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Vorlesungen ueber Qastheorie. Lzdzaig Boltzneaniz. 1,Theil : T/zeorie der Gase nzit einatomigew MoleRiilm, derepz Dimensionen gegerz die mittlere Wegliiiage veisrhmindeiz. Large 8~10,zi and 204 pages. .&i#z&. Yohaizn Ainbrosiiis Barfh. 1895. F‘)ice, 6 marks. T h e Kinetic Theory of Gases, as it stands to-day, constitutes one of the important applications of the theory of probability. This in itself is a sufficient explanation of the difficulty of the subject, of the controversies that have arisen over its fuiidaniental principles, and of the aversion with which it is often regarded by the student. Within a few months one of the fundamental parts of the theory has been made the object of a vigorous onslaught by M. Bertrand, who declares it to be arrant nonsense, as he has so frequently done of other theories. The Kiiietic Theory is important as being the only attempt to explain the fundamental properties of matter on a simple mechanical basis that has met with any success as to its agreement with the facts. That we should have such a theory for gases only is not surprising, in view of their simpler properties when compared with liquids and solids. If the student anxious to gain a knowledge of the Kinetic Theory should ask where it is to he obtained we sliould iniinediately refer hiin to the various papers of Clausius, Maxwell, Boltzmann and Tait. If however he has not access to the iiuinerous Transactions in which these have appeared, it will iiot be a difficult matter to name the available sources of information. T h e writer has before hini 011 the table all the works with which lie is acquainted that deal with the subject, and except for the two big volunies of Maxwell’s papers they do not form a large pile. Of these only three are devoted exclusively to the Kinetic Theory. One only, tlie earliest as to date, is in English, namely the ti-eatise of Watson. This deals almost exclusively with the establishinellt of a single

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theorem, that of Maxwell and Boltzmann on the distribution of the energy in the steady condition. The second, the treatise of 0. E. Meyer, is valuable for the plain accounts of the principles involved arid for the large collection of numerical data, the mathematical developnients being crowded into an appendix. The third treatise, which constitutes the last volume of Clausius’ Mechamkche T.V+vzetheorie, is an account of the subject by one of its creators, and furnishes the student with an excellent idea of the essential pasts of the theory, but is somewhat lacking in unity of treatment. Of works containing chapters devoted to the Kinetic Theory we may mention Maxwell’s Theory of Heat, which treats the subject in a very elementary manner, without any reference to the theory of probability , Ru h lni an n ’ s Mrclza E ischc Wtiermcfheorie , w 11ich contains an extended chapter on the subject, Voigt’s A’om#rirdiwz der Physik, which devotes a few brief pages to the matter, and Winkelmann’s N a ? z d h c h , where we find an excellent chapter by Jager. Finally, and best of all, we have Kirchhoff’s T’eorie der Wa7wte, of which the last eighty-six pages are devoted to the Kinetic Theory of Gases, the treatment being a very careful and lucid one, like everything that Kirchlioff ever wrote. Christ iansen ’s 6 1 e w elite .deer f h roretischeii Physik , which treats such a great variety of subjects in such an interesting manner, has nothing at all on the Kinetic Theory. I n view of the sniall number of available text-books, the appearance of a treatise by Professor Boltzmann will be welcomed by many persons, especially if they have read his very interesting lectures 011 Maxwell’s theory of electricity. Boltzinaiin is easily the first of living German theoretical physicists, and besides has contributed to the subject in question some of its most iinportant parts. T h e present volume deals only with the simplest type of inolecules, and therefose does not deal with tlie theorem especially connected with the name of Boltzmann, which conceriis the partition of the energy among the various parameters that determine the state of the molecule, except in the particular case treated by Maxwell, where the parameters are the rectangular coordinates of the molecule. I n the first section of the book the molecules are considered as sniall perfectly elastic spheres, i i i the second as point centers of repulsive

