476 



OHM ON THE GALVANIC CIRCUIT. 



the present case gives, when 2 I designates the length of the cir- 

 cuit, and the origin of the abscissae is placed in its centre*. 



sin ^-^fydy) 



4/2 



{2i — \)Ttx 



p {2i-l)7:y 1 



where the sums must be taken from i = 1 to i = co , and the 

 integrals from y=— lioy=+l. If we now substitute in 

 this equation for fx its value — v!, whereby according to our 

 supposition in the preceding paragraph, if a represents the ten- 

 sion at the place of contact, 



and then integrate, we obtain, since between the indicated 

 limits 



i-Try e^'J — e~^'i , aivlcosi-Tr 



I 



, /» . ZTry e'^ ■' —e '"'' , air i cos t w 



and 



e>y —t 



2 V e^^-e-^' 



t*"' — e~^' 2 I 



for the determination of v the equation 



cos -^ ~ — - . dy = 0, 



V = a . e z 



and, lastly, since u = u' + v 



(. i-TT (I -\- X) / 8 -2 A 



z -K sm -f^ -' y'^ \ 



Uief^'-e-'^'^) , _^/«2< ^ 



(. iiril + x) _.'-»/« A 



which equation, for /3 = 0, i. e. when it is not intended to take 

 into consideration the influence of the atmosphere, passes into 



-/TTT, 



u — -zr-,x-\a2,[^- sm — ^-' — -.e >C 1. P ^ 



21 \nr I F^~^^/ 



It is easily perceived that the value of the second member to 

 the right in the equations which have been found for the deter- 

 mination of u, becomes smaller and smaller as the time increases. 



* Sec Joanial de I'Ecule Pohjiechnlque, cap. six. p. 53. 



