through Mediums, and of its Reflection at their Surfaces. 165 



at any point of its surface. Let 9 = the angle which a line 

 drawn from any point of the surface to the centre makes with 



the diameter. Then /x cos 9 sin is the velocity which 



must be compounded with the velocity along the surface at 

 that point, to produce a resultant equal to the velocity which 

 would have taken place but. for the presence of the sphere. 



Consequently f*- cos 9 sin - — — is relatively impressed on the 



fluid in the direction of the radius. This quantity is different 

 for different values of 9. But the results obtained by consi- 

 dering the disturbance made by the whole surface of the ex- 

 pansible sphere, are applicable to the disturbance made by 

 every very small portion of the surface of this stationary sphere. 



Hence we may say, that u = jx cos 9 sin ; for because 



A 



in this case r does not vary, — j- is constant. It follows from 

 what goes before, that v the impressed velocity resolves itself 

 into — ^^ cos 9 cos — {r—a t) and — /* cos 9 sin — {r — a t). 

 The former of these, which is much less than the other on 

 account of the factor — -, is propagated with the uniform velo- 



city a, and is accompanied by change of density ; the latter is 

 transmitted instantaneously without change of density. At 

 the distance 11 from the centre of the sphere, these velocities 



respectively become —^ cos 9 cos ^ {r—at), and 



nT COS 9 sm — {r—a t). 



These conclusions will not be sensibly affected if the ex- 

 cursions of the particles of the incident waves be considerably 

 larger than r. 



The limits within which this paper must be confined allow 

 me only to state the theory in regard to light which I found 

 on the preceding mathematical reasoning, and on the hypo- 

 theses that preceded it. 



The two-fold reflection from small spherical bodies, as above 

 exhibited, may have reference to the two-fold mothfication 

 which light receives on entering any medium (lor instance, in 

 a direction perpendicular to the surface), viz. its reflection 

 and the diminished velocity of its transmission. Its reflection 



may 



