KINETIC OR MECHANICAL VIEW OF NATURE. 63 



many experimental contrivances, by which the re- 

 markable phenomena known as " gyrostatic " i.e., 

 the stable properties of bodies in rapid rotary motion l 

 could be studied, as also to the development of the 

 theory of knots and linkage. 2 In the resourceful brain 



(and electricity) is atomic (discrete, 

 grained), Dr Larmor has traced 

 the modern vortex theory further 

 back beyond Rankine to James 

 MacCullagh, who in his ' Essay 

 towards a Dynamical Theory of 

 Crystalline Reflexion and Refrac- 

 tion ' (Trans. Irish Academy, 1839), 

 " arrived at a type of elasticity (of 

 the ether) which was wholly rota- 

 tional, . . . somewhat after the 

 manner that a spinning flywheel 

 resists any angular deflection of its 

 axis " (p. 26 of his Adams prize 

 essay ' .Ether and Matter,' 1900). 

 " Rankine, never timid in his specu- 

 lations, expounded MacCullagh's an- 

 alytical scheme soundly and clearly, 

 in full contrast with the elastic 

 properties of matter, as represent- 

 ing a uniform medium or plenum 

 endowed with ordinary inertia, but 

 with elasticity of purely rotational 

 type " (ibid., p. 77; cf. p. 73) ; but 

 he also remarks that "up to the 

 period of Lord Kelvin's vortex 

 atoms . . . the earlier theories . . . 

 could only have been hypothetical 

 speculations" (p. 25 note). 



1 Helmholtz himself did not give 

 many practical illustrations of his 

 remarkable theories. Such were 

 first given by W. B. Rogers ('Amer. 

 Journ. of Science ' (2), vol. 26, p. 

 246) in 1858, without knowledge of 

 Helmholtz's theoretical investiga- 

 tions. In this country such illustra- 

 tions have become quite favourite 

 popular lecture experiments (see 

 Sir Rob. S. Ball's memoir). Smoke- 

 rings, solid and liquid gyrostats, and 

 a host of similar contrivances, have 

 impressed on us the hidden re- 

 sources of whirling motion. Prof. 



Tait, in his ' Recent Advances of 

 Physical Science' (3rd ed., 1885, p. 

 296), states that experiments on 

 smoke-rings which he performed, 

 suggested to Lord Kelvin the 

 vortex theory of matter. The 

 various papers of the latter have, 

 so far, not been collected in a con- 

 venient form. The earliest is con- 

 tained in the ' Proceedings of the 

 Royal Society of Edinburgh,' Feb- 

 ruary 1867. Then followed a 

 memoir in the ' Transactions ' (April 

 1867) on vortex statics (Proc. 

 R. S. E., December 1875) ; "Vibra- 

 tions of a Columnar Vortex " (Proc.. 

 March 1880). Prof. Hicks, and 

 especially Prof. J. J. Thomson 

 (Trans. R. Soc., 1884 ; 1881), have 

 contributed to the theory, and the 

 latter, in his Adams prize essay for 

 1882, has further tested the concep- 

 tion in its application to chemical 

 statics. See Hicks, 'Recent Pro- 

 gress in Hydrodynamics ' (Brit. 

 Assoc. Rep., 1881, p. 63, &c.), and 

 J. J. Thomson ' On the Motion of 

 Vortex Rings ' (1883, p. 114, &c.) 



2 The creator of this branch of 

 purely positional geometry is doubt- 

 less Johann Benedict Listing, who 

 was led to his researches by some 

 suggestions of Gauss. Gauss refers 

 to the subject in connection with his 

 unpublished researches into electro- 

 dynamics (1833, posthumously pub- 

 lished in 'Werke,' vol. v. p. 605). 

 Listing called this branch of 

 geometry " Topologie " (cf. Listing, 

 ' Vorstudien zur Topologie,' Gb't- 

 tingen, 1847). In the meantime 

 Riemanu had been (1851) led in his 

 mathematical representation of 

 functions on the surface called 



