OF AN ELECTRIC DISCHARGE. 19 



With regard, in the first place, to th^ fact that where a spark 

 occurred a residue remained in the battery, the influence of this 

 residue must not be rated too high. This residue, even in the 

 extreme case that the distance between the discs w^as equal to 



2 



the length of the stroke of the battery, could only be about — 



J. o 



of the entire charge*. By this, however, the total action of the 



2 



discharge would not be diminished by — of the whole, but only 



(2 \^ 1 



— ) , or — . The total action is, according to our princi- 

 pal proposition, equal to the increase of the potential, and the 

 potential in the case of any given battery is proportional to the 

 square of the quantity of electricity. Hence, if we denote the 

 quantity of the entire charge by Q, and that of the residue by 

 Qj, the increase of the potential is 



Wi~W = A(Q2-a^2)^ 



where A is a number independent of the quantity of electricity. 



This gives, according as we set, 



2 

 Gli = 0, or =T^Gl, 



W,-W=Aa2,or =^^'[l-(f3)]- 

 Further, besides those sparks which were intentionally called 

 forth by placing the discs or balls at a distance from each other, 

 w^e must also take those into account which w^ere the necessary 

 accompaniment of the mode of experiment. Riess, in order to 

 make the discharges as regular as possible, obtained them by a 

 peculiar apparatus constructed by himselff, which was so ar- 

 ranged that at every discharge two sparks sprang over. Now it 

 may be deduced from other experiments by RiessJ, that by ma- 

 king an interruption anywhere in the circuit, the distance across 

 which the spark will spring in any other portion of the circuit 

 will be diminished, and hence in the case before us, at the same 

 time that they create the new spark between the balls or discs, the 

 two other sparks must themselves become shortened, from which 

 we can infer a partial compensation as regards the work con- 



• See Riess, Pogg. ^nn. vol. liii. p. 11. 



t Pogg. /inn. vol. xl. p. 339. J Fogg. Ann. vol. liii. p. 11. 



c 2 



