76 Dr. C. V. Burton on a 



corresponding to a reduction of volume Fm ; this work 

 being pFm. There is also work done against the pressure 

 p-\-Bp at (x + Bx, y, z) corresponding to an increment of 

 volume (F + $F)m ; this work is, to a first order, 



(pF-\-pBF + FBp)m, 



where Bp = "dp I'd * ■ B.v, 



and SF = - BBp = - E.'bp/'dx . 8x. 



On the whole, then, the work done by the normal pressure 

 of the medium in the virtual displacement Bx is 





Of this the first term represents the work done in com- 

 pression, the potential energy of the system being increased 

 to that extent, while the remaining term is the work done 

 against the ideal forcive which was applied to the particle 

 to prevent its moving with appreciable acceleration. Thus 

 if a particle of mass m is at rest in the aether (or, as below, 

 in motion) at a point where an aetherial pressure-gradient 

 exists, there will be a force 



-■*(& §■ I) « 



exerted on the particle. If the particle were allowed to 

 move with a finite acceleration, the associated movements of 

 expansion and contraction would be correspondingly ac- 

 celerated, and work would thus be done in imparting this 

 form of kinetic energy to the aether. This only implies, 

 however, the existence of a corresponding term * in the total 

 effective inertia of the particle, the remaining terms being 

 probably of electromagnetic origin. Since here, as in the 

 usual acceptation of the term, the mass m signifies the total 

 inertia of the particle in question, we may remove the 

 restriction as to the particle being at rest, (2) being in any 

 case the force-components acting on m. It should be 

 particularly noticed that the virtual displacement from which 

 (2) was deduced was a displacement of m with respect to the 

 aether, and that consequently 



-mFM, =^. ~) is the force tending to 

 Vda oy ozJ J v 



accelerate the particle m with respect to the wther . (3) 

 * The possible magnitude of this term is considered in Appendix D. 



