Prof. Challis on the Dispersion of Light. 495 



surface of the sphere, which I shall henceforth designate by the 

 same symbol W x . Since / is a periodic function having the same 

 value of \ as T, after the substitution of c for r the second term 



c 



in the brackets will be of the order - x the first, and the third 



term of the order — 2 x the first. Hence the second and third 



terms are insignificant in comparison with the first, and may be 

 omitted. But whether they are omitted or not, we may put the 

 expression for W x under the general form 



W i: =(«T+/3^)sin<9cos<9, 



a and /S being unknown constants. We have thus arrived at a 

 formula for the alteration which the impressed velocity along the 

 second hemispherical surface undergoes by fluid action ; and as 

 the impressed velocity is T sin 0, the entire expression for the 

 velocity along that surface is 



T sin (1 +* cos 6) + /3^ sin cos 0. 



CLZ 



I have made use of this expression in the Philosophical Magazine 

 for February 1860 (p. 90), but I had not then obtained it by so 

 complete an investigation as that here given. We have now to 

 determine by means of the velocities along the two hemispherical 

 surfaces the total pressure on the sphere produced by the dyna- 

 mical action of the waves, the sphere being at first supposed 

 to be fixed. 



For the first hemispherical surface 



dW dT . ' 

 Ht=dt* m6 ' 



Hence integrating, and determining the arbitrary constant 



T w 



so that <t=ct,=. — where 6=-, it will be found that 

 kck, 2 



a q c dT „ 



a z cr — cVj + ~2 • -jr cos 0. 



K CLZ 



Consequently the whole pressure on the hemisphere, resolved in 

 the direction of the incidence of the waves, is 



2waV i crd0 sin cos from = to = |, 



