March, 191S] A Lecher System — Theoretical 105 



The distance from the thermocouple to the back of the 

 4 ::;7r 



receiver plates is ^. 



4. Vir 



Hence the total capacity of the wires is k( ^ —- j 



The energy on the plates is represented by 

 1^..., 1 \2A y\ V.s 



The condenser is at the point x — o. In the above expression 



•> J 



for put x = o and we have </> = "' cos 7 per unit length. 



K 



The equivalent wire-length of the condenser is ^ . 



But the plates are not charged all the while, hence V^ in the 

 expression for the energy on the plates must be taken 



V- = — - J—~^ cos^ 7 • — 1 cos-j/ tdt. 



K- ■iir- T -' 



Now — ( cos2j;tdt= cos-xdx = —. 



tJo vtJ o vt 



But the plates are charged n times a second, and since 

 v = 2irn and 7/r = l, multiplication by n gives ~ = — ^ 



where no= frequency of the fundamental tone and s the 

 frequency number. 



Integrating the above expression for the energy on the wires 

 we get as the expression for the total energy E, 



+ 3 sin 7 cos'' 7 (l-fsin-7) — 5 sin5 7COS7 + -I sin 7 cos 7 > I . 



Now the constant A depends upon the manner of setting 

 the receiver into vibration. Our case is similar to the acoustical 

 case treated by Lord Rayleigh.* The disturbing force which 



varies as cos '^^-^ is not applied at a single point, but is dis- 

 \ 



tributed over the distance ^ . The disturbing force over 

 one-half of this distance concerns itself with the Lecher system. 



* Theory of Sound. Vol. I, p. 189. 



