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IX. Notices respecting New Boohs. 



A Treatise on the Motion of Vortex- Rings. By J. J, Thomson, M.A. 

 {Adams Prize Essay.) London: Macmillan and Co., 1883. 



A DAMS Prize Essays, like University Prize Poems, are neces- 

 -^*- sarily of very unequal merit. There cannot always be among 

 the younger members, even of a great university like Cambridge, a 

 mathematician of strikingly original power ; it would be much less 

 surprising, though still hardly to be expected, that there should be 

 always an embryo Macaulay or a fledgling Tennyson. Besides, 

 while a youthful rhymester, full of confidence and " go," can usually 

 manage to hammer out in fair metre the requisite number of lines, 

 whatever be the subject prescribed, some of the subjects proposed 

 for the Adams Prize have found no one daring enough to venture 

 an attack on them. 



The essay before us is much above the average in point of merit. 

 No very striking originality (such, for instance, as burst forth in 

 Clerk-Maxwell's essay ' On the Stability of Saturn's Rings ') has, so 

 far as we have seen, been manifested, but a great deal of really 

 skilled hard labour has been usefully devoted to the clearing up of 

 an exceedingly important and excessively difficult question. And, 

 if Mr. Thomson's work serves to show rather the inadequacy of 

 our present weapons, and the absolute necessity for more powerful 

 ones, than the real nature of the impact between two vortex-rings, 

 it is none the less valuable on that account. Some was not built in 

 a day, is a saying quite as important as it is trite ; nor could it be 

 expected that the Vortex Theory (which, as we shall see, may con- 

 tain the complete solution of every physical problem, leaving nothing 

 to be explained except the nature of the wonderful fluid in which 

 the vortices exist) is to be more than, as it were, nibbled at in any 

 number of Adams Prize Essays. 



*~ Vortex motion, as a branch of hydrokinetics, we owe to Von 

 Helmholtz, of whose many splendid scientific achievements it is 

 perhaps the most brilliant. Cauchy and Stokes had done much to 

 pave the way ; but the exact nature of fluid motion where there is no 

 velocity-potential was unknown till the appearance of Von Helm- 

 holtz's paper in Crelle's Journal (1858). It was shown that, in a 

 frictionless incompressible fluid, of infinite extent, the rotating part 

 consists for ever of the same portions of the fluid, and that the axes 

 of rotation of successive elements are tangents to closed curves, or 

 rings. A group of such vortex-lines, passing through each point of 

 a very small closed curve, forms a vortex-tube or filament, a doubly- 

 connected space which continually encloses the same portion of 

 fluid. Von Helmholtz's treatment of circular vortex-filaments was 

 limited to the case in which there is one only, or of two or more 

 whose planes are parallel, and intersected at right angles by the 

 straight line in which the centres lie. Even with this restriction, 



