180 Mr PocMington, On the Configuration of a pair [Feb. 26, 



ponents of velocity of the fluid, O also is a function of 2. It 

 follows that the region in the plane of z is represented conformably 

 on the planes of w and D,. The boundaries in these planes can be 

 found. For, proceeding along AC, yjr is constant and (f) increases 

 from — 00 at J. to a certain value at B, and then diminishes to its 

 value at G. Along CD, cj) is constant and \Jr decreases to a value 

 which the arbitrary constant contained in it enables us to take as 

 zero. Along DEF, yfr is constant and </> increases. Along FG, (f) 

 is constant and -^Ir increases till at G it has its original value, and 

 finally along GI, -v/r is constant while <p first decreases and then 

 increases till at / it is infinite. The boundary in the w-plane 

 indicated by the above is the symmetrical figure shown in 



fig. 2. Again, from A to B, 6 = and log - increases from 



.A'- 



C G' 



E' 



F' 



Fig. 2, Plane of w. 



log ^ to 00 . From 5 to D, 6 = 77 and log - decreases from 00 to 



logy^, where U is the velocity of the fluid at .the surface of the 

 hollow. This velocity is constant, since the pressure there has 

 the constant value zero. From D to F, log - is thus constant, 



while 6 decreases from tt to — tt. From F to H, 6 = — ir while log - 



<1 



increases from log ^^1: to 00 . From H to I, 6=0 and log — de- 



Fig. 3. Plane of 0. 



