206 Prof. E. Edlund on the 



of action in the former case. The acceleration acquired 



■pi 

 amounts to only — . On multiplying by the mass pn, we 



shall have the total electromotive force equal to nE. Thus the 

 electromotive force can be expressed by wE, Avhether the cur- 

 rent be strong or weak. 



If r signifies the totality of the principal resistance, and if 

 i designates the intensity of the current, the total resistance 

 will be ri — which in this case signifies nothing else but the 

 counterpressure, upon the unit of section, opposed by the 

 resistance to the propagation of the current. We shall there- 

 fore have nri for the total value of the counterpressure upon 

 a surface of contact of n units magnitude. Designating by 

 L the total length of the circuit, we thus obtain the equation 

 of motion, 



L -j-=nE— nan* j 



whence 



As soon as the current has become constant we have 

 ._E 

 r 



It follows from this that the electromotive force represented 

 in Ohm's formula is independent of the extent of surface of 

 the electromotor — which, we know, is conformable to expe- 

 rience. 



(c) Let us imagine a closed galvanic conductor, of which 

 the length is I and the section everywhere equal to a, com- 

 posed of the same material throughout its length, and passed 

 through by a constant current of intensity i. If 8 is the mass 

 of aether in motion per unit of volume, and h the velocity of 

 the motion, we shall shall have i=ahh. To calculate the me- 

 chanical work done by the current during the unit of time, we 

 shall first consider a current-element comprised between two 



* The total length L of the circuit being equal to the sum of all its parts 

 L, l 2 , l 3 , l v &c, and these having respectively the sections a v a 2 , « 3 , « 4 , &c, 

 the total volume of the conductor will be aj x + a 2 l 2 +a 3 l 3 + &c. By mul- 

 tiplying this sum by the mass of aether 8 in the unit of volume, we obtain 

 the entire mass of the aether in motion. Now, if the augmentation of the 

 velocity during the time dt is respectively dh x , dh 2 , dh 3 , the total mass of 

 aether will receive, during the time in question, an augmentation of the 

 quantity of motion which will be expressed by (aJ l dh 1 + a,J 2 dh 2 +a 3 l 3 dh 3 

 + • • . )S. Now da 1 8/ij=LS« 2 M 2 =8a 2 8h 3 =bi\ whence, consequently, the 

 total augmentation of the quantity of motion of the tether will be ~Ldi. 



