1896.] and Rontgens X Rays. 51 



involving lengths comparable with the size of a molecule, if we are, 

 for example, considering waves whose wave lengths are comparable 

 with molecular distances, it is evident that we cannot assume that 

 p is zero ; we must regard p as having at each point of space a 

 finite value which will be given by the equation 



Suppose now that the ether is moving past the molecules with 

 a velocity whose components are p, q, r; or more generally let 

 p, q, r be the components of the ether relative to the molecule, 

 then this will produce convection currents whose components are 

 pp, qp, rp ; these convection currents will give rise to longitudinal 

 waves. 



Thus in this case the conditions for the production of such 

 waves are (1) that we should have some means of producing waves 

 whose length is comparable with molecular distances, (2) that we 

 should be able to set the ether in motion. 



Now it follows from the laws of electrodynamics that if we 

 regard the ether as a perfect fluid the pressure due to which is 

 equal in all directions, then it must in general be set in motion 

 when changes are occurring in an electric field. For each unit 

 volume in the electric field possesses a momentum whose com- 

 ponents are 



£{»-R}, £{Xo-.fa), ^{Yb-Xa}, 



where K is the specific inductive capacity, X, Y, Z the components 

 of the electric intensity, a, b, c the components of the magnetic 

 induction. Let U, V, W denote the differential coefficients of 

 these three quantities with respect to the time. Then a force 

 having the components U, V, W must act on each unit volume of 

 the field. This force will set the ether in motion unless it can be 

 balanced by the pressure due to- the ether, the conditions for this 

 are, if p is the pressure of the ether, 



dx ' dy ' dz 



dy dx dz dy dx dz 



unless conditions (a) are satisfied the ether will be set in motion. 

 These conditions are not, however, satisfied in general when the 

 electric field is changing; they are not, for example, satisfied in the 

 field produced by the ordinary dumb-bell vibrator. Thus a vary- 

 ing electric field will in general set the ether in motion, and thus 

 fulfil requirement (2) for the production of longitudinal electric 



4—2 



