OHM OX THE GALVANIC CIRCUIT. 48/ 



the atmosphere exercises a perceptible influence on a galvanic 

 circuit, or not, we will therefore enter into this case at greater 

 length. 



Since, according to § 12, the magnitude of the electric cur- 

 rent is given by the equation 



o du 



o = X w . -; — , 



ax 



d 76 



we have only in each separate case to obtain the value of -j— 



from the equation found for the determination of the electro- 

 scopic force, and to place it in the one above. Thus, for a cir- 

 cuit which has assumed its permanent state, but upon which 

 the surrounding atmosphere exercises no sensible influence, 

 according to § 22, 



where a represents the tension at the place of excitation, and b 

 the sum of the electroscopic forces immediately adjacent on 

 both sides of the place of excitation. We hence obtain 



This expression gives the magnitude of the current at each 

 place of the circuit ; but the law, according to which the altera- 

 tion of the current at various places of the circuit is effected, 

 may be rendered more easily intelligible in the following man- 

 ner. If, for instance, we differentiate the equation 



c, du 



dx 

 we obtain the equation 



^_ d'^u 

 dx~ dx^ ' 

 and by multiplying both together, 



w </ S „ ^d^u 



*-* d u d x^ 



If we now substitute for -——^ its value ^- u, as obtained from 

 d x^ 



d' u 



the equation = -r-^ — 0^ u, we have 



d x^ 



^ du 



dS ci ^ „, 



