96 Prof. E. Edlund on Galvanic Resistance as 



flows through d e. Tbe electromotive force of the electromotor 

 we will name E ; the principal resistance of it, R ; and the in- 

 tensity of the undivided current, J. We have then, by Kirch- 

 hofF's laws for the division of the current between several 

 conductors, 



E — + s) = RJ + iV, 



E — (iv + s + <r) = RJ + ii(r + p), 

 and 



J=i+i l , 



From this we get 



Er — R<x — r (w 4- s 4- cr) 

 and 



1 2nr + r 2 + Rp + rp ' ' ' * V } 



(3) 



. = E(r + /3 ) + Rq-— (r + p)(w + s) 



2Ur + r* + Rp + rp ' ' 



and consequently 



. . _ Ep + 2na + r<T-pw-ps m 



x ~ 2Br+7* + Kp+rp ' ' * W 



The difference i — 4 determines the position of equilibrium 

 of the magnetometer-needle when the liquid is at rest. But 

 when the liquid is set in motion, s is changed into s + ft, s + a 

 into s + o- + /£?!, and w into w + ir. Denoting the parts of the 

 current which flow through the liquid columns c d and d e re- 

 spectively by ijj and i //n we obtain in the same manner 



(5) 

 (6) 



(?) 



. Er + R/3 — Ro— R/3,— r(w + 7r + s + <r + /3 / ) 

 * //; ~ 2R?* + r 2 + Rp + r / 3 



and 



. _ E(r + p) + Ro- + Rff / — R/8 + (r + /o)(tfl + 7r + s + /8) 



*" 2Rr + r 2 + Rp + rp ~> 



whence l N — i Ui ~ 



Ep + 2Rj3 / -2 1 Rl3 + 2Ro- + ro- + rl3 / -rp-p(w + 7r + s + /3) 

 2Rr + ?' 2 + Rp + r/3 .' 



Subtracting the first difference (4) from the last (7), we 

 obtain the expression for the deflection which arises solely from 

 the fact that the polarization is altered by the motion of the 

 liquid. In this way we get 



Y" w) K j) 2Rr + r> + Hp + rp ' ' ( 8 > 



The value of p, however, is so inconsiderable that pir, p@, 

 Rp, and rp can be neglected. The deflection u, which arises 

 only from the alteration of the polarization by the motion of 



