16i Rev. J. Challis's Theory of the Transmission of Light 



the velocity from this cause at the distance R is -n^- ^t the 



instant that v is impressed. 



If the function f had been treated in the same manner, 

 like results would have been obtained ; but the direction of 

 propagation would have been towards the centre of the dis- 

 turbing sphere. In fact, this function would apply to a dis- 

 turbance made by a hollow spherical shell, and to the motion 

 it would give to the fluid in its interior. The function F is 

 plainly that which suits the case of disturbance we have sup- 

 posed, which is of such a nature as to determine but one arbi- 

 trary function. 



Suppose now that F {r—at) = msin — {r — at) 



A 



Then F'{r — at) = cos — {r—at) 



Hence v = cos — [r—at) sm — (r—at) 



m { TTV IT , . . TT , ,1 



= -^l — cos — {r-at) - sm — {r-at) C 



If we consider r, the radius of the disturbing sphere, to be 

 at all times very small compared to A, then whatever be t, we 



shall have — — = sin and cos = 1 nearly. Hence 



A 

 ■n at 



nearly. 



r' A 



Instead of supposing, as above, an expansible sphere to 

 disturb the fluid, conceive a series of waves to be incident on 

 a sphere of constant radius at rest. The fluid will be rela- 

 tively disturbed, and the preceding investigation will enable 

 us to determine the effects that will follow. Draw a diameter 

 of the sphere parallel to the direction of the incident waves : 

 at that extremity of it on which the waves are incident, the 

 fluid will be stationary ; at all other points of the hemisphere 

 on which the waves are incident, the fluid will glide along the 



sm-face. Let jx sin — -— be the velocity which would have 



taken place at any time t, at the point where the centre of the 

 sphere is situated, if the sphere had been removed. We sup- 

 pose r the radius of the sphere to be exceedingly small com- 

 pared to A. This will therefore be the velocity without sen- 

 sible error, which would have taken place at tlie sanie time 



at 



