystallization, take place with reasonable velocity, the process would be fatal, whereas, if they were cooled to the temperature of liquid air no such change would take place within finite time, and the organism would survive." Also the study of the various combinations of carbon and iron that may exist in steel, and the conditions of equilibrium that exist between them has proved a most important investigation in the field of what van 't Hoff calls solid solutions. Geology, dealing as it does with the greatest variety of physical processes, such as changes of state, fusion, crystallization, solution, conduction of heat, radiation, with complications depending on variations of pressure and temperature, presents many problems for the solution of which the resources of modern physics must be taxed. The fusing-points of the different chief minerals of the earth's crust, the effect of great pressure on their fusing-points and modes of crystallization, the crystallization of the various elementary min- erals out of a fused magma also studied at dififerent pressures, the effect of pressure not only on fusing-points, but on the viscosity and rigidity of minerals at high temperature, the heat conductivities of the various substances making the bulk of the earth's crust, all these are questions that must be thoroughly studied to enable the geologist to determine the probable condition both of temperature and pres- sure which prevailed during the formation of a given rock mass, and to throw light on the great problem of geology, the age of the earth. To this latter question, physics has already given a tentative answer. Lord Kelvin's discussion, based on the assumption of the earth as a mass cooling from a uniform high temperature, points to a period of between twenty and one hundred million years, within which geologic changes in the crust of the earth must have occurred; while Helmholtz and Kelvin's deduction of the time during which solar radiation can have been of such an intensity that life conditions on the earth were possible gives about twenty million years as the limit. But later investigations giving new data as to the properties of the materials of the earth's crust, as to the laws of variation of radi- ation with temperature, and as to absorption and radiation by the solar and earth's atmospheres, will all contribute to modify and make more precise these methods. Already some progress in this direction has been made. A few years ago, Clarence King gave a most inter- esting and ingenious rediscussion of Kelvin's cooling of the earth method, making use of the determinations made by Barus of the fusing-points of diabase at different pressures, and gives as the most probable result of the method the period of twenty-four million 84 PHYSICS OF MATTER years, a period in close agreement with that found by Helmholtz and Kelvin from the radiation of the sun. It should be remarked, however, that in discussing the state of things in the earth's interior, where the pressures so far transcend anything that can be approached in the laboratory, such constants as melting-points should be looked on with great suspicion. Assuming Laplace's law of distribution of density in the earth, the pressure at a depth of one two-hundredth of the earth's radius is 8600 atmospheres, while at the centre of the earth it becomes more than three million atmospheres. Now the largest pressures that have been used in high temperature experiments are less than three thou- sand atmospheres. It is evident, then, that any conclusion as to melting-points from laboratory data must be violent exterpolations, if deduced for the enormous pressures at depths greater than one one-hundredth of a radius within the earth, where the pressure will be over 17,000 atmospheres. But not only is there necessarily great uncertainty as to the fusing-points at these great pressures, but it seems probable that such a process as fusion marked by sudden increase in liquidity can hardly take place at all. In the phenomenon of fusion, the equilibrium of a substance may be regarded as conditioned by the external pressure, the cohesive pressure, and the internal pressure due to the translatory kinetic energy of the molecules, which may be called the kinetic pressure. In a state of equilibrium, the external pressure plus the cohesive pressure must equal the kinetic pressure, the last tending to produce expansion, while the two former act to cause contraction. At ordinary atmospheric pressures in the liquid and solid state, the cohesive pressure is enormously greater than the external pressure. In water at ordinary temperatures it is estimated about 6500 atmospheres, while in a solid such as steel it may have a value of perhaps 18,000 atmospheres. And not only is this cohesive force great relatively to the external pressure, but it decreases with great rapidity as the substance expands. Under these conditions it is easy to see that a slight rise in temperature with consequent expansion and weakening of the cohesive pressure while the kinetic pressure is increased may bring the substance to a point of trans- ition, a melting-point or boiling-point where great changes occur within narrow limits of temperature. But if we conceive the external pressure to be so great that the cohesive pressure is relatively