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JOSIAH WILLARD GIBBS,AN APPRECIATION* JOHNJOHNSTON, U. S. STEEL CORPORATION, NEWYORKCITY
It is somewhat of an anomaly that the fiftieth anniversary of the publication, in the Transactions of the Connecticut Academy, of the first part of Gibbs' great work on the equilibrium of heterogeneous substances should have been signalized in Holland by the publication of a Gibbs number of their chemical journal, the Chemisch Weekblad; whereas few, if any, in America took thought of the matter a t all. It is furthermore anomalous that the contributors to this number should include besides the Hollanders, a Frenchman, a Canadian, a Norwegian, two Englishmen, but no American. Truly a prophet is not without honor save in his own country. This is instanced in another way. Quite a number of foreigners visiting Yale have asked about a memorial to Gibbs, and have expressed astonishment a t the reply that there is none, apart from a bas-relief on the stairway of the Sloane Physics Laboratory--and this bas-relief is the gift of Professor Walther Nernst of the University of Berlin. One visitor, a distinguished Swedish scientist, was not satisfied until he hadlaid a wreath upon Gibbs' grave. This is a condition of affairs which, it is expected, will soon be remedied by the establishment a t Yale University of an appropriate memorial in the form of a Willard Gibbs professorship. Those appointed to this professorship would, it is contemplated, be men from other institutions qualified to give a course of lectures, extending over one or two terms, in some branch of Chemistry, Physics, or Mathematics, particularly in those fields especially associated with the name of Gibbs; and they would be considered as temporary members of the faculty giving courses regarded as a regular part of the university curriculum. The rotation of eminent men from many countries, each an outstanding figure in his own line of work, would serve as an inspiration to faculty and student alike, and thus would constitute a continuous memorial to Gibbs. At present one can merely adapt the epitaph to Sir Christopher Wren, "Simonumenturn repiris circumspice," in suggesting that the visitor read Gibbs' papers and ponder their manifold practical consequences, both direct and indirect. But his most important papers are again out of print and difficult of access, as indeed they have been for a considerable fraction of the period since their first publication. This difficulty will soon be removed by the publication-arrangements for which are well under wayof an inexpensive edition of his works. But another difficulty remains, for Gibbs' reasoning is so rigorous that few people have been willing to study his works sufficiently t o grasp their full implications; for to him "mathematics is a language," as he is reported to have stated in a faculty meeting engaged upon the Sisyphean task of determining the course of
* Reprinted from Yale Scientific Magmim.
study to be pursued by the average student. This difficulty of interpretation may, it is hoped, be alleviated by the publication of a volume or volumes, in which his work would be amplified and explained, with illustrations of its application to some of the multifarious experimental cases which have in the meantime been investigated; arrangements are now under way to have these essays written by those most competent in the special fields. This should serve to widen the appreciation of Gibbs' contribution to natural philosophy; for, particularly as regards many of the developments of great economic value, those who have benefited are quite unaware of the f a d that without Gibbs' work these developments would not have been possible. Nor is it a case of which it may be asserted that someone else would have done it; this would be true with respect to isolated theorems, but only a genius of the first order could imagine and arrange the whole as a connected philosophy. I t may well be remarked here that no mistake has yet been discovered in Gibbs' work-the accumulation of experimental observations has merely verified his predictions, and in no case run counter to them-though in the fifty years since publication many principles and theories of physical science then generally accepted as fundamentally true have proved to be incompletely valid or even erroneous. Salient Facts about His L i e Before endeavoring to set forth just what was achieved by Gibbs, let us recall the main facts of his life. Josiah Willard Gibbs was born in New Haven, February ll, 1839, the fourth child and only son of Josiah Willard Gibbs, Professor of Sacred Literature in the Yale Divinity School, and of his wife, Mary Anna, daughter of Dr. John Van Cleve of Princeton. He entered Yale College in 1854, graduated in 1858, and continued his studies in New Haven until 1863, when he received the degree of Doctor of Philosophy, the title of his dissertation being "On the Form of the Teeth of Wheels in Spur Gearing." He then spent three years as a tutor, the first two in Latin, the last in Natural Philosophy, and in 1866 went to Europe, first to Paris, then to Berlin, and finally to Heidelberg, where at that time both Rirchhoff and Helmholtz were active. In 1869 he returned to New Haven and in 1871 he was appointed Professor of Mathematical Physics in Yale College, a position which he held until his death, April 28, 1903. Scientific honors of all kinds came to him; medals, degrees, membership in academies and other learned societies; and he was in correspondence with Kelvin, Clerk Maxwell, Boltzmann, and other contemporary European leaders in mathematical physics.
