316 M. R. Kohlrausch's Theory of the 



iug at once the laws of all three curves. But assuming even 

 that we possessed this gift of divination, we should nevertheless 

 find the differential equation so complicated that its integration 

 is scarcely to be thought of. 



Under such circumstances we must make a virtue of necessity, 

 and in seeking to determine v^, we must take, instead of the 

 actual law of the curve of the disposable electricity, the curve 

 itself. p^ 



The expression 1 L <// 



Jo 

 is nothing else than the superficial area bounded by the curve, 

 the abscissa, and the ordinates at the beginning and end of the 

 time t, and we see immediately that the loss of electricity during 

 the respective times 



tj Iq, tg *1> ^3 'sj &c., 



which latter are represented in the figure by the portions aa', 

 ffl'a", ft"a"', &c. of the abscissa, are proportional to the spaces 



ab b'a' = {\dt =/i ; a'b'b"a" = (\dt =f^, &c. 



Jo Jt, 



Denoting by F the total surface abb'b" . . .cd, so that 



then we have aF as the loss of electricity up to the first discharge 

 of the battery. In like manner, the loss in the second operation 

 is proportional to the surfaces 



dykl'=f; d'ff"d"=f',8cc. 

 Denoting the entire sum of these spaces /' +/" +f" + . . . by 

 <}>, then the total loss of electricity during the second operation 

 will be expressed by a^. 

 Hence as 



V=«F + «(/>, 

 we obtain immediately 



V 

 F + </) 



V is given to us by observation, and thus our knowledge of a 

 depends solely on our knowledge of F and /. 



If the measurements made at the times ^„ tc^, t^, &c. lie so 

 nearly together that the portion of curve which they limit may 

 be regarded as a straight line, the surfaces /jj/g, &c. become 

 trapeziums, and we have 



