414 OHM ON THE GALVANIC CIRCUIT. 



reduced abscissce and represent them generally by y, we obtain 

 XY = ^., 



-X'Y' = ^.y-a 



X"Y" = ^.y- {a + a>), 



and it is evident that L is the same in reference to the whole 

 length A D or F M as ?/ is to the lengths F X, F X', F X", on 

 account of which L is termed the entire reduced length of the 

 circuit. Further, if we consider that for the abscissa corre- 

 sponding to the ordinate X Y the tension has experienced no 

 abrupt change, but that for the abscissa corresponding to the 

 ordinate X' Y' the tension has experienced the abrupt changes 

 a, a'; and if we represent generally by O the sum of all the 

 abrupt changes of the tensions for the abscissa corresponding 

 to the ordinate y, then all the values found for the various ordi- 

 nates are contained in the following expression : 



But these ordinates express, when an arbitrary constant, cor- 

 responding to the length A F, is added to them, the electric 

 forces existing at the various parts of the ring. If therefore we 

 represent the electric force at any place generally by u we obtain 

 the following equation for its determination : 



u = j-y-0 + c, 



in which c represents an arbitrary constant. This equation is 

 generally true, and may be thus expressed in words : The force 

 of the electricity at any place of a galvanic circuit composed of 

 several parts, is ascertained by finding the fourth proportional 

 to the reduced length of the entire circuit, the reduced length of 

 the part belonging to the abscissa, and the sum of all the tensions, 

 and by increasing or diminishing the difference between this quan- 

 tity and the swn of all the abrupt changes of tension for the 

 given abscissa by an arbitrary quantity which is constant for all 

 parts of the circuit. 



When the determination of the electric force at each place of 

 the circuit has been effected, it only remains to determine the 

 magnitude of the electric current. Now in a galvanic circuit of 