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force, and in the third the special assumption is treated making the law of the force that of the inverse fifth power, as suggested and developed by Maxwell. T h e problem of the Kinetic Theory in its simplest case niay be thus stated :--given a large number of equal small bodies flying about in a manner of which we know nothing, colliding with each other according to the principles of conservation of nionientuin and of energy, what fraction of the whole number will, after a great many collisions, possess any given velocity how many collisions will there be, on the average, in a given time, how far will the particles travel, on the average, between two successive collisions, and in what manner will they carry from one place to another certain properties, such a s mass, momentum, and kinetic energy. T h e first of these questions was asked and aswered by Maxwell. Of his law of distribution of velocities Maxwell gave two proofs. Of these the first is characterized by Kirclihoff as ((eiizfach, d e r ?iicht streizg ) ) , I t is, however, the only oiie usually given in the textbooks. I t depends only on the assumption that the probabilities of given values of the three rectangular coniponeiits of the velocities of a niolecule are perfectly independent This assumption has been niuch criticized, and is the main object. of Bertrand’s attack. This proof is not given by Boltzmann, who gives what is substaiitially Maxwell’s second proof. In this the effect of the collisions on the distribution of the velocities is considered, as it obviously mu5t be. T h e steady state is declared to b- reached when there is an exact equality between the number of collisions of two so-called opposite kinds. Boltzniann then goes 011 to consider the case where this equality is not observed, SO that the state of the distribution varies with the time, with the result that a certain quantity H is shown to be contiiiually diminishing. In the next section the quailtity H is shown to have a simple relation to the probability of the distribution in question, 50 that the ineatiing of the ( ( M[ -theorem ) ) is that the distribution of velocities is continually tending towards the most probable distribution, which is that given by Maxwell’s law. From Maxwell’s law immediately follows the equality of the mean kinetic energies of the molecules of two mixed gases in ther-

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mal equilibrium, and from this follows the law of Avogadro. It is remarkable that some of the principal results of the Kinetic Theory can be obtained without determining the distribution of velocities, for instance the laws of Boyle and Charles can be obtained even if we suppose all the molecules to have equal velocities. T h e simpler treatment is given by our author first, and afterwards the more complicated treatment involving the law of distribution. This method is pursued throughout the book, several theorems being proved in more and more complicated, but at the same time more strict, methods at various stages. After the treatment of the specific heats of a gas the physical meaning of the quantity H is taken up, and in the case of the simplest kind of molecules, it turns out that--H differs only by an additive constant and a constant factor from the entropy. Accordingly the fact that the entropy can only increase appears as a theorem of probability. I t is noteworthy that of the many attempts to found the second law of Thermodynamics on the laws of Mechanics, none has been successful, with the exception of this one for the case of a gas, and the cases treated by Helmholtz of monocyclic systems. This is not surprising, for we might expect that before obtaining the laws of phenomena by the laws of mechanics we must form some definite picture of the nature of the motions involved. T h e next subjects in order are the number of collisions in a given time, and the mean free path. Here various opinions have prevailed as to the way in which the mean should be taken. These difficulties are of a mathematical nature, and are cominon to various questions of probability, and do nQt affect the physical reasoning. They seem after all hardly worth troubling one’s self about, especially as the different methods affect the results only by slight numerical changes. Boltzmann, however, mentions the various definitions, although generally following those of Maxwell. Connected intimately with the mean free path are the questions of internal friction or viscosity, heat-conduction, and diffusion. These are all cases of the transportation of certain quantities mentioned above, and are interesting because of the knowledge that they give us as to the length of the free paths. T h e question of diffusion is probably the most complicated in connection with our theory, and has to be treated with certain approximations.

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T h e student who has read the first section of the volume, already described, will have obtained a pretty good idea of the scope of the Kinetic Theory, and as he goes on will find still more careful treatments of similar matters. These partake somewhat of the nature of treatments of Hydrodynamics, mixed with the ordinary ideas of the Kinetic Theory, and follow i n general the course of ideas of Maxwell's later papers, as does Kirchhoff also. Here we have an elaborate treatment of the entropy theorem, as well as a treatment of the behavior of a gas under the action of gravity. T h e last section of the book introduces the assumption that the molecules repel each other with a force proportional to the inverse fifth power of the distance. This is probably one of the least iniportant portions of the theory, for the main results have been obtained otherwise. We find here, however, a rather important section on a generalized idea of entropy, with some instructive remarks on Dissipation of Energy. In conclusion, the student desirous of studying the Kinetic Theory of Gases can hardly do better than take up this book. reading it slowly, and digesting every part before going on, confident that he will here find a clear and mathematically sound treatment of the subject, if one exists, ( ( b u tthat is another story. ) ) A Y ~ / L Z UGordon Webster.

