1914] on Fluid Motions 77 



ball. That a convex surface is attracted by a jet playing obliquely 

 upon it was demonstrated by T. Young more than 100 years ago 

 by means of a model, of which a copy is before you (Fig. 9). 



It has been impossible in dealing with experiments to keep quite 

 clear of friction, but I wish now for a moment to revert to the ideal 

 fluid of hydro-dynamics, in which pressure and inertia alone come 

 into account. The possible motions of such a fluid fall into two 

 great classes — those which do and those which do not involve rotation. 

 What exactly is meant by rotation is best explained after the manner 

 of Stokes. If we imagine any spherical portion of the fluid in its 

 motion to be suddenly soliditied, the resulting solid may be found 

 to be rotating. If so, the original fluid is considered to possess 

 rotation. If a mass of fluid moves irrotationally, no spherical 



Fig. 9. 



A plate, bent into the form A, B, C, turning on centre B, is 

 ^impelled by a stream of air D in the direction shown. 



portion would revolve on solidification. The importance of the 

 distinction depends mainly upon the theorem, due to Lagrange and 

 Cauchy, that the irrotational character is permanent, so that any 

 portion of fluid at any time destitute of rotation will always remain 

 so. Under this condition fluid motion is comparatively simple, and 

 has been well studied. Unfortunately many of the results are very 

 unpractical. 



As regards the other class of motions, the first great step was 

 taken in 1858, by Helmholtz, who gave the theory of the vortex- 

 rinof. In a perfect fluid a vortex-ring has a certain permanence and 

 individuality, which so much impressed Kelvin that he made it the 

 foundation of a speculation as to the nature of matter. To him 

 we owe also many further developments in pure theory. 



On the experimental side, the first description of vortex-rings 



