472 OHM OX THE GALVANIC CIRCUIT. 



already arrived at its permanent state, and we have treated it at 



a length which it merits from the abundance and importance of 



the phaenoraena connected with it. However, not to let even 



here the other circuits pass entirely unnoticed, we will briefly 



indicate the method to be pursued for the most simple case, and 



thus point out the path to be followed, although only at a 



distance. 



If it is intended to take into consideration the influence of 



be 

 the atmosphere on the galvanic circuit, the member — « must 



d'^ u 

 be added to the member x -^— g of the equation (a) in § 11, we 



then obtain for the circuit which has acquired a permanent 



state, for which -y- = 0, the equation 



d'^ u be 



or if we put — = /3-, 

 xw 



d'^ u -, 



The integral of this equation is 



u=c.e^^ + d . e-^^, 



where e represents the base of the natural logarithms, and c, d 

 any constants to be determined from the other circumstances of 

 the problem. 



If we now call 2 / the length of the entire circuit, and fix 

 the origin of the abscissae in that place of the circuit which 

 is equidistant from the point of excitation ; if, further, we de- 

 signate by a the tension existing at the point of excitation, wej 

 obtain 



a= {c-d) (e'^'-e-^O- 

 If we write the previously found equation thus, 



u = {e-d) e'^-^ + d{e^'' + e"^-"), 

 and substitute for c — d, the value just ascertained, we have 



ft pP>^ 



HIT + '^ («'"' + e-l"-). 



e^'-e 



If we now suppose for the determination of the other constant, 

 that the sum of the two electroscopic forces, situated at the 