LeSons de Chimie. H e n r i Gautiev et Georges Charjy. Second Edition, entircl_lf vecast. L a r g e octavo. ix and 48q)ages. GazdiierViZZa?s. Pavis. 189g. An elementary text-book for students in the Mathematical Course at the $cole Polytechnique, so the treatment is somewhat more mathenlatical than we are accustomed to find in our American text-hooks on Chemistry. T h e present volume contains the general principles as a first part, and the metalloids as a second part, which conipose the whole book so it is presumably followed by another volume containing the metals. T h e first part contains an excellent theoretical sketch of those physical changes which play so iniportant a part in chemical changes. Here the influence of I,e Chatelier, who advised in the preparation, is seen. Unfortunately so much space is given to the writing of chemical equations and discussion of atomic weights and ,

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equivalents, that the reader gets the impression that just here algebra has been mistaken for chemistry. In the second part the arrangement is according to the periodic law and the treatment of the subject is like that in any good American book. The book is up to date, argon and helium being considered ; it is good but in no way original. Clamace L . Speyers. The Development of the Periodic Law. F. P. Vexable. 32r pages. The Chemical Publishing Co., Easfon, Pa. 1896. Price $2.50. An account of the origin and development not only of the periodic law, but of Prout’s hypothesis, of the speculations on the genesis of the elements, and of the numerous attempts to represent algebraically or otherwise the relations existing between the atomic weights and the properties of the various elementary bodies. T h e arrangement is chronological. Between two and three hundred books and papers are quoted and discussed, and the interest of the work is much increased by numerous reproductions of tables, diagrams and charts. I n connection with the reprint in exteizso of a few of the most important papers (Doebereiner, Pettenkofer, Meyer, Mendelejeff) in Ostwald’s Klassiker, Nos. 66 and 68, the present work renders easily accessible a vast mass of literature dealing with this important subject, most of which has hitherto been hidden in obscure publications or scattered through the various scientific journals from 1815 to the present day. In dealing with the inception of the periodic law, the author protests against the prominence given by Lothar Meyer to the work of Pettenkofer. H e is of the opinion that ((while Pettenkofer undoubtedly gave expression to some of the ideas contained in Dumas’s Ipswich address rather more than a year before this address was delivered, it is equally certain that his paper did not follow the train of thought nor contain the brilliant speculations which attracted the attention of the world to the address of Dumas. For eight years Pettenkofer’s work was practically unknown, while Dumas’s had proved an incentive to a band of earnest workers, and was really the cause of Pettenkofer’s republication ) ) . T h e book is brought up to date by reviews of papers published

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in the current year, and is completed by a bibliography of ng less than 267 titles, a list of authors, and a very full general index.

W. Lash Miller-. A llanual of Physics. W Peddie. 2ud Edifiofz. vtii and 357 pages. G. P. Pz~fnam'sSons. New Yoi%l. 1896. Price $2.50 rzeff. I n this second edition the author has dispensed with the services of the calculus, and has employed mathematical methods of the ( elementary ) description only ; by making repeated use of the same niathematical devices throughout the book, he has succeeded in avoiding some at least of the disadvantages consequent 011 this method of treating the subject. I n order to give ( ( as complete a view of the essential unity and interdependence of the various branches of the subject ) ) as possible there are introduced among the chapters on motion, sound, light, heat, electricity and magnetism into which the work is divided, articles on ( ( The Physical Universe ) ) , ( ( Methods of Physical Science ) ) , ( ( t h e Basis of Physical Belief)), efc.; while with the purpose of ((bringing into prominence the necessity for and the value of scientific hypotheses-a matter regarding which very hazy notions are only too common ) ) twenty-five pages are devoted to an account of the niolecular theory, a short chapter to the ether) , and another to the electromagnetic theory of light; and the theory of energy is illustrated not only by the article 011 thermodynamics but by a special chapter on ( related physical quantities ) , This latter chapter is of peculiar interest to the student of physical chemistry as it is largely owing to the successful application of the theory of energy to problems within his own province, that the importance of the methods involved has come to be generally recognized. It is probable however, that the leaders in this department of science would be the very last to give their assent to Dr. Peddie's proposition, that the basis of the second law of thermodynamics is-the molecular constitution of matter ! T h e author has apparently considered it beyond the scope of his (manual ) to give any account of the recent advances in those departments of Physics to which the attention of the chemist has

