198 Josiah Willard Gibhs. 



future student of this subject, as the work of Lagrange did in 

 the case of ordinary mechanics. 



The greater part of the book is taken up with this general 

 development of the subject without special reference to the 

 problems of rational thermodynamics. At the end of the twelfth 

 chapter the author has in his hands a far more perfect weapon 

 for attacking such problems than any previous investigator 

 has possessed, and its triumphant use in the last three chapters 

 shows that such purely mechanical systems as he has been con- 

 sidering will exhibit, to human perception, properties in all 

 respects analogous to those which we actually meet with in 

 thermodynamics. No one can understandingly read the thir- 

 teenth chapter without the keenest delight, as one after 

 another of the familiar formulae of thermodynamics appear 

 almost spontaneously, as it seems, from the consideration of 

 purely mechanical systems. But it is characteristic of the 

 author that he should be more impressed with the limitations 

 and imperfections of his work than with its successes ; and he 

 is careful to say (p. 166) : " But it should be distinctly stated 

 that, if the results obtained when the numbers of degrees of 

 freedom are enormous coincide sensibly with the general laws of 

 thermodynamics, however interesting and significant this coin- 

 cidence may be, we are still far from having explained the phe- 

 nomena of nature with respect to these laws. For, as compared 

 with the case of nature, the systems which we have considered 

 are of an ideal simplicity. Although our only assumption is 

 that we are considering conservative systems of a finite num- 

 ber of degrees of freedom^ it would seem that this is assuming 

 far too much, so far as the bodies of nature are concerned. 

 The phenomena of radiant heat, which certainly should not be 

 neglected in any complete system of thermodynamics, and the 

 electrical phenomena associated with the combination of atoms, 

 seem to show that the hypothesis of a finite number of degrees 

 of freedom is inadequate for the explanation of the properties 

 of bodies." While this is undoubtedly true, it should also 

 be remembered that, in no department of physics, have the 

 phenomena of nature been explained with the completeness 

 that is here indicated as desirable. In the theories of electric- 

 ity, of light, even in mechanics itself, only certain phenomena 

 are considered which really never occnr alone. In the present 

 state of knowledge, such partial explanations are the best that 

 can be got, and, in addition, the problem of rational thermody- 

 namics has, historically, always been regarded in this way. In 

 a matter of such difiiculty no positive statement should be made, 

 but it is the firm belief of the j^i'esent writer that the prob- 

 lem, as it has always been understood, has been successfully 

 solved in this work ; and if this belief is correct, one of the 



