256 Formation of Coreless Vortices, 



form a vortex-sheet, that is to say, an interface of finite slip, 

 by any natural action. What happens in the case at present 



Fig. 1. 



under consideration, and in every real and imaginable case of 

 two portions of liquid meeting one another (as, for instance, 

 a drop of rain falling directly or obliquely on a horizontal 

 surface of still water), is that continuity and the law of con- 

 tinuous fluid motion become established at the instant of first 

 contact between two points, or between two lines in a class of 

 cases of ideal symmetry to which our present subject belongs. 



An inevitable result of the separation of the liquid from the 

 solid, whether our supposed globe or any other figure per- 

 fectly symmetrica] round an axis, and moving exactly in the 

 line of the axis, is that two circles of the freed liquid surface 

 come into contact and initiate in an instant the enclosure of 

 two rings of vacuum (G and H in fig. 2, which, however, 

 may be enormously far from like the true configuration). 



The " circulation " (line-integral of tangential component 

 velocity round any endless curve encircling the ring, as a 

 ring on a ring, or one of two rings linked together) is deter- 

 minate for each of these vacuum-rings, and remains constant 

 for ever after : unless it divides itself into two or more, or 

 the two first formed unite into one, against which accidents 

 there is no security. 



