Mr. T. T. P. B.Warren on Prof. Fleeming Jenkin's Formula. 1 73 



rate of loss on the whole for the same unitof time maybeascertained 



C 



by adding together the Napierian logarithms of the ratios — of 



Q 



the several coils and dividing by the number of coils, or log e — 



Q 



of the whole will be the mean of the Napierian logarithms for — 



of each coil, from which the rate of loss may be easily found. 



In ascertaining R by formula R= r , this new value 



K x log - 



C . c 



for — is taken, and K is made equal to the sum of the capacities 



of the several coils. We may arrive at the same result by using 

 the formula for the derived circuit, 



t t to 



X &c. 



Kxlog - K'x I02: - K" x log - 



-D * C ^ C C ° C C 



h — I. 



+ 7S+ 7T+&C 



K x log e - K' x log e - K" x log e - 



K, K', K" are the capacities of the several coils. In this case it 

 is not necessary that t should be the same unit of time. The pe- 

 riods of charging must in all cases be of the same duration. 



If at any temperature the rate of loss in time t be known, and 

 we require the rate of loss for the same core or cable at any other 

 temperature and for the same unit of time, we have to raise the 

 temperature-coefficient to the power expressed by the difference 

 between the temperatures (as in correcting dielectric resistances), 

 which, multiplied into the Napierian logarithm of the known 



/C\ C 



rate of loss ( — J, will give the Napierian logarithm of — corre- 

 sponding to the required loss. 



As the resistances are proportional to the times occupied in 

 losing equal percentages of charge, we may also obtain the loss 

 at any required temperature by knowing only the resistances and 

 the loss in one case only. 



