116 



Mr. A. L. Selby on two 



Let N be a point on PQ, W its image, QN=#, CP=/. 

 By § 3 the image of a doublet of intensity fix at N is of 

 intensity -/^CN'/a or — /*CQ . Q'N'/a. 



Fig. 2. 



The image of the system PQ is therefore a line of doublets 

 in which the intensity is proportional to the distance from Q', 

 and the image is similar to the system from which it is 

 derived. 



This result is easily transformed by the process used in § 3 

 into the following : — 



The image of a source yu, at P and a line -sink PQ of strength 



— Jk per unit length is a source \x . a/f at P' and a line-sink 

 P'Q' of strength - 



fia 



/.PQ'- 



It is clear that any system of sources and sinks of total 

 strength zero distributed along PQ has for its image another 

 such system distributed along P'Q\ For the given system 

 can be reduced to a system of doublets. 



§ 5. To determine the stress behueen two spheres X, Y, 

 pulsating in an infinite liquid. 



Fisr. 3. 



Let A, B be the centres of the spheres (fig. 3) ; a, b the 

 radii. Then a, b are the normal velocities at the surfaces. 



