20 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



sumed. In many cases the two latter sparks indeed disappeared 

 totally, inasmuch as the discharge did not take place until the two. 

 balls of the apparatus were in contact*. Hence one new spark 

 had made its appearance, and for this two old ones had disappeared, 

 which justifies the expectation that a lessening of the quantity 

 of work consumed, and a corresponding increase of heat would 

 be the result. It was, in point of fact, in these cases that Riess 

 observed the increased temperature of the connecting wire. We 

 thus see that in explaining these phaenomena it is not necessary 

 to assume that the work consumed by a spark is very small ; and 

 to me it appears that the experiments do not furnish ground for a 

 safe conclusion as to the magnitude of the same quantity of work. 



Although it thus appears that, on account of the unknown 

 quantities w^hich enter into the production of the total action, it 

 is impossible to demonstrate an exact quantitative coincidence 

 between the equation (21) and our principal proposition, we 

 could perhaps try the inverse method, and assuming both, and 

 their connexion with each other, to determine the said unknow'n 

 quantities, or at least their sum ; indeed the form of the equa- 

 tion seems to invite such an effort. It must however be remem- 

 bered that the equation itself, being an empirical one, must not 

 have absolute accuracy ascribed to it, as is also shown by the 

 numbers of Riess. In two series of experiments in which he 

 introduced w ires of different lengths and thicknesses, thus chan- 

 ging only the quantity / in the expression on the right side of 

 equation (21), he determined from each observation the con- 

 stant b. The values so found diverge from each other in the 

 first series between 0*01358 and 0*01101, and in the second 

 series between 0*00000926 and 0*00000840 1; and although these 

 differences, considering the great variety of the wires introduced, 

 cannot be regarded as considerable, still they are worthy of re- 

 gard, inasmuch as a certain regularity is observed in them. In 

 both series, when the reduced length I of the wire is increased, 

 the corresponding worth b is in general smaller. 



We will therefore follow this subject no further, and turn now 



* Pogg. Ann. vol. xliii. p. 79. 



\ Pogg. Ann. vol. xliii. pp. 68 and 73. The great difference between the 

 numbers of the first and second series is due to a difference in the unit made 

 use of. 



