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



of the tube, and tbat the charges producing this electrification 

 can move about, and by so doing produce a convection current. 

 Let us suppose, for example, that we have a vacuum tube, and 

 that in this tube all the atoms of the gas which are charged at all 

 are charged with electricity of the same sign and move with a 

 velocity p parallel to the axis of the tube, let the electric intensity 

 be parallel to this axis and equal to X, let K be the specific induc- 

 tive capacity of the medium in the tube, p the volume density of 

 the electrification. Thus in this tube there is a dielectric current 

 equal to 



at\4nr*' 



and a convection current equal to 



the total current parallel to the tube is thus 

 d {K 

 dt 



and this must be the same at all parts of the tube. For if u, v, w 

 are components of the total current 



du dv dw _ . 

 dx dy dz 

 and in this case v = 0, w = 0. 



Hence we have 



It 1**1 +*> £ 1**1 -/«■ 



where f(t) represents a function of the time. 

 The solution of this is 



fA + *hi (KX) ' 



KX = jf(t) dt + F(x- pt), 



where F denotes an arbitrary function of x — pt. This represents 

 a longitudinal wave of electric intensity, travelling with the 

 velocity p : the velocity of translation of the electrified atoms. 



When, as in the case of a vacuum tube, we have free charged 

 atoms present the existence of convection currents is quite obvious. 

 The following considerations show that such currents may, how- 

 ever, occur in a solid dielectric, with all its molecules intact, pro- 

 vided each molecule consists of a positively electrified atom paired 

 with a negatively electrified one. For though in this case p 

 will vanish if we take its value over a space enclosing a large 

 number of molecules, yet if we are dealing with phenomena 



