1887.] 



Formation of Coreless Vortices in a Fluid. 



85 



Fig. 2. 



itself into two or more, or the two first formed unite into one, against 

 which accidents there is no security. 



It is conceivably possible* that a coreless ring vortex, with irrota- 

 tional circulation round its hollow, shall be left oscillating in the 

 neighbourhood of the equator of the globe; provided (-fV 2 — P)/P he 

 ■not too great. If the material of the globe be viscously elastic, the 

 vortex settles to a steady position round the equator, in a shape 

 perfectly symmetrical on the two sides of the equatoreal plane ; and 

 the whole motion goes on steadily henceforth for ever. 



If (fV 2 — P)/P exceed a certain limit, I suppose coreless vortices 

 will be successively formed and shed off behind the globe in its 

 motion through the fluid, incessantly. 



* If this conceivable possibility be impossible for a globe, it is certainly possible 

 for some classes of prolate figures of revolution. 



