370 BELL SYSTEM TECHNICAL JOURNAL 



theory of optics developed by Maxwell. This conclusion is confirmed in 

 later discussion by Gibbs/ Larmor,^ and Heaviside.'' 



Kelvin, apparently unaware of MacCuUagh's work, was led by similar 

 considerations to the same result. He went farther and devised a physical 

 model which consisted of a lattice, the points of which were connected by 

 extensible, massless, rigid rods in such a manner that the structure as a whole 

 was incompressible and non-rigid. Each of these rods supported a pair of 

 oppositely rotating gyrostats. By a gyrostat he meant a spinning rotor 

 mounted in a gimbal so that it is effectively supported at its center of mass 

 and can have its spin axis rotated by a rotation of the mounting. The 

 resultant angular momentum of the rotors was the same in all directions. 



This model, considered as a continuous medium, exhibits a stiffness to 

 absolute rotation, the nature of which can be described by comparing it 

 with the elasticity of a solid. A solid is characterized by a rigidity n such 

 that small displacements u, v, w are accompanied by a stress tensor, one 

 component of which is 



^dv . du\ 

 dy)' 



dx 



For the ether model the corresponding component is 



dv du 



where tp is a small angular displacement of the element about the z axis. 

 More generally a small vector rotation A(p is accompanied by a vector re- 

 storing torque per unit volume, 



AT = -4wA^. (1) 



The quantity in therefore represents a stiffness to angular displacement 

 of the element. 



In the appendix it is shown that the lattice of gyrostats, treated as a 

 continuous medium, exhibits this kind of elasticity. It is also shown that 

 for infinitesimal displacements, the medium is described by the wave 

 equations (8a and 6a). 



^5 Collected Works of |. Willard C;il)l)s, Longmans Green & Co., New York l')2S, Vol. 

 II, p. 232. 



" Heavisidc, Klectroniai^nelic Theory, KriiesL licnii, Ltd., London, 189.i, Vol. I, j). 226. 



