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



currents, and a magnetic field ; the establishment of this field 

 would have to contend against all the inertia of the system. If we 

 have a part of field where initially dXjdx is finite but varies 

 rapidly from point to point, regarding dX/dx for simplicity as a 

 harmonic function of x, let us suppose that the wave length is 

 comparable with molecular distances : then if the molecule of a 

 substance consists of a positively and a negatively electrified atom, 

 the molecules could arrange themselves so as to produce a distri- 

 bution of dXjdx of the kind considered. 



Now if the molecules group themselves so that X keeps con- 

 stant at a point moving along with the ether, there will be no 

 current, no magnetic field, and no electrokinetic energy. There 

 consequently will be a tendency for the molecules in the tract of 

 the moving ether to arrange themselves so as to produce this 

 result. This alteration in the disposition of the molecules implies 

 a longitudinal wave of the electric intensity. If the wave length 

 of the original distribution of x exceeded molecular distances the 

 molecules would have to split up into atoms to reproduce this 

 distribution of X, and there will, in consequence of the inertia of 

 the system, be a tendency for them to do so. 



The equations representing the transmission of wave in the 

 moving ether are as follows : 



Using the same notation as on page 52, p, q, r now denoting the 

 velocity of the moving ether, we have 



d d d d\ K Y 



dt dx ^ dy dz) 4<tt ' 



with similar equations for v and w, we have also 



dy dz 



d (—+ — — d\ _dZ _dY 



\dt ^ dx ^ dy dz)'~dy dz ' 



A+ A, d_ + r A)\8- — - — 

 dt dx dy dz) dz dx' 



Hence when p, q, r are independent of x, y, z we have 



ir \d d d , d}* ( d? d? d?\ „ dO .,. 



» K U + Vdx + <lTy + r dz\ X = {d^ + W + dz>) X -Tx> 0) 



, a dX dY dZ 



where e =-r- +-J- + -J-, 



dx dy dz 



with similar equations for Y and Z. 



