86 Mr. F. T. Trouton on the Influence of 



displacement of the node or minimum sparking-position is 

 absent in this case. 



On reaching comparatively small dimensions the inward 

 shifting of the node takes place. This is probably best attri- 

 buted not to a change in phase on reflexion or diminution in 

 velocity in transit, but to the fact that the beam is rapidly 

 diminishing in intensity on passing outward from the re- 

 flector, and, as mentioned before, the minimum sparking-posi- 

 tion is a compromise between the phase and the intensity. 



It might be thought that this action would never displace 

 the node by a sensible amount, but the following consideration 

 shows this not to be so. Let 



where x is distance measured from the reflector, represent 

 the incident wave ; and let us make some assumption as to 

 the rate the intensity of the reflected disturbance diminishes 

 as the distance increases. Of several tried, that which hap- 

 pened to give results most nearly in agreement with the ob- 

 servations assumed the amplitude to diminish as the square 

 of the distance from a point situated behind the reflector at a 

 distance equal to its width. In this case, calling the width b, 

 we have as the reflected wave 



On addition the stationary wave is determined by 



where 



^-Ksr^O"" 4 -? 



Differentiating and equating to zero as being the condition foi 

 a minimum, we find the position of the node to be given by 



h + xf 



+ (& + #)— sin47r~ + cos4tt!-=0. 

 X \ A, 



When b, the width of the reflecting sheet, is taken as 4 cm., 

 this equation requires x to have the value of about 14*3. 

 That means a shifting inwards of the node by 2*7 cm., which 

 is a little more than is required to correspond with observa- 

 tion, the nodal position given in Table II. for a 4 cm. sheet 

 being at 14*6 cm. from the reflector. 



