222 Professor Joseph Larmor [May 1, 



pletion of these fundamental principles of the general science of 

 Energetics. When the illustrious originator of these ideas died in 

 1832 at the age of 36 he was in possession of the material to complete 

 the train of essential principles himself. 



Thus far Ave have secured a work-function iv (available energy) 

 for the applied forces at each temperature t, of form determinable by 

 direct experiment. If such a function were known for every tem- 

 perature, knowledge of the mechanical energy relations of the system 

 would be complete. Thomson accordingly proceeds to connect these 

 functions for adjacent temperatures by means of a Carnot cycle. In 

 fact, lie shows how to construct iv as a function of both the con- 

 figuration and the temperature, so that the same function shall, for 

 each constant temperature, rej^resent the energy then available for 

 work. 



The two functions, total energy e and work of available energy iv, 

 on which the complete science of Energy is thus founded, are naturally 

 to be compared with the two functions, energy U and entropy S, 

 Avhich were made fundamental by Clausius in the very same month, 

 April 1855 — the tendency of the entropy of a self-contained system to 

 increase being his mode of exact expression by Thomson's principle 

 of dissipation. In fact, the distinction between the two methods is 

 that Thomson's function iv refers primarily to a system fed with heat 

 so as to remain at constant temperature, while Clausius' function S 

 refers primarily to an isolated system. 



The principal operations of chemistry and physics are performed 

 at constant teniperature ; thus it is Thomson's function iv that is 

 fundamental in the modern science of Energy, having been re-intro- 

 duced by Willard Gribbs as " the characteristic function at constant 

 temperature, and by Helmholtz as "free energy." The entropy is 

 simpler to describe, and also to work with, except when the operations 

 are isothermal ; on the other hand, the " free energy " is a direct 

 physical conception connecting up heat-energy in line with all other 

 types of available physical energy, and thus transforming thermo- 

 dynamics into the universal science of the relations of the statical 

 transformations of Energy, namely. Energetics. 



The function entropy seems to have been never employed in Lord 

 Kelvin's investigations. As may be inferred from the above, it did 

 not lie directly in his line of thought, which concerned itself with the 

 physical entities energy and work. The idea of entropy is so directly 

 suggested by his principle of dissipation, and the early mastery of the 

 Carnot-Clausius equation /(<^H/T) = for a reversible cycle, in its 

 widest form, which is shown in his theory of thermoelectric phenomena, 

 that it could hardly have been strange to him ; conceivably he never 

 directly formulated it, because he had, in fact, developed a more 

 directly physical scheme. 



It is customary, after Thomson's own example, to call the relation 



