OF AN ELECTRIC DISCHARGE. 21 



to the second point of comparison between theory and expe- 

 rience, namely, to the case where the connecting wire remains 

 the same, but the magnitude of the battery and the quantity of 

 electricity distributed over it are changed. 



Here also the difficulty spoken of lies in our way. As we are 

 ignorant of the nature of a portion of the action of the discharge, 

 we are unable to say how this portion changes with the mag- 

 nitude of the battery and the quantity of electricity, and cannot, 

 therefore, from the effects observed at a particular place in the 

 circuit, conclude with security as to the totality of the action. 

 Only in regard to the heat developed in the continuous portion 

 of the connecting wire can we with certainty assume that every 

 alteration observed in any one portion is proportional to those 

 which take place in all other portions. 



Now when the connecting w4re has a great reduced length, it 

 may certainly be assumed that the greatest part of the total 

 action is applied to heating it; and in this case also, if a diver- 

 gence from the said proportionality should exhibit itself, the 

 differences caused by it will be comparatively small, so that 

 without any considerable inaccuracy we may assume that the 

 heating observed at any portion is proportional to the corre- 

 sponding total action. 



Now the total action, according to equations (18) and (19), 

 for an incomplete discharge is represented by 



^ . const., 



and for a complete discharge, such as took place in the expe- 

 riments of Riess, according to (18) and (20), by 



— __. const.; 



b 



and this is the exact expression which Riess established experi- 

 mentally for the heating in the connecting wire, inasmuch as 

 the equation (21) completely expressed*, is 



"-^uv <-' 



where a is a constant quantity f. 



* Pogg. Ann. vol. xlv. p. 23. 



t This coincidence between theory and experiment is also adduced by 

 Helmholtz (his Memoir, p. 43) ; the development of his formula is not however 



