to the Electrostatic Unit of Electricity. 295 



a, 



a' n b i =a' i b- 2 +v;-\-2o a'bGosb(2t / -t') ; sin b(2t l -\ r t")=^Rmb(2t+t') 

 a"'*b*=a*VS + v; + 2v a"bcosb(St / + t")- m-ib(3t l + t'")=^sinb(3t—t'") 



CI 



etc. etc. 



When t is small compared with the time of vibration of the 

 magnet, we have very nearly t'=—\t l \ t"=—t n t"'=—^t / 

 etc. 



a' 2 =2« a (l+ cos bt)=Aa*{l-\{bty) 



a'" 2 =]6a*(l-i(bty) 

 a""" -■lba \\-2{bty) 

 I «"""= 



AVhence 



a' =2a (\-i)bty) 

 a" =3a (l-my) 



a"'=4a a (\-my) 



a""=5a (l- W) 



ISTow « , a', a'\ a'" and a //r/ are the values of d with 1, 2, 3, 

 4 and 5 discharges and a , 2a , 3a , 4« and 5a are the values 

 provided the discharges were simultaneous. 



This correction is quite uncertain as the time, t n is uncer- 

 tain. 



In assuming that the impulses were equal we have not taken 

 account of the angle at which the needle stands at the second 

 and subsequent discharges, nor the magnetism induced in the 

 needle under the same circumstances. One would diminish 

 and the other would increase the effect. I satisfied myself by 

 suitable experiments that the error from this cause might be 

 neglected. 



The method of experiment was as follows : The store of 

 electricity was contained in a large battery of Leyden jars. 

 This was attached to the electrometer. The reading of the 

 potential was taken, the handle of the discharger was turned 

 and the momentary swing observed and the potential again 

 measured. The mean of the potentials observed, with a slight 

 correction, was taken as the potential during the time of dis- 

 charge. This correction came from the fact that the first read- 

 ing was taken before the connection with the condenser was 

 made. The first reading is thus too high by the ratio of the 

 capacities of the condenser and battery and the mean reading 

 by half as much. Hence we must multiply d by 1 — F where 

 F = *0013 for first ball of condenser and *0008 for other. This 

 will be the same for 1 or 5 discharges. From 10 to 20 obser- 

 vations of this sort constituted a set, and the mean value of -, 



which was calculated for each observation separately, was 

 taken as the result of the series. 