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been of late more particularly directed. In the chapters on electricity, for instance, the book has been brought up to date by an account of Hertz’s electric waves, but no mention is made of the work of Hittorf, Kohlrausch atid Arrhenius ’on the electrolysis of solutions ; Gr.otthus’s antiquated theory is given, and illustrated by a diagram ; and Faraday’s law is stated incorrectly. T h e subject of Osmosis is disposed of in twenty lines, dissociation and chemical combination in twenty-five, and though the sections on molecular theory begin with Lucretius and include an account of the vortex-atom, no mention is made of the important extension of that theory necessitated by the work on solutions carried out withiti the last ten years.

W. L a s h Miller. Notes on Qualitative Analysis, for Students of the Rensselaer Polytechnic Institute. W. P.Mason. 3 d Edition. Chm’calPiiblislzing Co. Easton, /’a. r896. Price 80 cents. ( ( T h e market is unquestionably much overstocked with books upon this subject, and the author’s only excuse for making the addition to the number is that it nieets the requirements of his own classes. There is small doubt that were it not for the expeiise of printing, every teacher of chemistry would use a text book made by himself with either pen or scissors, . . the attempt has been made in those notes to induce the student to make use of works .of reference. . It is hoped . . . what is here given may . . . create a desire to know rather than a desire to pass. It is to be regretted that the energies of the student are so often bent towards blindly following the words of the text. . . ) ) Is it in order to avoid this propensity on the part of his readers that the author, following a time-honored custom-has provided them, at the end of his volume, with such a convenient set of tables for complete analysis ? If so he may rest assured of a certain measure of success, for it is surely the general experience that this arrangement renders it difficult to persuade the ordinary ( student ) to read the words of the ( t e x t ) at all ! W. Lash Mille?*.

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Elektrometallurgie. pages.

octavo, viii and 3 9 3

GV.. Borclms.

Sccond Editiox.

Large r4

H. BYiLhn. Brazinschweig, r896.

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marks, bozind 16 mai-ks. T h e author has given a very complete account of the applications of electricity to the preparation of metals,-including electrical heating as well as electrolytic processes under this head. I n addition he has described many futile inventions, showing the faults in each. To the student this part of the book will be especially valuable. The training of the iiiodern chemist is singularly defective from a practical point of view. T h e difficulties, which a manufacturer has to meet, are rarely problems which have already been worked out in the books. For this reason, what the technical chemist needs is not a vast accunlulation of facts but a great deal of common-sense and an ability to apply general principles to particular cases. At present, men in the Universities make some organic preparations and then spend several years upon researches in which the aim is to isolate and analyze new conipounds, little or no attention being paid to improving the methods. It is doubtful whether such a training has any scientific value, but it is admirably calculated to unfit a man for making a success in life. There is a crying need for a book on theoretical organic chemistry which will do what this book of Borchers does for practical metallurgy. A student who should invent successively the different processes described by Borchers would find that he had acquired a remarkable power to solve problems. Passing from the student to the manufacturer, a single instance will sufficeto show the assistance which this book might be to mining companies. It is reported that the Anaconda Company has recently put in a large plant for the Thofehrn process, while we learn from Borchers that this process cannot be considered the latest or best method of obtaining copper electrolytically. I L7i/dcr D.Bancrofi. Les applications de 1’ glectrolyse la m6tallurgie. M , [J, L e Vewier. Small octavo, 5 6 pages. Gadhiev- b’illars et j l s . Paris. 1896. This pamphlet gives an elementary account of some of the newer processes in electrometallurgy. Thirty-six pages are devoted to the methods of obtaining copper by electrolysis with incidental remarks upon current, electromotive force, impurities and the question of cost. I n the remaining twenty pages reference is made to