insignificant, then we should not expect to find any sharply marked changes of state for small changes of temperature or pressure. To make the case definite assume a temperature of 1000 degrees absolute scale, and a pressure of 1,000,000 atmospheres, and suppose the cohesive pressure is 10,000 atmospheres. Under these circum- RELATIONS TO OTHER SCIENCES 85 stances a rise in temperature of ten degrees or a one per cent increase in temperature may be expected to produce a one per cent increase in the kinetic pressure at the original volume; but as the external pressure is constant and the cohesion is insignificant, we may expect a one per cent increase in the volume in which the molecular motions take place or an increase in the mean distance between molecules of one third of one per cent. Such an expansion will be accompanied by slightly lessened cohesive force, less rigidity, and less viscosity, probably; but nothing like a sudden change of state is suggested. The fact that at pressures greater than the critical pressures there can be observed no sharp transition from the liquid to the gaseous state with rise of temperature is quite in accord with the above con- siderations, and it seems probable that in case of solids under great pressure nothing like melting will be observed, but rather a gradual loss of rigidity or transition to great viscosity, and that the viscosity will decrease steadily with rise in temperature. But a new aspect is now given to the problem of the age of the earth by the discovery of radioactivity and its attendant phe- nomena. The earth, instead of being thought of as a cooling body, is now conceived as having within itself a source of almost un- limited energy. Locked up in each atom is believed to be a store of energy so vast that the breaking down of comparatively few of them in the radioactive process will supply the kno'WTi outflow of heat from the earth. Rutherford has shown that the observed dissemination of radio- active substances in the earth's crust is probably sufficient to ac- count for the outflow of energy from its surface. Thus the method of estimating the age of the earth from the consideration of it as a cooling body, a method which until lately seemed to physicists to be based on essentially sound premises, and deserving of confidence because of its greater simplicity as compared with the methods by which geological and biological estimates are obtained, is now by the very progress of physics itself abandoned as unreliable. So also has the study of radioactivity thrown new light on the question of the maintenance of the sun's heat. It is now seen that possible atomic transformations accompanied by the liber- ation of the vast stores of energy locked up within the atoms of matter may permit an enormous extension of the time during which the sun may have been radiating with something like its present intensity. In conclusion it may be remarked that a new world is opened to the investigator by the discovery of radioactivity. The atoms of matter are no longer thought of as necessarily fixed and un- changeable. Besides the older problems of matter questions now arise as to evidences of atomic disintegration and change from 86 PHYSICS OF MATTER more complex to less complex forms, and also the possible develop- ment of more complex atoms from simpler ones. Already we begin to see the effect of these recent discoveries and ideas on other departments of science. The clue at last seems to have been found to those long-standing enigmas of nature, thunder- storms, the Aurora Borealis, the zodiacal light, and the tails of comets. But these achievements belong perhaps rather to the realm of the physics of the ether and of the electron, than to that of the physics of matter. PRESENT PROBLEMS IN THE PHYSICS OF MATTER BY FRANCIS EUGENE NIPHER [Francis Eugene Nipher, Professor of Physics, Washington University, St. Louis, Mo. b. December 10, 1847, Port Byron, N. Y. Phil.B. State University of Iowa, 1870; A.M. State University of Iowa, 1875; LL.D. Washington Uni- versity, 1905. Instructor in Physics and Chemistry, State University of Iowa, 1870-74; Professor of Physics, Washington University, 1874. Member of Academy of Science of St. Louis, American Physical Society; Fellow of Amer- ican Society for the Advancement of Science. Author of Theory of Magnetic Measurements; Introduction to Graphical Algebra; Electricity and Magnetism; and many scientific papers.] In dealing with the subject allotted to me by the officers of the Congress, I must say that I have not presumed to solve the problems which present themselves at this time, nor do I feel competent even to state many of them. But it is instructive, in a time like this, to attempt a general survey of some of the great questions of the day, with a view of noting their bearing upon the knowledge of the past. We are continually made to feel that all of our inquiries and results must be reexamined, and our conclusions broadened and modified by new phenomena. Charles Babbage, whose last published work was, if I mistake not, a review of the London Exposition of 1851, in the Ninth Bridge water Treatise, gave incidentally, by way of enforcing his thoughts, a review of his earlier work on calculating-machines. His work covered the simple case of a machine composed of wheels and