quiry, both living and dead, in corroboration of our assertion; but we shall content ourselves with the instance at hand, -the name of Professor Mach, who stands in the front rank of those, who, having distinguished themselves in practical positive research, are now lending their thrice-proved powers to the elucidation of the grave and perplexing problems at its base. It is rarely given to a man to compass such signal achievements in so many departments. A professional physicist and skilful experimentalist, Professor Mach has enriched all the departments of his science, mechanics, acoustics, optics, heat, electricity, by ingenious experiments, methods, practical machines and contrivances for instruction, and notably by his critical and mathematical interpretations. His acoustic and optical experiments, and his photography of flying bullets are most popularly known here. By the side of all this, he has rendered to psychology, both theoretical and experimental, contributions which, it is safe to say, in profundity and import are more lasting and comprehensive than those upon which the fame of many eminent standard-bearers of this department rests. The same is true of philosophy and of the criticism of science. His early essay (1872) on the Erhaltung der Arbeit is a mine of suggestiveness, long neglected by the philosophical public, but containing in one form or other many utterances which have since become watchwords of scientific criticism The germs of his philosophical thought here presented have, along with a wealth of other new matter, been developed in his subsequent published lectures and essays, in his Mechanics, and in the book on Heat now under consideration. And all this with an exhaustless plentitude of insight into the various related sciences has been presented in a few terse volumes.

The present work on Heat pursues the same aim as the author's Mechanics. It seeks to clear up, by the light of a practical, rational theory of knowledge, the foundations of the science of thermotics and to eliminate therefrom all the superfluous notions, all the unwarranted metaphysical conceptions that have crept into it in its development. The book has a threefold character-historical, scientificocritical, and philosophical. There are chapters on the history of thermometry, on that of the conduction and radiation of heat, on the history of calorimetry, thermodynamics, energy, etc., critical chapters on the upshot of all these subjects and on physics generally, and finally philosophical sections, discussing such subjects as Names and Numbers, Continua, The Development of Science, The Sense for the Marvellous, Language, etc. Through all there runs a humanistic trend. We shall consider the work briefly under the three aspects noted-the scientifico-critical, the philosophical, and the humanistic-giving illustrative examples of each. Some of the philosophical matter we intend translating for The Open Court.

The instance of scientific criticism most within the reach of philosophical readers is the author's considerations touching the subject of thermometry. The development of thermometry, beginning as did most other things in modern physics with Galileo, embraces a period of two hundred and twenty-five years (1592-1817). It began with the recognition of changes of volume as a measure of degrees of heat,

passed from air as the standard thermoscopic substance through the liquids to the solids, and after various vicissitudes, by the researches of Boyle, Mariotte, and Gay-Lussac, reverted again to air or rather to the gases, finding its culmination in the law that all thermometric substances except gases exhibit distinct individual behaviours, and in the consequent quest for a rational thermometric scale.

In the criterion of change of volume as a measure of thermal intensity, we have, contends our author, first a convention and second an arbitrary choice. The starting-point is the sensation of heat. That sensation of heat and change of volume should run parallel is not determined by our choice. They are two distinct elements; we know their connexion only from observation; and experience alone can tell us how far their parallelism extends. We register the voluminal changes, attach to these numbers, make the latter the substitute of thermal intensity, and pursue with respect to the arithmetical scale speculations which we re-apply to the real thermal states themselves, thus arriving at the idea of absolute temperature, absolute zero of temperature, etc. But absolute temperature, any more than absolute rest or motion or time, does not exist. In seeking it we are seeking a Platonic prototypal idea, seeking in reality a notion which we ourselves have hypostatised, applying results which we have reached in the development of an ordinal formal criterion to a scale of real facts for the upshot of which we have under all conditions to await the verdict of experience.

Amontons was the first to hit upon the idea of a "coldest point" or absolute zero of temperature. His idea in a modified form persists in physics to-day. It is based upon the conception that the tension of a gas is produced by its heat. For every degree increase Celsius from o° onward the volume or expansive force of a gas increases by, and vice versa for the decrease. The number is the coefficient of expansion of the gas. Taking away 273 times we arrive at zero volume or zero expansive force. The point -273° C. is called the absolute zero of temperature.

