464 Prof. Challis on the Dispersion of Light. 



is not necessarily exact because the motion is vibratory, and that 

 a factor depending on the given circumstances of the motion 

 always exists by which it may be made integrable. 



I proceed next to the application of the same principles to the 

 problem with which we are more immediately concerned, namely, 

 that of determining the pressure at any point of the surface of a 

 sphere at rest on which a series of waves is incident. Let the 

 waves be denned by the equations 



T=feacr l = msm — {fcat + x-\-c) } 



x being reckoned from the centre of the sphere in the direction 

 contrary to that of the propagation of the waves. T now ex- 

 presses the velocity of the wave at any distance x from the origin 

 at the time t ; and, so far as regards the reaction of the hemi- 

 spherical surface on which the waves are incident, the fluid is 

 relatively impressed just as in the preceding problem. Hence, if 

 we neglect the small variation of ar^ at a given instant within the 

 space over which the effect of the impression is sensible, we shall 

 have, as before, 



2 Q da 6 2 cos<9 dT _ 

 Ka 'dr- + ~l^'!t= > 



r and 6 being polar coordinates referred to the fixed centre of the 

 sphere. By integration along a line of impression, that is, along 

 the prolongation of a radius of the sphere, we obtain 



9 +, \ b* cos 6 dT 



the integral satisfying the condition that a = a 1 for large values 

 of r, and x being omitted in the value of T, as is allowable on 

 account of the small magnitude of the sphere. The pressure due 

 to the condensation at any point of the hemispherical surface is 

 given by the equation 



a - bcosO dT 



whence the total pressure in the direction of the incidence of the 

 waves, or 2irb*§a*a sin 6 cos ddO from = to 0=kj wi U De 



found to be 



w JTa- 2b dT\ 



The determination of the pressure on the other hemispherical 

 surface is a problem of much greater difficulty, the solution of 

 which I do not profess to have completely effected ; but I con- 



