170 Mr. T. T. P. B.Warren on Prof. Fleeming Jenkin's Formula. 



R= resistance in B.A. units, 



t = time in seconds during which C falls to c, 



K= capacity in farads, 



C= charge (full tension), 



c ass charge remaining at end of time /. 



I showed in a former communication that R will not be the 

 exact resistance of a core or cable at the end of time t, in con- 

 sequence of electrification on charging, and that this electrifica- 

 tion will be proportional to the loss of charge during the first 

 unit of time. 



The first proposition is to show that the rates of loss for static 

 charge, and also the resistances, are as the "Napierian logarithms 



C C 



of — , and not as the simple multiples of — • 



Pirst (t and K being the same in both cases), let - corre- 

 spond to a loss of 5 per cent. 



Let £ = 60 seconds, K = "5 farad, 



R = K 6 !„, , =^9 millions. 

 •5 x -04980 



C 



Secondly, let — correspond to a loss of 20 per cent., or four 



times as great in the same time t, 



R= -5x-£3I4 = 538milli0ns - 



Thus, although the loss is four times as much in the one as in 

 the other, the resistance is 4*55 times less ; that is, the resist- 

 ances are not proportional to the simple multiples of loss in the 

 same time t. 



This may appear at first sight anomalous, but can be shown 

 to be correct as follows ; and from a general consideration of the 

 formula for loss of static charge, 



loo* 



jjn = nt, 



log- 



where C is the full tension, c the charge remaining at end of 

 time t, and c' the required charge at end of n times t. If, then, 

 a core lose 5 per cent, of its charge in one minute, we shall find 

 that it will require (4*55 times t) 4*55 minutes to lose 20 per 

 cent ; or, conversely, a core losing 20 per cent, of its charge in 