His Most Important Works In 1873, when 34 years old, he published in the Transactions of the Connecticut Academy two papers, one entitled "Graphical Methods in
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the Thermodynamics of Fluids," the other "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces;" and, following these, in 1876 and 1878, the two parts of the great paper "On the Equilibrium of Heterogeneous Substances," which is generally "considered his most important contribution to physical science, and which is unquestionably among the greatest and most enduring monuments of the wonderful scientific activity of the nineteenth century" (Bumstead).' His subsequent principal writings in the years 18811893 deal with multiple algebra and vector analysis (the latter finally published in 1901 as a treatise edited by Professor E. B. Wilson); with the electro-magnetictheory of light, a series which appeared between 1882 and 1889; and lastly a work entitled "Elementary Principles in Statistical Mechanics," in which he returned to a theme closely connected with his work on thermodynamics. At his death were found a few fragments, intended as portions of a supplement to the "Equilibrium of Heterogeneous Substances;" these are published in the "Scientific Papers." It is of interest to note that one of the topics he proposed to treat is "entropy as mixed-upness," a point of view which during the last few years has been widely adopted. Of his work, the classic paper on "The Equilibrium of Heterogeneous Substances" has exerted the greatest influence, in particular upon the development of chemistry; indeed, according to Ostwald, "To general chemistry he gave form and content for a hundred years." The Copley medal of the Royal Society was, in 1901, awarded to him as "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical and thermal energy and capacity for external work." Larmor in the article "Energetics" in the Encyclopedia Britannica wrote: "His monumental memoir . . . . made a clean sweep of the subject, and workers in the modern experimental science of physical chemistry have returned toit again and again to find their empirical principles forecasted in the light of pure theory, and to derive fresh inspiration for new departures." As an illustration of the succinct style in which this memoir is writtena style in which every word counts and no word is redundant-I quote the first paragraph: "The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it is capable. As the differenceof the values of the energy for any two states represents the combined amount of work and heat received or yielded by the system when it is brought from one state to the other, and the difference of entropy is the limit of all the ' "The Scientiic Papers of J. Willard Gibbs," edited by Henry Andrews Bumstead and Ralph Gibbs Van Name, 2 valurnw, 1906. (Volume 1 now out of print.)
dQ (dQ denoting the element of the heat possible values of the integral t
received from external soiuces, and t the temperature of the part of the system receiving it), the varying values of the energy and entropy characterize in all that is essential the effects producible by the system in passing from one state to another. For by mechanical and thermodynamic contrivances, supposed theoretically perfect, any supply of work and heat may be transformed into any other which does not differ from it either in the amount of work and heat taken toqether or in the value of the internal -
9. But i t is not only in respect to the external t
relations of a system
that its energy and entropy are of predominant importance. As in the case of simply mechanical systems (such as are discussed in theoretical mechanics), which are capable of only one kind of action upon external systems, eviz., the periormance of mechanical work, the function which expresses the capability of the system for this kind of action also plays the leading part in the theory of equilibrium, the condition of equilibrium being that the variation of this function shall vanish, so in a thermodynamic system (such as all material systems actually are), which is capable of two different kinds of action upon external systems, the two functions which express the two-fold capabilities of the system afford an almost equally simple criterion of equilibrium." I t ends abruptly with equation 700, which is in effect the correct equation for the electromotive force of what Gibbs calls "a perfect electrochemical apparatus," or a reversible cell; it comprises some 300 pages of close reasoning in which many important theorems are enunciated, and rigorously derived, for the first time. His Genius Unappreciated To convey an adequate idea of just what Gibbs achieved is no easy task, as may be imagined from the fact that it took another genius of the first rank-Clerk Maxwell, who formulated electrodynamics, unified many phenomena apparently diverse, and was enabled to make predictions which have culminated in radio, if indeed they can be said to have culminatedto apprehend what Gibbs had done: and a period of a quarter of a century had to elapse before it was appreciated, except by a small number of outstanding men. Many of you have formed some acquaintanctperhaps only a nodding acquaintance-with dynamics, and have learned painfully the way in which a body moves under certain conditions, e. g., in free flight, or down an an inclined plane; or what happens when two bodies collide; these elementary calculations are always subject to the simplifying assumption that the slowing up due to friction may be neglected. The justification for
