of Attractive and Repulsive Forces. 181 



the moving force of the aether is greater in the condensed 

 half of the wave than in the rarefied half in the proportion of 

 the greater density. 



13. It is evident that the condensation of an uncompoimded 

 wave at any point of a plane cutting transversely a diameter 

 of the sphere drawn in the direction of the incidence of the 

 waves will be the same at all points of this plane, excepting 

 so far as the reaction of the sphere produces variation of the 

 condensation at and near the spherical surface. The conden- 

 sation immediately due to this reaction will be extremely small, 

 because it contains as a factor the ratio of the diameter of the 

 sphere to the wave-length (' Principles/ p. 283). Hence the 

 accelerative action on the sphere will be very nearly propor- 

 tional to the moving force of the fluid in a transverse plane 

 passing through the centre of the sphere (see art. 33 of the 

 communication on Attractive and Repulsive Forces, in the 

 Philosophical Magazine for September 1872). Consequently, 

 by the argument at the end of art. 12, there will be no ten- 

 dency in the incident waves to produce any residual motion of 

 translation of the sphere. Also, if we take account of the con- 

 densation to which the variation of the motion of the fluid 

 along the surface of the sphere is due, no translator^ action 

 will result therefrom, because this motion is just as much ac- 

 celerated on one hemispherical surface as it is retarded on the 

 other, the velocity being zero at each extremity of the before- 

 mentioned diameter, and the condensation being symmetrical 

 with respect to a transverse plane passing through the centre 

 of the sphere. This, however, does not apply to condensation 

 due to composite plane-waves, because by reason of the com- 

 position the condensation on the second hemispherical surface 

 undergoes alteration, the mode and amount of which it is the 

 purpose of the following investigation to determine. 



14. It is, first, to be remarked that those component vibra- 

 tions the directions of the axes of which cut the surface of the 

 sphere will on that account be intercepted. But notwithstand- 

 ing this circumstance, inasmuch as the incident component 

 waves, so long as they are not interrupted, comport themselves 

 as if they were not compounded, the amount of condensation 

 at any point of the first hemispherical surface will in either 

 case be the same, This identity, however, does not hold good 

 as respects the other hemispherical surface. For, conceive the 

 sphere to be cut by any plane transverse to the direction of 

 incidence, and to be enveloped by a cylindrical surface the 

 axis of which is in the same direction ; then the component 

 vibrations whose axes pass through the portion of this plane 

 which lies between the sphere and the cylindrical surface, will 



