80 MOTION OF A LIQUID IN TWO DIMENSIONS. [CHAP. IV 



Either of these systems may be taken as the equipotential 

 curves, and the other system will then form the stream-lines. 

 In either case the velocity at the points (+ a, 0) will be infinite. 



If these points be accordingly isolated by drawing closed curves 

 round them, the rest of the plane xy becomes a triply-connected 

 region. 



If the circles #1 # 2 = const, be taken as the stream-lines we 

 have the case of a source and a sink, of equal intensities, situate 

 at the points ( a, 0). If a is diminished indefinitely, whilst pa 

 remains finite, we reproduce the assumption of Art. 63, 3, which 

 therefore corresponds to the case of a double line-source at the 

 origin. (See the first diagram of Art. 68.) 



If, on the other hand, we take the circles rjr^ = const, as the 

 stream-lines we get a case of cyclic motion, viz. the circulation in 

 any circuit embracing the first (only) of the above points is 27T//,, 

 that in a circuit embracing the second is 2?ryLt ; whilst that in a 

 circuit embracing both is zero. This example will have additional 

 interest for us when we come to treat of ' Rectilinear Vortices.' 



