on Stationary Electrical Waves in Wires. 385 



order to restore maximum brightness in the tube, the bridge A 

 must now be displaced in the same direction through twice the 

 u bridge-shortening." The difference in the positions of A, 

 according as B is on or off the wires, gives us therefore a 

 means of finding the correction to be applied to the observed 

 bridge-positions to get the true nodes in the wires. 



We want to express that the circuits AB and BC are in 

 resonance. In order to find approximately the period of 

 oscillation of such circuits we can proceed as follows : — Sup- 

 pose a simple harmonic potential-difference V sin nt to be 

 kept up between the wires at one end of the circuit, and find 

 an expression for the oscillations produced in the circuit. 

 The amplitude of these oscillations will become infinite when 

 n corresponds to the natural period of the system. A formula 

 has been obtained by Cohn and Heerwagen for a circuit 

 like BC. I have not found any discussion of the circuit AB. 



We neglect the resistance of the wires and put "S for their 

 capacity and L for their induction per unit-length, both sup- 

 posed constant. This will be only approximately true as we 

 approach the ends of the circuits. The equations connecting 

 the current C and potential-difference V are 



dx ' dt 



dx dt 



dx being the element of length, 



d?V d 2 V 



•■' dx 2 " U ° dt 2 ' 3 

 or if V varies as sin nt 

 d 2 V 



where q — n \/Li8= - = , 



2tt 

 \ 



v is the velocity of radiation, and \ the wave-length along 

 free wires; 



.'. V = (A cos qx + B sin qx) sin nt. 



This gives — C = ^- (A sin qx— B cos qx)Qos nt. 



Take first the circuit BC. Here we have 

 V=V sin nt when x=0, 

 and C = S 2 — ^- when x=c } 



