Electric Residue in the Leijden Jar. 31S 



generated of our being able to arrive at a strict law^ the coinci- 

 dence of which with the observations will render probable the 

 hypotheses on which the said law is founded. 



Let us in the first place determine v^. 



In fig. 3 let ab represent the quantity of electricity Qq=L(j 

 communicated at the beginning ; b b' b" b'" . . . c the curves of 

 the disposable charges L^ observed at numerous points, lying 

 near each other, and referred to the abscissa ad, which is the 

 representant of the time. This is reckoned from the moment 

 when the jar was charged, and we have therefore after the times 

 ?j, t^, tg, the disposable charges L,, L^, Lg. After the time T, 

 which is expressed by the length ad in the figure, the jar will be 

 discharged, consequently a quantity of electricity Lx correspond- 

 ing to the line dc will have been removed. 



At the end of the times i' = da', i" = dd", i"'=dd"', &c., the 

 quantities p', p", p'", &c., as concealed residues, make their ap- 

 pearance, the sum of which is 



p' + p" + p>i'+ ... =p. 



We know that we have recovered the quantity hf + p from 

 the jar, and hence conclude that what is wanting to inake up 

 the original charge Qq, has been lost in the air during the time 

 of operation ; calling this last portion V, we have 



V = Qo-(Lt + /o). 



If in the figure ef-=p, we have/<?=V. 



This total loss must now be distributed over the times in which 

 it has taken place ; more especially for the determination of r^, it 

 is necessary to inquire what portion vt has been lost up to the 

 particular times t, at which the disposable charge of the jar has 

 been measured. 



This charge is constantly proportional to the loss of electricity, 

 consequently 



dv^=-u\ndt ; 



and the integration of the expression to the right between the 

 limits ^ = and t = t would, if we could perform it, and knew 

 the value of a and the law of the cui've L^, at once give us the 

 magnitude of v^. 



Now, in the first place, it is manifest that the constant « 

 which has reference to the loss of electricity in the case of a 

 Leyden jar, cannot be directly determined ; secondly, that we 

 have no hope of finding the law of the curve expressing the 

 disposable charges, before we know the law of the residue in 

 the jar. Inasmuch as v^, L^, and r^ are all dependent on each 

 other, the solution of the problem appears only possible by find- 



