April 28, 1916] 



SCIENCE 



605 



though specific heats are discussed at some 

 length. 



Nearly all of the important physical chem- 

 ical relationships are expressed in mathemat- 

 ical form. The derivation of those relation- 

 ships which are based on thermodynamic prin- 

 ciples is given in an appendix. The differ- 

 ential equations are obtained by means of an 

 ingenious device termed a " Perfect Thermo- 

 dynamic Engine," which appears to be a modi- 

 fication or rather an amplification of the 

 familiar cyclic process. This method of 

 treatment should be of great service to those 

 students who lack the analytical turn of mind. 



As stated in his preface, the author has made 

 a radical departure from the classical treat- 

 ment of the second law of thermodynamics. 

 He has attempted to formulate this law in 

 mathematical form by means of elementary 

 kinetic considerations. The Carnot cycle has 

 been entirely omitted. The wisdom of this 

 procedure may be questioned, for the method 

 involving Carnot's cycle is both simple and 

 instructive. It brings out, moreover, the im- 

 portant fact that the second law is a principle 

 of that general character which is not depend- 

 ent upon the mechanism involved in a given 

 process, and that conversely it can give us no 

 information as to the character of the mechan- 

 ism involved therein. The necessity of sup- 

 plementing thermodynamics with results ob- 

 tained from the kinetic hypothesis is thus 

 almost self-evident, but it is well to avoid 

 leading the student to infer that simplicity is 

 one of the chief virtues of the statistical 

 method. The author's argument on pages 

 104 and 105 is not over clear. The two proc- 

 esses there described are not identical as to 

 initial and final conditions, nor is it apparent 

 how these two processes are related to each 

 other. The treatment given tends to confuse 

 the work of a Carnot's cycle with the second 

 law of thermodynamics, while it does not 

 clearly point out that the second law involves 

 an inequality, not an equality. The entropy 

 function, which is of fundamental importance 

 in the treatment of the second law, is nowhere 

 mentioned, nor is the Helmholtz equation 

 formulated. 



The subject of solutions is treated at length 

 and from a much more general point of view 

 than is commonly the case. Electrolytic solu- 

 tions, so far as aqueous solutions are con- 

 cerned, are fully treated. An excellent dis- 

 cussion is given of equilibria involving the 

 ions of water, including hydrolytic and indi- 

 cator reactions. 



In treating the phase rule the author intro- 

 duces the composition number, which is the 

 mol-fractions of the smallest number of molec- 

 ular species present in a given phase which 

 must be specified in order to fix the composi- 

 tion of the phase in question. The composi- 

 tion number of a system is defined as " equal 

 to the largest composition number of any of 

 the phases of the system." The last definition 

 leads to a certain restriction of the phase rule 

 which is avoided in the usual method of treat- 

 ment. This becomes clear in the case of a 

 two component system in which the three 

 phases present in equilibrium are all pure 

 substances, as, for example, in the system, 

 CaCO,, CaO, CO,. The author's definition 

 leads to the necessity of considering that one 

 of the phases contains all of the substances in 

 question, for example, that the vapor phase 

 contains CaCO, and CaO as well as C0„. 



In the discussion of the composition-tem- 

 peratiire diagram of solid solutions (p. 356), 

 the author has failed to give the interpreta- 

 tion of the field lying between the curves for 

 the solid and liquid solutions. A few other 

 minor corrections may be noted. The defi- 

 nition of the viscosity coefiicient (p. 51) is in 

 error; the maximum work is not clearly dis- 

 tinguished from the free energy (p. 110) ; the 

 terms "divariant" and "binary," "trivari- 

 ant" and "ternary," etc., are confused with 

 each other (p. 342). 



The book comprises 27 chapters and an ap- 

 pendix, and covers the entire field with the 

 exceptions noted above. It is only in excep- 

 tional instances that anything but the most 

 favorable criticism can be made. The author 

 has made an important contribution to the list 

 of texts available for the use of students. The 

 volume should find its way generally into the 

 chemist's library. In the hands of a compe- 



