Conductors conveying Steady or Transient Currents. 243 



where U' is the same function of t f that U is of t, and where 



, x , k 



tan 7 = — - H 



nx Q n 



The second term in the above, which expresses free vibra- 

 tions in the receiver, may be made zero, because it contains 

 the initial disturbance of the receiver as a factor ; and the 

 first term, which expresses forced vibrations, simplifies down to 



x + C = ~° .e-^f^^cos (qr-pt + u)-*-^ cos (qr-'pt'+/3)\ (14) 

 4nrc \p—n w x p + n w x J v ' 



where tana=- , and tan/5= — 



k, — m k — m 



If there is anything like agreement between the natural 

 periods of vibrator and resonator, the first of these two terms 

 overpowers the other. 



Another way of writing the solution is 



x + = ^-°- • Sm (/3 - U) e~ mt . sin (qr -pt + * + /3). . (15) 

 ^trcn k ~~ m 



Appendix. 



It is in accordance with theory to assert that the action 

 of two given magnets on each other varies inversely with 

 the permeability of the medium ; that the action of two 

 currents on each other varies directly as the permeability of 

 the medium ; and that the action of a current on a given 

 magnet is independent of the properties of the medium. 



To avoid misunderstanding, it must be perceived that the 

 statement refers to a given magnet, not to a magnet of 

 numerically specified strength, because about that there 

 would be some ambiguity according to the medium in which 

 it was measured. 



Similarly, the static action between two charges is inversely 

 as the dielectric constant of the medium ; the action between 

 a given charge moving at the approximate light-speed and a 

 given magnet is independent of the medium, except in so 

 far as its properties affect the velocity of light; while the 

 dynamic action between two given charges moving together 

 at the light-speed is proportional to the permeability. 



It may be as well to have direct experimental verification 

 for some of these things. 