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this simplification is that the result is that which is approached more and more nearly as the frictional resistance is diminished indefinitely. These problems deal only with a single body, or a t most with two bodies, and pay attention only to their mass or size, but not a t all lo their chemical constitution nor to any changes in them which may arise as the result of the motion or collision. Now if one is to get a rational basis for foretelling if and to what extent chemical change will proceed in a system-this being in effect the task which Gibbs set himself--one has a very much more complex problem. For the smallest amount of material which we ordinarily deal with practically is comparable t o a teaspoonful of water, but this contains of the order of loz3 particles. This is an almost inconceivably large number; an illustration may help to show how large. If a being a t the beginning of geologic time--say a thousand million years a g e h a d begun to count, not by units but by millionpone million, two million, three million, and so onhe would only now be approaching this number. Extraordinary Accuracy in Complicated Formulas Thus Gibbs set himself the far more formidable task of formulating what would happen when very large numbers-to be reckoned in millions of millions of millions--of particles, and of particles of different kinds, in different states, solid, liquid, gaseous-are brought together; and what would be the effect upon such a system of particles of changes in the external conditions of temperature and pressure. He was examining the state of equilibrium of systems and discovering how this state of equilibrium is influenced by change in the conditions to which the system is subject; but in this case, again, to postulate equilibrium does not really limit the applicability of the results, for in an actual case we can make allowance for those factors which resemble friction in that they impede the processes of change. In other words, he was seeking a measure of the tendency of any system to change; the farther from equilibrium, the greater is this tendency, and it becomes zero only when equilibrium has been attained. To achieve this purpose he could not, of course, consider the particles individually, but had to use what are in effect statistical method-to use as characteristics of the system quantities such as temperature or pressure which represent a statistical averaxe related to the motion of the particles. This kind of idea may, perhaps, be illustrated by an example familiar to you. The annual death rate in a stable community is a definite figure, which is now changing rather slowly, apart from some special cause such as a new epidemic. If we take it that New Haven has a population of 200,000 and a death rate of 15, we can predict that there will be close to 3000 deaths in 1928; we cannot foretell whether any given person will die. This is the basis upon which the life insurance company makes its bet
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with you as to the duration of your life--a bet in which you can make a financial gain only by dying before your statistical expectation of life has run. I n other words, this method considers the aowd and not the individual; and the larger the aowd, the more uniform will the mortality be, and so the more certain are the results of this statistical method of inquiry. The number of mamages, divorces, and b i r t h s t h e unions and disunions of individuals and their resultantsmay be treated in a similar way, the whole comprising vital statistics. I n a sense, then, Gibbs is considering vital statistics of atoms, the birth rate and death rate of each of the kinds of particle composing the system, and from this deducing what the stationary state of the system will be. And in his systems he has an advantage in that he is dealing with such enormous numbers of particles that the results, instead of being merely probable, are in fact certain. The great merit of this mode of attack is its freedom from assumptions of any kindother than the laws of thermodynamics, the truth of which has been experimentally demonstrated so that any exception is extraordinarily improbable -in other words,its great generality; though this, on the other hand, renders more difficult the application of Gibbs' results to specific questions. Gibbs then derives, by absolutely rigorous reasoning, equations in terms of these characteristic statistical quantities for each kind of particle present, equations which enable one to predict how the system will react toward outside influences. In order to make this precise prediction in any specific case, one must know the values of the several characteristic quantities which must, in general, be determined by special experiments. Our knowledge of these constants is still very incomplete, and there will be work for many generations of chemists before it is complete. But each one, being characteristic of a substance, can be applied to any case in which that substance as such takes part, and need not be determined separately for the numberless permutations which are possible. For we know a t least a million different individual chemical substances belonging t o many thousands of different families, and this is but a small fraction of those that remain to be discovered and identified] and any one of these may, in principle, react with or a t least influence the behavior of any other. Great Influence on Development of Chemistry With the more general realization of the significance of Gibbs' work, about the beginning of the present century, chemistry took a new tack and addressed itself to problems which in a sense had hardly been recognized as problems previously. I n the 90's many chemists and physicists were almost of the opinion that the main outlines of physical science were known, and that little remained to do except to fill in more or less unimportant details; now we realize how grotesquely inadequate this picture was, and that what we know is an infinitesimal part of what remains to be known.
