L. Page — A Century's Progress in Physics, 313 



dition the size of the degree indicated by the mercury 

 thermometer. This scale, which is equivalent to that of 

 the ideal gas thermometer, was used subsequently by 

 Eowland in his exhaustive determination of the mechan- 

 ical equivalent of heat by an improved form of Joule's 

 method. He found different values for different ranges 

 in temperature, showing that the specific heat of water 

 is by no means constant. Since then electrical methods 

 of measuring this important quantity have been used to 

 confirm the results of purely mechanical determinations. 



The definition of a new quantity, entropy, was found 

 necessary for a mathematical formulation of the second 

 law of thermodynamics. This quantity, which acts as a 

 measure of the unavailability of heat energy, was given 

 a new significance when Boltzmann showed its connec- 

 tion with the probability of the thermodynamic state of 

 the substance under consideration. If two bodies have 

 widely different temperatures, a large amount of the 

 heat energy of the system is available for conversion 

 into mechanical work. From the macroscopic point of 

 view this is expressed by saying that the entropy is small, 

 or if the motions of the individual molecules are taken 

 into account, the probability of the state is low. The 

 interpretation of entropy as the logarithm of the thermo- 

 dynamic probability has thrown much light on the 

 meaning of this rather abstruse quantity. Gibbs's 

 "Elementary Principles in Statistical Mechanics" treats 

 in detail the fundamental assumptions involved in 

 this point of view, its limitations and its consequences. 

 In his "Equilibrium of Heterogeneous Substances" 1 

 he had already extended the principle of thermal equi- 

 librium to include substances which are no longer homo- 

 geneous. The value of the chemical potential he intro- 

 duced determines whether one phase is to gain at the 

 expense of another or lose to it. It is unfortunate that 

 the analytical rigor and austerity of his reasoning com- 

 bined with lack of mathematical training on the part of 

 the average chemist, delayed true appreciation of his 

 work and full utilization of the new field which he 

 opened up. 



Liquefaction of Gases. — Meanwhile the problem of 

 liquefying gases was attracting much attention on the 



1 J. W. Gibbs, Trans. Conn. Acad. Arts and Sci., 3, 108 and 343. Abstract 

 by the author, this Journal, 16, 441, 1878. 



