308 Mr. Challis on the Theory of the 



2nd. The function F applies to propagation from a centre, 

 the function f to propagation towards a centre. 



3rd. When the propagation is entirely from the centre, 



tj = as = - F (r— at), 

 r ^ 



when entirely towards the centre 



V = — as = -f{r + at), 



4th. The primary form of the functions F and / is 



. ir(r — «<) 



toX sin . 



The same reasoning as before about the discontinuity of the 

 motions is applicable. 



The possibility of the motion towards a centre is proved by 

 experiments on air, which shew that surfaces of a certain shape 

 may by reflection concentrate sound in a focus. In like manner, 

 if a slight agitation be made at the centre of the surface of 

 water in a circular basin, the wave emanating from it, after 

 being reflected at the side of the basin, will return to the centre 

 again. 



15. Suppose a series of waves to be propagated in such 

 a manner, that the velocities and condensations shall be equal 

 at all equal distances from a fixed point. This may be con- 

 ceived to be effected by means of an elastic globe placed in the 

 fluid, and made to expand and contract in a determinate man- 

 ner, and in the same degree in all directions from its centre. 

 The equations applicable to the motion are, 



V = as = - F(r — at + c). 



r 