levers, capable of computing the successive terms of any series. The simplest case is an arithmetical series, the differences between the successive terms being unity. This is the device which we now use in the street-cars for counting fares. He asserted the possibility of making a machine, capable of computing the terms of such a series, or of any other, continuing the operation for thousands of years; and pointed out that the machine may be so designed that it will then compute one single arbitrary term, having no relation to the series which had pre- ceded. It may then resume the former series, or it may begin com- puting a geometrical series, or a series of squares or cubes of the natural numbers. A scientific investigator, who is not permitted to see the mechanism, begins to observe and record the series of numbers which are being disclosed on the dials. He soon learns the mathe- matical law of the series. He observes the time-sequence of the suc- cessive terms, and computes the date when this order of things began. He then makes use of his knowledge of other machinery, and makes a working drawing of the hidden mechanism which produces these results. He verifies his work by years of subsequent observations. With what amazement does he finally behold that single arbitrary 88 PHYSICS OF MATTER term ! With what amazement does he then see the machine begin to compute the squares or the cubes of the numbers it had previously disclosed ! The date when that machine was created and set to work has been rudely called in question by the new and seemingly lawless behavior of which it appears to be capable. And yet the observer still feels that the principles of mechanism have not been shaken by this unlooked-for disclosure. He again begins his work, with broader conceptions of the plan of this machine. And his subsequent work is along precisely the same lines, and by the same methods as his previous work. It is in exactly this way that all scientific work has proceeded, and I wish to point out a few interesting cases of this kind. I find it impossible to do this without presenting the present aspect of these problems in connection with the work of the past. This plan gives a perspective which not only adds to the interest but to the clearness of the presentation. The nebular hypothesis was an attempt by Kant, Laplace, and Herschel to trace the evolution of the solar system from a glowing mass of incandescent vapor or gas. As the theory was considered and developed, an immense number of correlated phenomena were found to be in harmony with this hypothesis, and a few discordant phenomena were also found. The operation was, moreover, based on a few fundamental and well-established laws, governing the pre- sent condition of the system; such as gravitation, radiation of heat, etc. The case became more and more convincing, as the knowledge of the last century was applied. All of this caused the astronomers and physicists to find it very easy to give to the hypothesis their tacit assent. Later, Sir William Thomson, now Lord Kelvin, took up the ques- tion of underground temperature, and determined the limit in time since which the earth must have begun to solidify. He also assumed that the present order of things had come down to us from the past, and that the present order of things consisted in the radiation of heat from a cooling earth. The time-interval which Kelvin thus determined was in entire harmony with the nebular hypothesis, but the results were received with something like consternation by geologists, and those who had followed Darwin in the study of the evolution of organic life upon the earth. Afterwards Kelvin sought to show that the process of solidification might have required but a short interval of time, and the evolutionists have found that evolution goes on by steps or sudden changes rather than by a continuous succession of imperceptible increments. The geologists have never been reconciled to Kelvin's results, and their protests have of late seemed to be on the increase. Of late the PRESENT PROBLEMS 89 situation has changed in various ways. The discovery of radioactive matter in wide diffusion in the earth's crust has reopened the whole question of underground temperature as related to the age of the earth and its past history. Nevertheless, if the nebular theory in any form, or any similar theory, represents the process of evolution of the solar system, a large amount of heat due to gravitational contraction must have resulted, and must have been disposed of by radiation. During several years I have been giving attention to the condi- tions of evolution of a gaseous nebula. The equations of equilibrium for such a mass have been developed.