224 Professor Joseph Larmor [May 1, 



entropy in the theory of equihbrium, and can be extended more 

 naturally to those dynamical problems in which motions take place 

 under the condition of constancy of entropy of the elements of a 

 solid, . . . just as the other method can be more naturally extended 

 to dynamical problems in which the temperature is constant." Gibbs 

 then refers back to a previous note explaining the wider generality of 

 his own method : its most salient feature is, however, the far wider 

 development, by its author, into the doctrine of the chemical poten- 

 tials of the constituent substances. 



As throwing- light on the stage at which scientific thought had 

 arrived at the time Thomson was thus formulating the general science 

 of Energetics, the following quotation from Helmholtz's important 

 lecture,* ' On the Interaction of Natural Forces ' — delivered first at 

 Konigsberg, February 7, 1854, and in which he was the first to refer 

 the replenishment of solar heat to gravitational shrinkage — is perti- 

 nent to our history. " These consequences of the law of Carnot are, 

 of course, only valid provided that the law when sufficiently tested 

 proves to be universally correct. In the meantime there is little 

 prospect of the law being proved incorrect. At all events we must 

 admire the sagacity of Thomson, who, in the letters of a long-known 

 little mathematical formula which only speaks of the heat, volume 

 and pressure of bodies, was able to discern consequences which 

 threatened the universe, though certainly after an infinite period of 

 time, with eternal death." 



Later, in 1861, in writing of the constant surprises that arose in 

 his work on acoustics, and the impression borne in upon him that new 

 results develop themselves in the mind according to laws of their own, 

 so that it seems to be hardly things essentially of his own invention 

 that he is reporting, Helmholtz suggests that " Mr. Thomson must 

 have found the same thing in his own work on the mechanical theory 

 of heat." t 



The end of this early period of pure scientific activity came when 

 Thomson's enthusiastic encouragement of the costly practical enter- 

 prise of Atlantic submarine telegraphy entangled him in the solution 

 of a whole class of practical problems, which only he could undertake, 

 and which constituted one of the most strenuous tasks of his career. 

 After the first cables had failed, in 1857-8, through wrong methods 

 of working which entirely misconceived the situation, Thomson was 

 given a free hand to make the most, under these expensive conditions, 

 of the problem — in fact to get signals transmitted at profitable speed 

 through a conductor, which, as he insisted, merely diffused electricity 

 along it as heat travels along a bar, instead of conveying it in com- 

 pact pulses or waves. Here he succeeded by following out the pre- 



* English translation (by Tyndall), 1. 1873, p. 172. 

 t Life, p. 205. 



