408 OHM ON THE GALVANIC CIRCUIT. 



Consequently if that Avhich has been stated with respect to the 

 circuit of two members is to acquire a sense no longer subject 

 to any arbitraiy explanation^ this uncertainty must be removed. 

 The first fundamental law effects this in the following way : — 

 For since the state of the ring alone, independent of the time, 

 is regarded, each section must, as has already been stated, re- 

 ceive in every moment the same quantity of electricity from 

 one side as it gives off to the other. This condition occasions 

 upon such portions of the ring as have perfectly the same con- 

 stitution at their various points, the constant and uniform 

 change in the separation which is represented in the first figure 

 by the straight line F G, and in the second by the straight 

 lines F G and H 1. But when the geometrical or the physical 

 nature of the ring changes in passing from one of its compo- 

 nent parts to another, the reason of this constancy and uniform- 

 ity no longer obtains ; consequently the manner in which the 

 several straight lines are combined into a complete figure must 

 first be deduced from other considerations. To facilitate the 

 object, I will separately consider the geometrical and physical 

 difference of the single parts, each independently. 



Let us first suppose that every section of the part B C is m 

 times smaller than in the part A B, while both parts are com- 

 posed of the same substance ; the electric state of the ring, 

 which is independent of time, and which requires that every- 

 where throughout the entire ring just as much electricity be 

 received on one side as is given off from the other, can evi- 

 dently only exist under the condition that the electric trans- 

 ition from one particle to the other in the same time within 

 the portion B C is m times greater than in the portion A B ; 

 because it is only in this manner that the action in both 

 parts can maintain equilibrium. But in order to produce 

 this m times greater transition of the electricity from element 

 to element, the electrical difference of element to element within 

 the portion B C must, according to the first fundamental posi- 

 tion, be m times greater in the portion A B ; or when this deter- 

 mination is transferred to the figure, the line H I must sink m 

 times more on equal portions, or have an m times greater 

 " dip" than the fine F G. By the expression '' dip" [Gefdlle), 

 is to be understood the difference of such ordinates which be- 

 long to two places distant one unit of length from each other. 

 From this consideration results the following rule : The dips of 