^ A cosmical mass of gas was assumed, satisfying everywhere the Boyle-Gay-Lussac law, capable therefore of expanding, of being compressed, and of transmitting pressure, and having a centre towards which it gravitates. Such a mass of gas is a simple heat-engine. The piston face is any spherical concentric surface. The load on the piston is the weight of superposed layers, external to the piston face. The radially in- wardly directed pressure is exactly that required to balance the outward pressure of the inclosed mass. As radiation and contraction proceed, the load on the piston increases, in a perfectly definite way, due to increase in weight of each element of mass as it approaches the gravitating centre. Whatever may be the nature of the gas, as determined by the numerical value of the Boyle-Gay-Lussac con- stant, at some time in its history contraction will have proceeded until some fixed or definite mass shall have been compressed within a fixed volume of definite radius. The equations show that the pressure at the surface of this mass, that is to say, the load on the piston, will then be entirely independent of the nature of the gas. The difference between gases will only be shown in the time re- quired for them to reach this assumed stage in their gravitational history, A gas which permits the heat of compression within the piston face to escape most quickly into the refrigerator external to the nebula will reach this stage most quickly. When this has been done, pressures and densities at the piston face are wholly inde- pendent of the nature of the gas. The total work of compression done on the mass within the piston face up to this time is also independent of the nature of the gas. But the temperatures at the piston face will be inversely as the numerical value of the Boyle-Gay-Lussac constant. It is evident, therefore, that the law of contraction cannot be indeterminate as in the case where the load is imposed by the hand of man. There is, therefore, in addition to the Boyle-Gay-Lussac law, another definite relation between any two of the three variables involved in that law. The application of well-known equations of ^ Transactions, Academy of Science of St. Louis, xiii, no. 3; xiv, no. 4. 90 PHYSICS OF MATTER thermodynamics led to the result that the density at any such piston face was directly proportional to the nth power of the pressure. The value of n is found to be 0.908 for all gases like oxygen, hydrogen, nitrogen, and air. The operation is, therefore, one lying between iso- thermal and isentropic compression, and near to the former. The specific heat of gravitational compression is therefore negative. The unit mass of gas at any point rises in temperature during compres- sion, and for a rise of temperature of 1°C., it gives off by radiation a definite amount of heat. If, now, such a nebula be supposed to extend to an infinite distance from the gravitating centre, the mass of the nebula will be infinite. Pressure, density, and temperature then all become zero at an infinite distance. Suppose such a nebula to have reached such a stage in its contraction that the mass of our solar system, 1,99 X 10^^ grammes, is internal to Neptune's orbit, then it turns out that the pressure there will be about what it is in Crookes tube, 1.74X 10~^ atmospheres. The density will be far less than in a Crookes tube, viz.: 1.40 X 10~" c. G. s. The temperature for a hydrogen nebula will be 3000°C., and for other gases it will be higher in inverse ratio as the value of the Boyle-Gay-Lussac constant. If the mass of the nebula be made finite, the conditions become still more interesting. Let the condition be imposed that the mass of the nebula is that of our solar system, and that it has so contracted that Neptune's mass only is external to Neptune's orbit. Then the temperature at Neptune's place drops to about 1900°C., for hydrogen,^ and both pressure and temperature become very much less than before. P 1.49 X lO"^"; d 1.93 X 10-»^ The thickness of the spherical shell which would contain Neptune's mass is about a million miles (1.65 X 10"" cm.). At the external surface of this nebula, the con- dition imposed makes P, d, and T zero, as the equations show. Nevertheless, a large fraction of Neptune's mass would be gaseous and far above its critical temperature. It seems to me impossible to think of a nebula having such properties generating by any reason- able rotation a system of planetary bodies. With Neptune's mass on the surface of such a nebula consisting of matter having a density and pressure less than a thousandth of these values in a Crookes tube vacuum, how could we conceive of this matter being gathered into a single planet? A much more reasonable hypothesis is one discussed by G. H. Darwin in 1889, in the Philosophical Transactions of the Royal Society.^ Darwin discussed the properties of a swarm of solid meteoric masses, and gives very strong proof of the proposition that ' In a nebula of mixed gases, each gas will, of course, have its own temperature, as is well understood. ' On the " Mechanical Conditions of a Swarm of Meteorites, " and on " Theories of Cosmogony," Phil. Trans. 