Prof. Challis on the Force of Gravity. 447 



further half of the sphere is not directly caused by the waves, 

 but results from the momentum of the fluid which passes that 

 plane. But the sum of the momenta of the condensed portion 

 of a wave is greater than that of the rarefied portion. Hence the 

 expression for the pressure [a^s) on any point of the further he- 

 mispherical surface must contain a term involving q, not wholly 

 periodic, and as the condensation prevails the non-periodic part 

 must be positive. In fact it was shown that the above value of 

 V conducted to an expression for fl^(s— o-), which contains the 

 term 



2aKr dr 



the non-periodic part of which is positive if q be positive. 



Again, from the reasoning of the former article, it appears 

 that q is independent of the radius of the atom. For it was 

 found that whether or not the effect of the spherical surface in 

 causing the fluid in contact with it to move in a circular path, 

 be taken into account, the foregoing difl'erential equation, of 

 which P is the principal variable, is equally obtained. Whence 



b'^dV dY 



it follows that the value of —i^, that is, of —-17, is independ- 

 ent of the curvature of the spherical sui'face, and consequently 

 that q in the above expression for V is independent of c. 



We are now prepared to draw some general conclusions re- 

 specting the permanent motion of translation of a spherical 

 atom submitted to the action of the assumed series of waves. 

 The expression for the part of the pressure which causes such 

 movement was found to be 



TT^c^qmn^ 



1. According to an hypothesis already stated, the ultimate 



atoms of bodies diS"er in size, but not in intrinsic inertia. Nor 



can one atom be said to be denser than another, because density 



is a quantitative quality of bodies, depending wholly on their 



being aggregations of atoms. Hence the quantity of inert matter 



47rc^ 

 in the atom of radius c is — «— • Consequently,dividing the above 



value of the pressure by this quantity, it will follow that atoms 

 of different magnitudes are equally accelei-ated. 



2. From hydrodynamical principles it is proved that \, the 

 breadth of the waves, does not vary with the distance to which 

 they are propagated from the origin. The phajnomeiia of light 

 exhibit, according to the undulatory hyjiothesis, actual instances 

 of this law. Hence the acceleration of the atom varies as m^ ; 



