OHM ON THE GALVANIC CIRCUIT. 431 



circuit is given by the quotient of the dift'erence between the 

 electrical forces existing at the extremities of the portion and 

 its reduced length. It is true, this rule was only advanced 

 above for the case in which the circuit nowhere divides into 

 several branches; but a very simple consideration, analogous to 

 the one then made, derived from the equality of the abducted 

 and adducted quantity of electricity in all sections of each pris- 

 matic part, is sufficient to prove that the same rule holds good 

 for every single branch in case of a division of the circuit. Let 

 us suppose that the circuit be divided, for instance, into three 

 bi'anches, whose reduced lengths are A, x', \"; and, moreover, 

 that at each of these places the undivided circuit and the single 

 branches possess equal electrical force, and consequently no ten- 

 sion occurs there, and designate by a. the difference between the 

 electrical forces at these two places ; then, according to the 

 above rule, the magnitude of the current in each of the three 

 branches is 



whence it directly follows that the currents in the three branches 

 are inversely as their reduced lengths ; so that each separate one 

 may be found when the sum of all three together is known. 

 But the sum of all three is evidently equal to the magnitude of 

 the current at any other place of the non-divided portion of the 

 circuit, for otherwise the permanent state of the circuit, which is 

 still constantly supposed, would not be maintained. If we 

 connect with this the conclusion resulting from the above con- 

 siderations, namely, that the magnitude of the current, and the 

 nature of each homogeneous part of the circuit, give the dip of 

 the corresponding straight line, representing the separation of 

 the electricity, we are certain that the figure of the separation 

 belonging to the non-divided portion of the circuit must remain 

 the same so long as the current in it retains the same magni- 

 tude, and vice versa ; whence it follows that the variability of 

 the current in the non-divided portion necessarily supposes 

 that the difference between the electrical forces at the extremi- 

 ties of this portion is constant. If we now imagine, instead of 

 the separate branches, a single conductor of the reduced length 

 A brought into the circuit which does not at all alter the magni- 

 tude of its current and its tensions, then, according to what has 

 just been stated, the difierence between the electrical forces 



