354 Dr. Balth. van der Pol on Measuring without Electrodes 



Here C and R are the capacity and resistance respectively 

 concentrated at the end of the wire system, the capacity 

 per unit length of the Lecher wires, and c the velocity of 

 light. 



Further, the ratio p 2 of the reflected energy and the 

 incident energy at B (fig. 1) is found to be 



. (q-l)' + y 2a 



P (a+l) 2 + 6 2— (a+l)2 + & 2 ' ' * W 



and it is seen from (2) that total reflexion will take place 

 (p 2 = l) when 



a = corresponding to R = co, 



and a = co „ „ R = 0, 



as previously stated. 



When therefore the concentrated capacity of fig. 1 is 

 kept constant but the resistance R is increased gradually 

 from infinity to zero, we must, in order to keep the Lecher 

 system in resonance with the exciting E.M.F. of constant 

 frequency, gradually shorten the distance I from one given by 



,2ttI 2ttC 



cot = — — 



X XC 



to I = 0. 



At the same time the current in the parallel wire system 

 at all these resonance points will first, when R=co,bea 

 maximum, it will then gradually fall till it reaches a mini- 

 mum ; next it will increase again, till, when finally R — 0, 

 the current reaches a maximum again. 



If further, C is kept small, it will be seen that during the 

 first stage of the process just described, i. e. from where 

 R=x> to a point where R has still a considerable value, the 

 numericals a and b are very small and the resonance length 

 of I is principally determined by the value of the added 

 capacity 0, for here (1) reduces to 



tan — - = — 2b, 



From (2), however, it follows that during this stage the 

 reflexion coefficient p 2 and, at the same time, the current in 

 the Lecher system is principally determined by the value of 



