54 Professor Thomson, Longitudinal Electric Waves, [Jan. 27, 



Eliminating A, B, G we find two values for on, the first is given 

 by the equation co 2 = l//uiT which corresponds to the transverse 

 waves as in this case I A + mB + nC = ; the second by the equa- 

 tion 



a=pl + qm + rn. 



This represents a longitudinal wave propagated with the 

 velocity 



pi + qm + m. 



We see that 



* r z 



I m n 



"V-^K **—& wr -pK 



so that unless 



p : q : r = I : m : n ; 



i.e. unless the direction of propagation of the wave is parallel to 

 the direction in which the particles are moving the electric 

 intensity is not at right angles to the wave front. 



We see from these equations that a longitudinal wave of 

 electric intensity parallel to a fixed direction, say x, can be propa- 

 gated by a medium containing moving charged atoms even though 

 the velocity of these atoms is not parallel to x. Thus suppose the 

 wave of electric intensity parallel to x is being propagated by the 

 atoms moving with a velocity whose components parallel to x, y, z 



are p, q, o, then since Y= 0, Z= we have n = 0, m = -J^ , where 



T^is the velocity of the transverse electrical waves through the ether. 

 Thus the wave front is not at right angles either to the direction 

 of motion of the charged atoms or to that of the electric intensity. 

 If the velocity of the charged atoms is small compared with the 



velocity of light m will be small, I nearly unity, hence m = -^ 



approximately. Now m is the angle which the normal to wave 

 front when q is finite makes with the direction of the electric 

 intensity. Hence this angle varies as the square of the ratio of 

 the velocity of the atoms to the velocity of light. The angular 

 deflection of the front of the waves produced by a transverse 

 velocity imparted to the atoms would be almost infinitesimal 

 compared with the deflection of the atoms themselves. 



When the charged atoms move in a magnetic field they are 

 deflected from their rectilinear course, so that as the preceding 

 investigation shows a wave in which the electric intensity is 

 parallel to a fixed direction would be deflected, but the deflection 

 would be infinitesimal compared with those produced by the 

 magnetic field on the cathode rays. 



