244 FLUID MOTIONS portion of the fluid in its motion to be suddenly solidified, the resu solid may be found to be rotating. If so, the original fluid is consider* possess rotation. If a mass of fluid moves irrotationally, no spherical po would revolve on solidification. The importance of the distinction dej mainly upon the theorem, due to Lagrange and Cauchy, that the irrotat character is permanent, so that any portion of fluid at any time destitu rotation will always remain so. Under this condition fluid motion is paratively simple, and has been well studied. Unfortunately many oi results are very unpractical. As regards the other class of motions, the first great step was take 1858, by Helmholtz, who gave the theory of the vortex-ring. In a pe fluid a vortex-ring has a certain permanence and individuality, whic much impressed Kelvin that he made it the foundation of a speculs as to the.nature of matter. To him we owe also many further developir. in pure theory. On the experimental side, the first description of vortex-rings that I '. come across is that by W. B. Rogers *, who instances their production du the bursting of bubbles of phosphuretted hydrogen, or the escape of sn from cannon and from the lips of expert tobacconists. For private ol vation nothing is simpler than Helmholtz's method of drawing a part: immersed spoon along the surface, for example, of a cup of tea. Here hf ring only is developed, and the places where it meets the surface are sh as dimples, indicative of diminished pressure. The experiment, made < larger scale, is now projected upon the screen, the surface of the liquid its motion being made more evident by powder of lycopodium or sulj scattered over it. In this case the ring is generated by the motion half-immersed circular disk, withdrawn after a travel of two or three inc In a modified experiment the disk is replaced by a circular or semi-circ aperture cut in a larger plate, the level of the water coinciding with horizontal diameter of the aperture. It may be noticed that while the forward motion of the plate occasions a ring behind, the stoppage of plate gives rise to a second ring in front. As was observed by Reuschf, same thing occurs in the more usual method of projecting smoke-rings f a box; but in order to see it the box must be transparent. In a lecture given here in 1877, Reynolds showed that a Helmholtz ] can push the parent disk before it, so that for a time there appears to little resistance to its motion. For an explanation of the origin of these rings we must appeal to frict for in a perfect fluid no rotation can develop. It is easy to recognize t friction against the wall in which the aperture is perforated, or againsb * Amer. J. Sci. Vol.'xxvi. p. 246, 1858. t Pogg. Ann.-Vol. ex. p. 309, 1860.