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This has again enhanced the romance of physical science, the sport of chemical work; for to penetrate into the unknown, to discover what is beyond the horizon, is the most attractive and enticing kmd of amusement. In this change of attitude in chemistry Gibbs' work played a large part, leading as it did to the development of what has become known as physical chemistry; for his work-and particularly that small part of i t known as the phase rule-proved to be an unfailing guide in the interpretation of experimental results. What the phase rule does in effect is to enable one to classify the multifarious, apparently altogether diverse, systems encountered experimentally into a small number of categories; those withm any category behave in essence identically, whether simple or complex. This results in a great economy of thought and effort, as otherwise we would have to consider as a separate individual, each a law unto itself, every one of the large number of systems with which we have to deal practically. In other words, we do not have to consider each chemical substance as an absolute individual which must be completely known before we can describe its response to changed conditionsthough this is not yet universally realized. Gibbs' work has provided a philosophy, a system of molecular ethics, a correlation of behavior of substances which simplifies our task of description in a way entirely comparable with the simplification effectedby Newton in describing the paths of the heavenly bodies. It is altogether fundamental to progress in the science of chemistry, to the vision of the subject-matter as a connected whole, with evolution from the simple to the complex, instead of as an unruly mob of isolated facts. Many tributes to the value of Gibbs' work, both to the progress of science and to the development of industrial processes, could be cited if space permitted; it will suffice to quote a few sentences from a paper written by Professor F. G. Donnan: "Gibbs ranks with men l i e Newton, Lagrange, and Hamilton, who by the sheer force and power of their minds have produced those generalized statements of scientific law which mark epochs in the advance of exact knowledge . . The work and inspiration of Gibbs have thus produced not only a great science, but also an equally great practice. There is, today, no great chemical or metallurgical industry which does not depend, for the development and control of a great part of its operations, on an understanding and application of thermodynamic chemistry and the geometrical theory of heterogeneous equilibria." In short, he is regarded by those most competent to assess his work as on a par with men such as Newton or Maxwell; and his fame, in its scope and international character, is greater than that of any other Yale man, or of any American scientist. Indeed Lord Kelvin said here, a few years
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ago, that by the year 2000 Yale would be best known to the world for having produced Willard Gihbs. In conclusion, may I apply to Gibbs his own very apt words to be found in his obituary notices of Clausius (one of the founders of thermodynamics) and of his colleague and friend Hubert Anson Newton (Yale 1850; Professor of Mathematics 185551896): "The constructive power thus exhibited, this ability to bring order out of confusion, this breadth of view which could apprehend one truth without losing sight of another, this nice discrimination to separate truth from error-these are qualities which place the possessor in the first rank of scientific men . . . But such work as that of Clausius is not measured by counting titles or pages. His true monument lies not in the shelves of libraries, hut in the thoughts of men, and in the history of more than one science. "But these papers show more than the type of mind of the author; they give no uncertain testimony concerning the character of the man. In all these papers we see a love of honest work, an aversion to shams, a distrust of rash generalities and speculations based on uncertain premises. He was never anxious to add one more guess on doubtful matters in the hope of hitting the truth, or what might pass as such for a time, hut was always willing to take infinite pains in the most careful test of every theory. To these qualities was joined a modesty which forbade the pushing of his claims. and desired no reputation except the unsought tribute of competent judges." May I express the hope that we may endeavor humbly to follow in his footsteps?
