-49- 

 by (5) and (6). Thus v/e obtain the final result 



295 



(13) 



/, r oo 



The term D^ is due to the point source 

 4. The construction of <|>i« 



^ '°' Xj 



at Q^ 



The function 4> ^ Is required to satisfy the boundary 



conditions (4), If the plane were not present, <i> - would 



a3 

 be the velocity potential due to a dlpole of strength ^ 



A cos 

 placed at 0, namely, -^ ^ — • Th© boundary condition on the 



plane, however, is violated and to satisfy it, introduce the 

 Image radial dlpole of strength - 4- situated at the reflected 

 point ^2. (^®® *^® diagram on page 45 )• To remedy this boundary 

 condition on the sphere, which has now been violated. Introduce 

 the image of this radial dlpole relative to the sphere* This 



r 

 ^ 



at the 



image is another radial dlpole of strength 



inverse point Q'« (See Milne -Thorns on, p. 42] 



The successive reflections are described in the following 

 table: 



etc* 



