to the Electromagnetic Units of Electricity. 311 



Whence a' =2a (l-\ Q>tjf). 



a" =3a (l-i(^i) 2 > 

 a'"=4tf (l-t(^) 2 > 

 a»»=5a (l-(50 2 > 



Now a , a', a", a" 1 , and a"" are the values of 8 with 1, 2, 3, 4, 

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

 provided the discharges be simultaneous. 



Hence the correction, A, has the values 0, J(^i) 2 ; i(^i) 2 > 

 | (bh) 2 , and (frO 2 with 1, 2, 3, 4, and 5 discharges. The 

 value of ^ is about one fifth of a second, and hence (bt l ) 2 = 

 •009 nearly. The values of A are then 0, '0011, *0030, '0056, 

 and -0090. 



This correction is quite uncertain as the time t x is un- 

 certain. 



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 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 

 reading was taken before the connexion 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 

 the other. This will be the same for 1 or 5 discharges. 



From ten to twenty observations 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. 



Before and after each series the times of vibration, t and T, 

 and the readings, j3 and «, were taken. The logarithmic 

 decrement was observed almost daily. 



