Galvanic Pile, and Electromotive Forces. 509 



and afterwards during exactly as long a time at the distance 

 r + p, the molecule will receive during the total time a quan- 

 tity of motion equal to 



at o . a*o _ ^ , n(h + l) , 



where higher powers of p may be neglected, because it is as- 

 sumed that p is an extremely small quantity. We gather from 

 this that the attraction which during the time 2t tends to 

 bring the molecule nearer to the contact-surface is greater if 

 the molecule is during one half of the time at the distance 

 r—p, and during the other half at the distance r + p, than if 

 during the entire period the molecule is at the distance r. If, 

 then, the molecule m describes in the time 2t a closed path 

 about its initial position of equilibrium which is divided into 

 two equal parts by a plane passing through the molecule's 

 position of equilibrium and parallel to the contact-surface 

 between M and 1ST, the variation of the distance from the con- 

 tact-surface, or p, is a function of the time t, and for cor- 

 responding points in each half of the path is equal in amount, 

 although with contrary signs. The augmentation of the quan- 

 tity of motion which arises in consequence of the movement of 

 the molecule m about its position of equilibrium can then be 

 expressed by 



If the molecule m in the same time, 2t , describes about the 

 position of equilibrium a path of like form with the preceding, 

 but with a tangential velocity p times as great in every point, 

 the distance at every point from the position of equilibrium is 

 also p times as great as at the corresponding point in the 

 former path. But the variations in the distance of the mole- 

 cule from the contact-surface also then become p times as great 

 as before, and can therefore be expressed by pp. The augmen- 

 tation of the motion which results from the movement of the 

 molecule about its position of equilibrium becomes, conse- 

 quently, in this case 



n(n+l) s f #sa S,, 



The total quantity of motion in question, A, which the mo- 

 lecule m acquires while it describes in the same given time 

 paths of like form with different velocities about its position 

 of equilibrium, can therefore, B and C denoting constants, be 

 expressed by 



