414 



Profs. John Perry and W. E. Ayrton. [May 27, 



were taken. After some minutes the right and left readings due to 

 the reversal of the cell could be observed on the ordinary scale placed 

 two metres away from the electrometer ; but at the commencement of 

 the insulation after discharge, the soaking out was far too rapid to 

 allow of numbers on the scale being read, consequently the following 

 device was employed to allow of our obtaining the early part of the 

 curve with accuracy. In the slit of the lamp were two cross-wires, 

 an image of which by means of the mirror in the electrometer and of 

 an auxiliary lens was formed on a cylinder 13 centims. in diameter 

 and 100 centims. in length, revolved fairly rapidly by clockwork 

 around a horizontal axis. The comparatively rapid motion of the 

 image of the cross-wires was then accurately followed by an observer, 

 who with a pencil dotted its position from to time on a sheet of paper 

 wrapped round the revolving cylinder. On unwrapping the paper 

 the dots made by the pencil enabled the curve of rise of potential to 

 be drawn accurately from the beginning in each case. 



In these experiments as the jar is insulated, it, &c, equal 0, 



and the solution of the differential equation (1) is 



v=A+Be- Rt +Ce-y^ .... . (2), 



where /3, 7, &c, are such that x+{3, a + 7, &c, are factors of the 

 expression 



x n + ax n ~ l + ax n ~~ + .... -\-mx. 



Hence if we determine /3, 7, &c, we determine the constants of the 

 differential equation (1). Our method of reduction was as follows : — 



If is less than 7, 7 than $, and so on in equation (2), then, after 

 certain intervals of time, certain of the exponents became unimportant ; 

 and if the time is sufficiently great, equation (2) reduces itself to 



v=A+Be-M (3). 



If a curve is obtained experimentally connecting v and t, it is easy 

 to determine A, B, and ft. Thus from the observations given in the 

 first two columns of the following table, corresponding with one of 

 our several experiments with the Leyden jar (v being very slightly 



corrected by a curve), ~ was determined for the various times. 



Then the values of v and — for the same times bein^ used as co- 

 eft 



ordinates of points on a sheet of squared paper, we found that for the 

 last 140 hours of our experiment the points lay, with very consider- 

 able accuracy, in a straight line ; and hence during this time we may 

 assume equation (3) to correctly represent the law of the soaking out 

 of the residual charge. These plotted points enabled A to be deter- 



