KINETIC OR MECHANICAL VIEW (iF NATIHF:. 63 



many experiiiiental contrivanceB, by which tlie it- 

 iiiaikable phenomena known as " ^yrostatic " — ix., 

 the stiible properties of liodies in rapid rotary motion ' 

 — could be studied, as also to the development of tlie 

 theory of knots and linkage." In llie resourceful brain 



(and electricity) is atomic (discrete, 

 grained), Dr Larnior has traced 

 the modern vortex theory further 

 back beyond Raukine to James 

 MiicCuilagh, 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 win illy 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 I\IacCullagh'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 elasticitj' of purely rotational 

 type" (iV)id.,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 l)een 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 I8.08, without knowledge of 

 Helmholtz's theoretical investiga- 

 tions. In this country such illusti-a- 

 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., 18S."), p. 

 296), states that experiments on 

 smoke-rings which he performed, 

 suggested to Lord Kelvin the 

 vortex theory of matter. Tlie 

 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, kc), and 

 J. J. Thomson ' On the ilotion of 

 Vortex Rings' (1883, p. 114, kc.) 



- 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 

 unpublislied researches into electro- 

 dvnamics (1833, posthumously pub- 

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

 Listing called this branch of 

 geometry " Topologie " (cf. Listing, 

 ' Vorstudien zur 'rojiologie,' Giit- 

 tingen, 1847). In the meantime 

 Riemann had been (1851) led in his 

 mathematical representation of 

 functions on tlie surface uiUcd 



