68 IRROTATIONAL MOTION. [CHAP. Ill 



the boundary, together with a uniform distribution of double sources over 

 each of the barriers necessary to render the region occupied by the fluid 

 simply- Connected. In fact, with the same notation as in Art. 53, we find 



//&amp;lt;*- i *+ Hi ^ H 



where $ is the single- valued velocity-potential which obtains in the modified 

 region, and $ is the velocity-potential of the acyclic motion which is generated 

 in the external space when the proper normal velocity - d$/dn is given to each 

 element dS of a membrane coincident in position with the original boundary. 



Another mode of representing the irrotational motion of a 

 liquid, whether cyclic or not, will present itself in the chapter on 

 Vortex Motion. 



