OHM 0.\ THE GALVANIC CIRCUIT. 411 



L K' are directly proportional to the lengths of the parts A B, 

 B C and C D, and inversely proportional to the products of the 

 conductibility and section of the same part, consequently the 

 relations of the lines G F', I H' and L K' to each other are 

 given. Further, that G F + I H' + L K' = G H - K I + (D L 

 — A F = L M) is also known, as the tensions represented by 

 G H, K I and D L — A F are given. From the given relations 

 of the lines G F', I H', L K' and their known sum, these lines 

 may now be found individually ; the figure F G H I K L is evi- 

 dently then entirely determined. But the position of this figure 

 with respect to the line A D remains from its very nature still 

 undecided. 



If we recollect, that proceeding in the same direction AD, the 

 tensions represented by G H and DL — AF orLM indicate 

 a sudden sinking of the electric force at the respective places of 

 excitation, that represented by I K on the contrary a sudden rise 

 of the force ; and that tensions of the first kind are regarded and 

 treated as positive quantities, while tensions of the latter kind 

 are considei'ed as negative quantities, we find the above ex- 

 ample lead us to the following generally valid rule : If we divide 

 the sum of all the tensions of the ring composed of several parts 

 into the same rmmber of portions which are directly proportional 

 to the lengths of the parts and inversely proportional to the pro- 

 ducts of their conductibilities and their sections, these portions 

 will give in succession the amount of gradation which must be 

 assigned to the straight lines belonging to the single parts and 

 representing the separation of the electricity ; at the same time 

 the positive sum of all the tensions indicates a general rise, on 

 the contrary the negative sum of all the tensions a general depres- 

 sion of those lines. 



I will now proceed to the determination of the electric force 

 at any given position in every galvanic circuit, and here again 

 I shall lay down as basis fig. 3. For this purpose let a, a', a" 

 indicate the tensions existing at B, C, and between A and D, 

 so that in this case also a and a" represent additive, c' on the 

 contrary a subtractive line, and A, X', x" any lines which are 

 directly as the lengths of the parts A B, B C, and C D, and in- 

 versely as the products of the conductibilities and sections of 

 the same parts ; further, let 



a + a' + a" ~ A 



