Models of the Aether. 333 



Integrating the second term under the integral by parts, and 

 omitting the superficial terms (which may be at infinity, or 

 wherever energy enters the space under consideration), we have 



0fa***.JJJp(*+g 



Hence it appears that the quantity S, which is of the dimensions 

 of energy, must be proportional to the energy per unit- volume 

 of the medium a result which shows that there is a pronounced 

 similarity between the dynamics of a vortex- sponge and of 

 Maxwell's elastic aether. 



A definite vortex-sponge model of the aether was described 

 by Hicks in his Presidential Address to the mathematical 

 section of the British Association in 1895.* In this the small 

 motions whose function is to confer the quasi-rigidity were not 

 completely chaotic, but were disposed systematically. The 

 medium was supposed to be constituted of cubical elements of 

 fluid, each containing a rotational circulation complete in itself : 

 in any element, the motion close to the central vertical diameter 

 of the element is vertically upwards : the fluid which is thus 

 carried to the upper part of the element flows outwards over 

 the top, down the sides, and up the centre again. In each of 

 the six adjoining elements the motion is similar to this, but in 

 the reverse direction. The rotational motion in the elements 

 confers on them the power of resisting distortion, so that waves 

 may be propagated through the medium as through an elastic 

 solid ; but the rotations are without effect on irrotational 

 motions of the fluid, provided the velocities in the irrotational 

 motion are slow compared with the velocity of propagation of 

 distortional vibrations. 



A different model was described four years later by 

 Fitz Gerald, f Since the distribution of velocity of a fluid in the 



* Brit. Assoc. Rep., 1895, p. 595. 



t Proc. Roy. Dublin Soc., December 12, 1899; Fitz Gerald's Scientific 

 Writings, p. 472. 