But if we took the coefficient of expansion of mercury, and pursued the same train of reasoning, we should reach —-5000° C. as the absolute zero of temperature. And again, other methods, a priori equally rational, of measuring temperature, have been proposed. If we took Dalton's, for instance, using water as the thermoscopic substance and quantities of heat as the criterion, we should find —160° C., using mercury, 2021° C. as the absolute zero; mixing water and sulphuric acid we should get something between -830° and 1720° C.; and many other combinations, giving other results, are conceivable.

We have thus a multitude of "absolute zeros," all of which rest upon different hypotheses, which being substituted for the facts all give a different result. What we are doing is not studying the facts but the representations of the facts. That there is a limit in either direction to the scale of representation does not bring with it that there is a limit to the facts. The tone-sensations may be represented by rates of vibration, which being numbers have a lower but no upper limit; they

may also be represented by the logarithms of these numbers, which are unlimited in either direction (running from ∞ to +∞). The tone-sensations themselves. however, are limited in both directions. The fact is that when the tensions of a gas become zero, the indexes of the registered temperature vanish; the gas is no longer serviceable as a thermoscope; we must seek something else. In fine, experience alone can determine whether the thermal states are limited in either direction; like potential, velocity, etc., the notion of temperature is a notion of level, differing from the rest in that some of its levels are determinative.

Such is a skeletal abstract of Mach's criticism of the notion of temperature. We should like similarly to reproduce the discussions relating to conduction, radiation, thermodynamics, the principle of Carnot, and to the sources of the principle of the conservation of energy, but the reader may gain something of an idea of the last two points from the already published Popular Scientific Lectures, to which we refer him.1

The section on calorimetry is notable, and we catch here considerable of the author's philosophy of science, which upholds the ideal of a descriptive, phænomological formulation of the facts of the world as distinguished from a symbolical or allegorical formulation (mechanistic, substantive, etc.). Thus Black conceives the notions of "quantity of heat," specific heat," and "latent heat," to explain the phenomena of mixed heated masses, of melting, vaporisation, etc. His procedure

was sure, brilliant, and what is more marked a distinct conquest in science. Representing the masses by m, m', the changes of temperature by 0, 0, the specific heats by s, s', and latent heat by λ, Black discovered, or so pursued his quest, that the following equations were fulfilled :

m0+m'0' =0 m0 + s'm'0' =0 sm0+2m'=0

In this lies his real achievement. When he went farther and pictured the above abstract quantitative expressions of the facts under the guise of substance, etc., he did more than was necessary; his symbolisation helped him but impeded his suc

cessors.

The goal of all physical research is the fulfiling of such equations, the fixing of the quantitative connexions of the things of the world by abstract mathematical signs, entirely stripped of superfluous allegorical adjuncts, and embracing in one scheme all possible cases. Such are the dynamical equations of Lagrange, and the theory of Fourier on the conduction of heat, which is here characterised as a model of physical inquiry.

We will now look at an example of the humanistic side of the work, its glimpses into the mental workshops of the inquirers. The author is speaking of Black's views of scientific research. After quoting a few passages in point, he says: "There

1 Pp. 137-185.

"is an unmistakable echo of Newton's genius in these passages. Chemistry was "really not Black's profession. He was a professor of medicine and a busy prac"titioner. 'He gave such unremitting attention to his patients,' says his biogra"pher, 'that it scarcely seems possible he could have found the least time for his "other occupations.' We have here, it would seem, a partial explanation of Black's "attitude as an inquirer. There is a reason for the success which physicians and 'engineers not infrequently encounter in scientific inquiry; for in their case the "scientific training which the best of them carry into their professions, is in con"stant contact with life and rarely impeded by the narrow views of the schools. . . . "Black is one of those rare men who win our love in all we know of them, and in "every page of their writings. The inornate, honest, pretensionless simplicity "with which he sets forth his thoughts, is reached by few. Whatever he under"takes he seems to compass without effort. We might say of him, to use an expres'sion often applied to the poets: 'He is a thinker by the grace of God.'"'

