84 



Sir W. Thomson. On the 



[Feb. 3 y 



Fig. 1. 



fluid, or in a real fluid such as water or air, to form a vortex 

 sheet, that is to say an interface of finite slip by any natural 

 action. What happens in the case at present 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 continuous 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 perfectly symmetrical 

 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 (Gr and H in fig. 2, 

 which, however, may be enormously far from like the true configura- 

 tion). 



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 determinate for each of these 

 vacuum-rings, and remains constant for ever after : unless it divides 



