88 



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



are 



If A = P H- iQ, the corresponding terms in 



Plogr-Qe, PO + Qlogr ............... (2), 



respectively. The meaning of these terms is evident from Art. 64 ; 

 viz. 2?rP, the cyclic constant of i|r, is the flux across the inner 

 (or outer) circle ; and 2?rQ, the cyclic constant of </>, is the circu- 

 lation in any circuit embracing the origin. 



For example, returning to the problem of the last Art., let us 

 suppose that in addition to the motion produced by the cylinder 

 we have an independent circulation round it, the cyclic constant 

 being K. The boundary-condition is then satisfied by 



= u cos - 



(3). 



The effect of the cyclic motion, superposed on that due to the 

 cylinder, will be to augment the velocity on one side, and to 

 diminish (and, it may be, to reverse) it on the other. Hence 



when the cylinder moves in a straight line with constant velocity, 

 there will be a diminished pressure on one side, and an increased 

 pressure on the other, so that a constraining force must be applied 

 at right angles to the direction of motion. 