1889. PRESENT PROBLEMS 91 a system of planetary bodies may originate in this way, although he is very cautious and conservative in stating conclusions. The great importance of this theory of planetary origin from the standpoint of planetary geology and the evolution theory seems to demand that it should receive more attention than it has yet received. The tem- perature of the great mass of such a swarm will be very much lower than in the case of the gaseous nebula. The larger part of such a mass will approach absolute zero in temperature. According to this hypo- thesis, even Mercury may have been solid when it separated from the parent mass, although in its later stages a large mass might become a gaseous nebula, as the sun now is. But in case of a body like our earth, of such relatively small size, and so far removed from the heated core, there does not seem to be any necessity for the assump- tion that it was ever in a fused condition. In view of these new developments, it seems peculiarly important that a discussion of the limits of maximum temperature which the mass of our earth has reached in the past should now be taken in hand again. Suppose a swarm of meteorites to fill the space internal to the moon's orbit, having a total mass equal to that of our earth. Assume that the mass is in rotation, so that the moon is about to separate from the parent mass. It would probably be too radical to assume that each element of mass has either the same actual velocity or the same angular velocity. Various hypotheses, more or less probable, are possible. Assume an initial temperature approach- ing zero absolute. It seems clear that the highest temperature reached in passing to the present condition of things may be far below the temperature of fusion. A body falling directly from the moon's distance to the earth will develop 59/60 of the kinetic energy it would acquire in falling from an infinite distance. The earth is yet being bombarded by meteoric matter having such velocities. But the operation is taking place so slowly that the heat has time to become dissipated by radiation, so that no appreciable rise in temperature of the earth results. To what extent may this condition have held in the past? Darwin discussed the tendency of the larger masses in such a swarm to accumulate towards the centre. It is a kind of sorting process. These larger masses would be in general of a metallic character. The more brittle rocks of smaller density would therefore form the outer layers of our earth. May not the heterogeneous character of our so-called igneous rocks be explained in this way? And the shrinking of the earth would then perhaps be in part the flowing of this porous mass into con- tinuity. And it may incidentally be pointed out that the existence of the belt of meteorites known as the asteroids is a most significant indication of the conditions which must have existed at a certain stage in the history of our solar system. 92 PHYSICS OF MATTER The problems of the present which have aroused general interest are those which pertain to the physical constitution of matter. And here we are at once confronted with the question, What do we mean by matter? How is matter to be recognized? Of late we have been hearing such phrases as "the electrical theory of matter." There seems to be a marked tendency towards the idea that matter and its properties are alike electrical phenomena. Some even intimate that the molecular theory of gases, and the atomic theory of the chemist are tottering to a fall. We have long known that matter in motion is a form of energy. This energy of moving matter is continually being converted into molecular or atomic vibration, and then escapes from us, apparently, forever, in the form of ether waves. We have also long known that electricity in motion is a form of energy, and that the energy so manifesting itself is also all finally converted into heat, and then into ether waves. Now this parallel certainty suggests an electrical theory of matter, but it also suggests, equally, a material theory of electricity. And so far from being antagonistic, these two theories are identical. There is nothing whatever to show that electricity has ever been separated from something which has what we have been accustomed to call mass. Rowland * found that when the charged sectors on his rotating disk were rotated, a magnetic field was produced, corresponding to that produced by a current of electricity. If the motion of the matter which carries the positive electric charge is in a positive direc- tion, the field is the same as that produced when a negative charge is moved in a negative direction. Rutherford has recently found phenomena of radioactive matter which have a most vital interest in connection with Rowland's work. The a and ^ particles which are shot off from such matter are mov- ing in the same direction, and they are oppositely deflected in a mag- netic field. They behave like superposed or perhaps juxtaposed electric currents of opposite sign flowing in the same direction. If in these radiations the a and /? particles were moving in opposite directions, then in a magnetic field they would be deflected in the same direction. This at once raises a question concerning the nature of an electric current in a conducting wire. Let us assume that we start with the positive and negative charges on the terminals of the Holtz machine. What is it that is taking place when the terminals are joined by wires leading to a galvanometer? We get a current which we are wont to say is due either to a positive current flowing in a positive direction, or to a negative current flowing in an opposite direction. If we cease to apply work to the rotating wheel, it comes to rest, and the potential of the conducting wire becomes uniform throughout. Its extremities which terminate in front of the charged ' American Journal of Science, [3] xv, 30-38, 1878. PRESENT PROBLEMS 93 inductors are therefore so charged as to produce this uniform poten- tial in the presence of these charged inductors, and the polarized glass of the