474 OHM ON THE GALVANIC CIRCUIT. 



modilied by the cotemporaneous circumstances, must occur 

 from that which is pecuhar to the rapid current to that be- 

 longing to the state of perfect equilibrium. Here, then, is a 

 wdde field open for future researches. 



23. In cases where the permanent state is not instantaneously 

 assumed, as it usually is in dry piles, we should, in order to be- 

 come acquainted with the changes of the circuit up to that period, 

 proceed from the complete equation 



d u d- u b c , . 



because in this case we cannot consider -r- = 0, and the mera- 



dt 



be 

 ber — u must either remain in it, or be removed from it, accord- 

 ed 



ing to whether it is considered worth while to take the influence 



of the atmosphere on the circuit into consideration or not. If 



be 

 we again place, as in the previous paragraph, /3^ = — , and, 



also — = x', the preceding equation changes into the fol- 

 7 



lowing: ^^-^' /^ R-.y\ 



dt~ \dx''~^ ")' 



and we immediately perceive, that on admitting j3 = 0, the 

 action of the atmosphere is left out of the question. 



In the present case u represents a function of x and t, which, 

 however, in pi'oportion as the time t increases, becomes gra- 

 dually less dependent on t, and at last passes over into a mere 

 function of x, which expresses the permanent state of the cir- 

 cuit, with the nature of which we have already become ac- 

 quainted. If we designate this latter function by «<', and place 

 u = u' + V, then v is evidently a function of a; and t, which indi- 

 cates every deviation of the circuit from its permanent state, 

 and consequently after the lapse of a certain time entirely dis-l 

 appears. If we now substitute u' + v for u in the equation (#),] 

 and bear in mind that u' is independent of t, and of such] 

 nature that 



dx^ r- J 



the equation 



d V , /d- V „. \ , ^ , 



