at 



288 M. A. F. Sundell on Galvanic Induction. 



disappears, and the whole induction is 



. f (cos 6 cos j , 



jj ** 1# .... (2) 



This expression represents the induction in the first moment of 

 the phenomenon. In order to obtain the electromotive force for 

 the whole duration of the induction, the function under the 

 signs of integration must be multiplied by a function of r, viz. 

 br } in which b is a constant, whence results 



■wffi"^ 1 '**. (?) 



The axis of the ^-coordinate may be taken in the negative direction 

 through the inducing element ds ; and the ^-coordinate may be 

 reckoned negative parallel to the direction of the current in ds. 

 Integrating for ds v the direction along the secondary circuit is 

 taken opposite to that of the primary current. If It is the radius 

 of the primary circuit, R 2 that of the secondary circuit, and x } y,z 

 are the coordinates of ds i} we have 



r=\/R 2 + R? + ^ + 2%, 



cos0= > 



r 



cos O l ds l — dy } 



and 



C* k oos cos k k cc 



abi 1 1 ds ds l = Habi \ 1 -g dy ds. 



(*) 



Observing that for two elements ds i of equal length and in a 

 symmetrical position to the ys'-plane the function xdy has the 

 same sign, and that each single element of the primary circuit 

 has the same position relative to the secondary circuit, we can 

 write expression (4) thus : — 



triwr^Bw p__v^ F?^ , . (5) 



J-Ri r J-Ri (R 2 + Rf + ^ + 2K2/)l 



In the above experiments the windings of the coils may be 

 regarded as circles with their centres on the 5--axis and their 

 planes parallel to the ^-plane. Expression (5) can, of course, 

 be used for calculating the intensity of the induced electromo- 

 tive force according to different values of R, R L , and z. The 

 spirals in a coil have not quite equal radii; nevertheless the 

 results of the calculation will be accurate enough for comparison 

 with the observations if a mean value for the radii be used. As 



