PROFESSOR AT KONIGSBERG 117 



Clausius in the first instance attacked Helmholtz's derivation 

 of the law of the development of heat in electrical discharges 

 from the law of the conservation of energy. As stated in 

 a letter to du Bois-Reymond, he had not noticed that the 

 definition given by Helmholtz of the ' potential of a mass-in- 

 itself ' differed from the ordinary definitions. Helmholtz gives 

 the particulars of this dispute some years later in a letter to 

 Tait of March 17, 1867: 



'As to my discussion with Clausius, there was no essential 

 difference between us as to the mechanical equivalent, except 

 that Clausius takes the heat of the spark into account, while 

 I believed it might be neglected, and that I took the potential 

 of a body in itself as the sum of m a m b /r ab without excluding 

 the repetitions of the indices (ab) and (ba\ while Clausius fol- 

 lowed the other mathematicians in excluding these repetitions, 

 so that what he terms potential was only half as large as what 

 I defined as such. Substantially both were equally correct/ 



Helmholtz was able to refute the second objection raised 

 to his work with equal ease, that, namely, criticizing the 

 conclusions he deduced from the law of Riess, to the effect 

 that with different charges, and a varying number of similar 

 Leyden jars, the heat developed in each individual part of 

 the wire closing the circuit must be proportional to the 

 square of the quantity of electricity, and inversely proportional 

 to the surface of the jars. This charge does not really touch 

 Helmholtz, or the conclusions which he deduced under the 

 assumption of this law, since Clausius attacked the correctness 

 of the law of Riess in itself, and disputed its universal validity, 

 while Helmholtz said in his paper that the law was in need 

 of experimental confirmation. In regard to a misunderstanding 

 of a passage in Holtzmann's book, Helmholtz candidly admitted 

 his mistake, as appears from a letter to Ludwig. Clausius's 

 main attack on the work of Helmholtz was directed against the 

 proof of the proposition, that the principle of the conservation 

 of vis viva holds good only where the working forces can 

 be resolved into forces due to material points, acting in the 

 direction of the lines joining the points, while their intensity 

 depends solely upon the distance. Upon this Helmholtz 

 founds a long and important argument with which his epoch- 

 making thermodynamic work, the greatest achievement of the 