We have similar utterances on Carnot and on the other founders of thermodynamics. Particularly good is the comparison of Joule and Mayer. In speaking of the beautiful experiments of the former, the following sentence, which will please Englishmen, occurs: "The situation with regard to Joule is the same as with re"gard to Mayer, excepting a characteristic English trait. Sound methods of phys"ical inquiry seem almost inborn in Englishmen, or are certainly inbred. English "'inquirers are never clouded by metaphysical fogs, at least never make them the "'cardinal issue. In Joule's case, every idea is put to the test of experiment, every "experiment reacts upon his ideas. The unceasing mutual adaptation of theory "and experience may be followed with great clearness in Joule's work."

We should like to quote more such passages, for the author's pages abound in them. And of the work as a whole we hope to have given a vivid, though fleeting, impression, as a masterpiece of genial inquiry which can be read by philosopher and scientist alike. No one interested in these questions should leave his mind uninfluenced by the rich, beneficent stimulus which it offers. T. J. McC.

TRAITÉ ELÉMENTAIRE DE MÉCANIQUE CHIMIQUE FONDÉE SUR LA THERMODYNAMIQUE. Par P. Duhem, Professeur de Physique Théorique à la Faculté des Sciences de Bordeaux. Tome I. Introduction. Principes fondamentaux de la thermodynamique. Faux équilibres et explosions. Paris: Librairie Scientifique A. Hermann. Rue de la Sorbonne, 8. 1897. Price, 10 francs. The present book scarcely falls within the line of the work of The Monist, but as the principles which it employs, the theories which it develops, are now in the foreground of scientific criticism, and as the position of its author as one of the first of living theoretical physicists makes it a standard authority on its subject, we cannot pass it by without some slight reference and without the full measure of commendation. The work will embrace two volumes. The first, which is now just out, expounds the preliminary analytical and mechanical notions employed in the

study of chemical thermodynamics, develops the general physical principles of the same science, notably in their bearing upon chemistry, and finally, in its consideration of false equilibria and of explosions, enters into the detailed application of the foregoing theoretical parts. The work is predominantly mathematical, but for its subject is simple and not wanting in æsthetic qualities, to which the outward labors of the publishers have added a welcome and agreeable typographical emphasis. Duhem's treatise aims at marshaling in compact and systematic form all the main results of mathematical physical chemistry, which hitherto have largely lain scattered and isolated in scientific reports, and so forms an indispensable work for the scientific library.

T.

HISTOIRE DE LA PHILOSOPHIE EUROPÉENNE. Par Alfred Weber. Sixième édition. Paris Fischbacher. 1897. Pages, 500.

HISTORY OF PHILOSOPHY. By Alfred Weber, Professor in the University of Strassburg. Authorised Translation by Frank Thilly, A. M., Ph. D. From the Fifth French Edition. New York: Charles Scribner's Sons. 1896. Pages, 630.

LEIBNIZENS STREIT GEGEN LOCKE IN ANSEHUNG DER ANGEBORENEN IDEEN. Von Frank Thilly. Heidelberg: Universitäts-Buchdruckerei von J. Hörning. 1891.

France is not as rich in histories of philosophy as Germany, and it is remarkable that the author of this most scholarly and comprehensive work on the History of Philosophy is an Alsatian who had the advantage of passing through French as well as German universities, and has combined in a happy alliance the advantages of both.

Alfred Weber is a descendant of one of the old Alsatian families which were mentioned centuries ago in the chronicles of the free city of Strassburg. He was Professor at the University of Strassburg while Alsace was still in the possession of France. When the Germans seized the country he remained in his position and is at present still there as head of the Philosophical Department.

nature.

During his younger years, Weber was powerfully attracted by the religious philosophy of Schelling who was one of the apostles of a monistic conception of the world on the basis of natural science, -not in a narrow sense of the so-called physical sciences which would exclude a due consideration of the more significant branches of anthropology and psychology, but in the broadest sense of the word Weber was also influenced by Hegel, but he never allowed himself to become a blind follower of the philosophy of the Absolute. After a study of Schopenhauer's works, Weber wrote a little pamplet in which he embodies his criticism of the great pessimist by emphasising that the will to live with the growth of civilisation changes into a will to realise the good. Schopenhauer has utterly neglected in his system of thought this will to realise the good, and yet how much more power