rotor. The ends of the conductor are therefore oppositely charged. There is on its surface a neutral line of no charge. During the motion of the rotor these opposite charges are oppositely directed in the conductor. They are continually being added together. Equal quantities of unlike signs are continually being added together. Are we to assume that equal currents of unlike signs are superposed? Is a positive current in a positive direction identical with a negative current in a negative direction? Mathematically we should say yes. The resulting current, moreover, is uniform throughout the circuit, when measured by its external electromagnetic effects. We may loop in calibrated galvanometers at any point in the circuit, and they tell the same story. But what do the results of Rowland and Rutherford teach us? The /? particles carry the negative charge. The negative charge is part and parcel of something which has a positive mass. The a particles are perhaps a combination of more ^ particles in combination with other particles having (or being) a positive charge of greater numerical value. We have found long ago that the pro- ducts of an explosion are not necessarily composed of matter in its most elementary form. But these a particles are also part and parcel of something which has a positive mass. Are we to think of this conductor as being the seat of some action by which positive masses are being urged in a positive direction and positive masses are also being urged in an opposite direction? Are we to think that the mass of such a conductor, carrying a direct cur- rent, is slowly increasing, and that after many thousands of years this increase will become appreciable, resulting, perhaps, in a clogging of the conductor, and a decrease in its conduction? In that case a cur- rent of positive electricity moving in a positive direction is not a current of negative electricity moving in a negative direction. In that case the nature of positive and negative currents of electricity flowing in opposite directions is fundamentally different from that of the flow of heat and cold in opposite directions, for it involves the motion of masses in opposite directions. It would be interesting to examine whether the long-continued use of a conductor carrying a continuous current may not result in conferring upon it radioactive properties. The results of J. J. Thomson ^ on the phenomena shown by a Geissler tube 15 meters in length are very significant in this con- nection. He finds the positive luminescence to travel in a direction opposite to that of the cathode stream in the Crookes tube, with a velocity somewhat more than half that of light. The older results of Wheatstone ^ also show that the current from a Leyden jar travels in ' Recent Researches in Electricity and Magnetism, p. 116. ' Phil. Trans., Royal Society, London, 1834. 94 PHYSICS OF MATTER opposite directions within the conductor which joins its coatings. The middle point of the conductor is last reached by the discharge. If the discharge is maintained and a steady current is finally pro- duced, this current must apparently consist of positive and negative electricity flowing in opposite directions. If air be pumped out of one boiler and into another, two kinds of pressure are thus generated. If these pressures are added together, by connecting the boilers by means of a conductor, these pressures are added together, and both disappear. If we tap these charged boilers, the discharge from one will attract, and from the other will repel, an uncharged testing sphere. If the testing sphere be itself charged, we shall find that like charges repel, if both are positive, and attract, if both are negative. It is unnecessary here to enlarge upon the well-known differences between the positive and negative terminals of an exhausted tube. All of these phenomena will finally be helpful in arriving at the nature of the difference between positive and negative electricity. But I will refer to certain phenomena which do not seem to be so well known. Every one is famihar with the small points of light which may often be seen dancing in a crazy fashion over the cathode knob of the Holtz machine. A similar appearance can be seen on the negative carbon of a direct current arc, and in the negative bulb of the mercury vapor- lamp. These points of light may be made to pass from the cathode knob of the Holtz machine to the surface of a photographic dry- plate, exposed in open daylight.^ Separate the knobs so that no spark will pass. Place the plate near or between them. Connect the knobs with two small metal disks, each armed with a pin-point, so bent that it makes contact with the film. The point of the pin may rest upon the short mark of a lead pencil, drawn upon the film, the pins pointing towards each other on the plate. Points of light, like the so-called ball-lightning discharges, will come from the cathode terminal and successively travel slowly over the plate, leaving a black- ened trail of reduced silver behind. By means of a lead pencil held in the hand with the point near the cathode pin-point, these dis- charges may be induced to make their appearance on the film, and may be deflected into various directions after they have appeared. When left to themselves these minute specimens, of what may per- haps be