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the electrolytic separation of nickel, zinc, antimony, tin, silver and gold. It is a pleasure to note that the author is familiar with the recent work published in German and English. bVilder D.Baizc?*oft.

The Gases of the Atmosphere. The Hisfovy of their Discovevy. bvilliant Ramsay. Small octavo, viii and 240 pages, with eight j o y fvaifs. The Macmillan Co. N e w York, r896. Price $2.00. T h e discovery of a new chemical element is from its very nature of more popular interest than most other pieces of pure scientific research even if the new element is alniost devoid of chemical properties, but aside from this fact, the appearance of this book by Professor Ranisay, written in popular style, is amply justified from the fact that it presents in detail a superb exainple of the methods of modern chemical investigation, as contrasted with the older and cruder methods. And it is very fitting that an historical account of the discovery of the other gases in our atmosphere should lead up to the main subject. T h e volunie is timely, and the matter clearly and logically treated. T h e first half of the book is taken up with the discoveries of carbon dioxid, nitrogen, oxygen, hydrogen, the composition of water and of the atmosphere, interspersed with short biographical sketches. Then conies the well known discovery of argon by Lord Rayleigh and Professor Ramsay. Perhaps the most interesting parts of the Iiook are the last chapters upon the physical properties of argon and its place in the scheme of the clieinical elements. Here are given the experiments and the reasons therefrom for the conclusion that it, like mercury, is monatomic, and that it is not a mixture of two elements. T h e fact is mentioned that the iiiost trustworthy value obtained for the ratio of the specific heats might allow the presence of about two per cent of diatoinic molecules, but upon the whole, the presumption is against such a mixture. As to the fact that thereseenis to be no fit place for argon in the periodic table the author brings forward the suggestion that it inay not be impossible that the presence or absence of intense chemical properties may have some effect upon the mass of elements as deter-

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mined by their weights, and refers to the experiments of Airy and of Landolt , A volume such as this, designed for readers not especially familiar with the technicalities of the science, has worth only when in the treatment of the subject there is combined with clearness and lucidity, accurate scientific methods of treatment, and the above work certainly falls into this class. I t is eminently scientific. T h e book is well printed on good paper and the portraits of the older chemists make it more attractive. One slight error was noticed. On page 2 2 5 the freezing point of chlorin is used for the boiling point, (- 102' for- 33.6') and this necessitates a numerical change in line one of the following page. G. W. Coggeshall.

Annuai& pozir I' ail 1897, publit! p a y le Bzweaii des Longitudes. h-18,v and 9r8 pages, with fwo JRagnetic Maps. Gauthier- Villays e t j l s , Paris. Price r.50fya?ics. I n addition to the great inass of physical and astronomical data which it contains every year the Aiznuaire of the Bureau des Longitudes for 1897 presents articles written by prominent men of science on Finance, Statistics, Geography, Mineralogy, etc., among which may be specially noted the following : Note upon the Proper Motion of the Solar System, by M. F. Tisserand ; Cathode Rays and Rontgen Rays, by M. H . Poincare ; T h e Epochs in the Astronomical History of the Planets, by M. J. Janssen ; Note on the Fourth Meeting of the International Committee for the Execution of a Photographic Map of the Heavens, by M. F. Tisserand ; Note on the Labors of the International Cornmission for Fundamental Stars, by M. F. Tisserand ; Address delivered at the Funeral of M. H. Fizeau, by M. A. Cornu ; Address delivered at the Funeral of M. Tisserand, by M M . H. Poincark, J . Janssen, and M. Loewy ; Investigations at Mont Blanc in 1896, by M. J. Janssen.