LECTURES AND ESSAYS 



[1869- 



not in general convenient, but it is often applicable where 

 there are only three points. 



The lines of flow can, however, be readily described 

 with any degree of accuracy when there is one sink, by 

 describing segments of circles with constant difference of 

 angle through the sink and one source, and drawing 

 through the other source straight lines with the same 

 difference of angle. The stream lines will be diagonals of 

 the quadrilaterals into which the field is thus divided. 

 The process may be extended to the case of two sources 

 and two sinks by taking the intersections of two sets of 

 circles. 



When there are two sources and one sink, the singular 

 points may be found by an easy geometrical method. 

 Let A, B, be sources, C the sink, and P a point of zero 

 velocity. The resultant velocity due to A and C is in the 

 tangent to the circle PAC, and also since P is a singular 

 point in the line PB. Therefore 



Similarly 



BPC = PAC. 



APC - PBC. 



Hence PCA, BCP are similar 

 triangles, and there are two points 

 of zero flow, P and P , lying in the 

 line bisecting the angle C, and such 

 that PC is a mean proportional to 

 BC and AC. The directions of the 

 orthogonal branches at P bisect 

 the angle APB and its supplement. 

 For the initial line is a tan 

 gent at the singular points if 



sin 2(9 



_ 

 - 



(19). 



Let now APC - a, BPC = - - a = /3, and assume the bi 

 sector of APB as initial line. Then 



