334 Models of the Aether. 



neighbourhood of a vortex filament is the same as the distribu- 

 tion of magnetic force around a wire of identical form carrying 

 an electric current, it is evident that the fluid has more energy 

 when the filament has the form of a helix than when it is 

 straight ; so if space were filled with vortices, whose axes 

 were all parallel to a given direction, there would be an 

 increase in the energy per unit volume when the vortices 

 were bent into a spiral form ; and this could be measured by 

 the square of a vector say, E which may be supposed parallel 

 to this direction. 



If now a single spiral vortex is surrounded by parallel 

 straight ones, the latter will not remain straight, but will be 

 bent by the action of their spiral neighbour. The transference 

 of spirality may be specified by a vector H, which will be dis- 

 tributed in circles round the spiral vortex ; its magnitude will 

 depend on the rate at which spirality is being lost by the 

 original spiral, and can be taken such that its square is equal 

 to the mean energy of this new motion. The vectors E and H 

 will then represent the electric and magnetic vectors; the 

 vortex spirals representing tubes of electric force. 



Fitz Gerald's spirality is essentially similar to the laminar 

 motion investigated by Lord Kelvin, since it involves a flow in 

 the direction of the axis of the spiral, and such a flow cannot 

 take place along the direction of a vortex filament without a 

 spiral deformation of a filament. 



Other vortex analogues have been devised for electro- 

 statical systems. One such, which was described in 1888 by 

 W. M. Hicks,* depends on the circumstance that if two bodies 

 in contact in an infinite fluid are separated from each other, and 

 if there be a vortex filament which terminates on the bodies, 

 there will be formed at the point where they separate a hollow 

 vortex filamentf stretching from one to the other, with rotation 



* Brit. Assoc. Rep., 1888, p. 577. 



} A hollow vortex is a cyclic motion existing in a fluid without the presence of 

 any actual rotational filaments. On the general theory cf. Hicks, Phil. Trans, 

 clxxv (1883), p. 161 ; clxxvi (1885), p. 725 ; cxcii (1898), p. 33. 



