Mr. T. T. P. B.Warren on Prof. Fleeming Jenkin's Formula. 169 



As in one and the same body higher tones correspond to smaller 

 wave-lengths, so in two different substances the smaller velocity of 

 sound corresponds for the same pitch to smaller wave-lengths. 

 Hence, of two different bodies, for the same specific internal re- 

 sistance and under circumstances in other respects similar, the 

 deadening of tones of equal height must be greater for the 

 body with the smaller velocity of sound. 



In the vibration-experiments all the threads used exhibited 

 qualitatively the same deportment in reference to deadening; in 

 the experiments on the conduction of sound, a difference was 

 so far observed in the behaviour of the various conductors used, 

 that only in a small number (caoutchouc rod, slightly stretched 

 hemp cord, thin lead wire) was there any difference in the dead- 

 ening for the higher and lower tones. This may have arisen from 

 the fact that the specific internal resistance in the case of the other 

 bodies of which the conductors were formed had too small a value. 

 Probably, however, it only arose from the fact that the velocity 

 of propagation of the waves in the other conductors was too great. 

 Hence, with an increase in the velocity of propagation of the waves 

 in the experiments on the conductivity of sound, the difference 

 in the intensity of sound at the two ends of the conductor must 

 decrease, for two reasons : — first, according to what has been above 

 said, because with the velocity of propagation the wave-lengths 

 increase; and, secondly, because with an increase in the velocity 

 of propagation, for the same length of path which conducts the 

 sound, the time during which the deadening influences act is 

 diminished. 



XXII. Notes on Professor Fleeming Jenkin's Formula. 

 By Thomas T. P. Bruce Warren*. 



THIS formula was, I believe, first published in the ( Cantor 

 Lectures ' in 1865, but, beyond insertion, has received no 

 notice in works on telegraphy ; even by electricians, generally, 

 it appears to have been treated as of little or no importance. 



The object of this paper is to point out some of the results 

 arising from its application to cable-testing. 

 In the formula 



R=( — pV, 



V Kxlog,^ 



of a smaller vibrating division than in that of a larger one ; so that for a 

 double reason the ratio of the deadening force to the mass moved, on which 

 the deadening depends, has a greater value for the shorter waves than 

 for the longer ones. 



* Communicated bv the Author. 



