446 Prof. Challis on the Force ofCh-avihj. 



If the tex'ms in these equations involving k'^ be omitted, it will 

 be assumed, as before, that the propagation in the direction of r 

 is instantaneous. Hence the equations are satisfied with suffi- 

 cient approximation by the values 



consequently 



^ =-^' sin ^ + -^ sin e cos 6. 

 ad r^ ir 



This equation applies to motion along the surface of the atom, by 

 putting for r its radius c. Now since, if V be the velocity along 

 the surface, 



-TT = TK = — -^-4- sin ^— -^-| — sill ^ cos 6, 



at cad (T c* 



we have by integration, 



V = —3 — sm 6 + ^ ^ ■ sin 6 cos 6, 



F, being substituted for — \fidt, and F^ for — [fqdt. 



The value of V adopted on independent considerations in the 

 solution of Problem IV. was 



dW 



W sin 0—q — r- sin d cos 6, 



at 



W being equal to m sin ( ^- \-cj. Hence this value comes 



under the form obtained above, and is thus proved to be con- 

 sistent with the general hydrodynamical equations. The second 

 term applies only to the hemispherical surface on which the waves 



are not directly incident, and vanishes where ^= « ^nd = 'rr. 



In the former article it was incorrectly said to vanish where 6 = 



and 0= „. 



The reason that the factor q is always positive may be stated 

 as follows : — A plane being conceived to be drawn through the 

 centre of the sphere perpendicular to the direction of the inci- 

 dence of the waves, the action of the fluid in contact with the 



