230 Mr Sharpe, Liquid Motion from a Single Source 



Figs. 4 and 5, in which OE = /jb7ra/2c accurately, OS = fiirajc 







S 







D 





E 









^K\ 





C! 



B 



O 





X 



Fig. 4. 



B c 



Fig. 6. 



accurately, and from (19) OB = /u,afc to a first approximation, the 

 second approximation being given by 



.(26). 



c c 3 



Now suppose we keep fju, c and a constant but increase b, 

 we see from (26) that OB is increased, and from (18) that a x 

 is decreased, and because b has been increased, by Art. 4 the 

 reflecting power of the boundary has been increased. In Fig. 5 

 therefore the velocity at a distance is greater than in Fig. 4. 

 This is exactly analogous to a remark made by Lord Rayleigh in 

 his Sound, Art. 280, where in treating of conical pipes with a 

 source of sound at the vertex of the cone, he says that when the 

 angle of the cone is decreased the intensity is increased. It will 

 be noticed in Fig. 5 that the boundary is more cramped in the 

 neighbourhood of the source than in Fig. 4. See also Sound, 