called ball-lightning, tend to follow the lines of the field, but their paths are somewhat affected by the paths of prior discharges. If one of these points of light is seen on the pin which arms the cathode terminal, there will usually be none upon the film of the dry-plate. It may be brought upon the plate by holding a pencil-point near it. These ball discharges come from the cathode and travel to or towards the anode. They cannot be induced to come from the anode, * Transactions of the Academy of Science of St. Louis, x, no. 6. PRESENT PROBLEMS 95 or to travel against the negative current. The anode terminal has a visible discharge which appears to pass from it, and the photographic plate at the anode looks somewhat like a picture of a relief map of the delta formation at the mouth of a river. If a conductor be laid upon the plate between the two pin-points, there are then two gaps in the circuit. Each has an anode and a cathode. This conductor may be a metal disk armed with pins 180 degrees apart, which face the discharge points. It may be a pencil- mark upon the film or even a spot of reduced silver on the film. The same discharge will start from the cathode terminal of this inter- mediate conductor and will travel slowly in the negative direction. With an induction coil giving an eight-inch spark, these ball dis- charges can be formed on the surface of wood. In all cases it is evi- dent that chemical work is being done by the slowly advancing ball or point of light, and it is interesting to observe that it is the cathode discharge only which seems to be active. The reason for this may be partly electrical and partly chemical. The anode terminal of the machine may be grounded on a gas-pipe, and the cathode terminal only armed with a point, and the plate may be placed far away from the machine, connection being made between its cathode terminal and the pin-point on the film, with the same results. It may be added that these plates may be of the most sensitive character, and may be freely exposed to daylight for days before they are used. They may also be developed in the light in a bath not very strongly alkaline. The plate will develop clear, with the discharge tracks dark. The picture will not reverse photographically. It probably would do so if the plate were exposed to direct sunlight while the electrical ex- posure is made. With an induction coil having an alternating potential on its terminals, these ball discharges may be obtained from both terminals. They will travel towards each other if on the same plate, but they will not unite. In a closed circuit, one part of which is moved across the lines of a magnetic field, as in the case of a dynamo, we must suppose that the positive and negative currents, if both exist, are superposed in that part of the wire in which the electromotive force originates. The currents are superposed at their origin. The same ether machin- ery which urges the positive current in one direction urges the nega- tive current in the opposite direction. With the Holtz machine, we have one half of the machine positively and the other half negatively charged. If the knobs are widely separated, and conductors each armed with the pin-point be led off in opposite directions, each ter- minating on the film of a photographic plate, the cathode will deliver a ball discharge upon its film, while' the anode will not. The machine terminal which is not being used may, if desired, be grounded 96 PHYSICS OF MATTER on a gas-pipe. If a pencil-mark be made upon the plate near the anode it will be acted upon inductively, and a ball discharge will pass from it to the anode pin-point. The positive discharge will go in the oppo- site direction from the pencil-mark, but it leaves no trace. It appears that this ball discharge upon the surface, which results in a destruc- tion of the insulation of the surface, is a characteristic of the negative current. What would be the result if a suspended Maxwell coil were to be looped into either of these unipolar circuits? Would this case neces- sarily give the same result that Maxwell obtained?^ Of course we know that the result which Maxwell sought to detect is very small. We are more particularly concerned with the nature of the action than with the magnitude of the result. If the a particles are so large that they can contribute little or nothing to the current through a metallic conductor, then the positive current may practically be left out of consideration. But it seems doubtful whether the a par- ticles are ultimate in their character, and here is where experimental work is yet needed. It would be exceedingly interesting to study these ball discharges upon a photographic plate under diminishing pressures, as they gradually become a cathode discharge, in a Crookes tube. A Crookes tube may be connected by only one of its terminals to the Holtz machine. The free terminals of the machine and tube may be connected to wires hung on silk fibres and making contact with many pointed ground plates hung on long silk fibres in air. The terminals are then in fact grounded on the dust particles in the air. Either one of these air contacts may be replaced by a ground on the gas-pipe. In all of the possible arrangements covered in this description the tube will give excellent X-ray pictures. =0 +H air