346 A CENTURY OF SCIENCE 



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 m 

 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 

 part of experimental physicists. Faraday had succeeded 

 in making liquid a number of substances which had 

 hitherto been known only in the gaseous state. His 

 method consists in evolving the gas from chemicals 

 placed in one end of a bent tube, the other end of which 

 is immersed in a freezing mixture. The high pressure 

 caused by the production of the gas combined with the 

 low temperature is sufficient to bring about liquefaction 



