466 OHM ON THE GALVANIC CIRCUIT. 



dy (j^y - a! + cj. 



If we now integrate the first of the two preceding expressions 

 from y = to y = \, we then obtain for the whole quantity of 

 electricity contained in the part P, 



"""' [21,^' + "'^J ' 

 in the same manner we obtain, by integrating the second ex- 

 pression from ?/ = A to ?/ = A + X', for the entire quantity of 

 electricity contained in the portion P' 



x' co'2 [A (x'^-^ + 2 X A') - a' A' + C A'I . 



But the sum of the two last found quantities must, in accordance 

 with the above-advanced fundamental position, be zero. We 

 thus obtain the equation required for the determination of the 

 constant c, and it only remains to be observed that A and A' are 

 the reduced lengths corresponding to the portions P and P'. 



We have hitherto always tacitly supposed only positive ab- 

 scissae. But it is easy to be convinced that negative abscissce 

 may be introduced quite as well. For let — y represent such 

 a negative reduced abscissa for any place of the circuit, then 

 L — y is the positive reduced abscissa pertaining to the same 

 place, for which the general equation found is valid; we ac- 

 cordingly obtain 



u = j-{'L — y) — + c 



u= —j-y-{0-A) + c. 



But O — A evidently expresses, if regard be had to the general 

 rule expressed in § 16, the sum of all the tensions abruptly 

 passed over by the negative abscissa, whence it is evident that 

 the equation still retains entire its former signification for ne- 

 gative abscissae. 



19. If we imagine one of the parts of which the galvanic 

 circuit is composed to be a non-conductor of electricity, i. e. 

 a body whose capacity of conduction is zero, the reduced length 

 of the entire circuit acquires an indefinitely great value. If we 

 now make it a rule never to let the abscissae enter into the non- 

 conducting part, in order that the reduced abscissa y may con- 

 stantly retain a finite value, the general equation changes into 

 the following : 



J 



