456 Mr. J. Larmor. A Dynamical Theory of [Dec. 7, 



of energy associated with the molecule, but is determined by the cir- 

 cumstances of the encounters with other molecules. The distribution 

 of energy between the various vibration-types of the molecule, accord- 

 ing to the law of Maxwell and Boltzmann, will not affect its con- 

 figuration, while there is also perfect independence between the 

 hydrodynamical motion of the medium due to the molecule and the 

 radiation produced by it. 



As regards the rotational elasticity of this hydrodynamical aether, 

 on which we have made all radiative and electrical phenomena 

 depend, it was objected, in 1862, by Sir George Stokes* to Mac- 

 Cullagh's aether, that a medium of that kind would leave unbalanced 

 the tangential surface-tractions on an element of volume, and there- 

 fore could not be in internal equilibrium ; and this objection has 

 usually been recognised, and has practically led to MacCullagh's 

 theory of light being put aside, at any rate in this country. Now, it 

 has been already mentioned that a precisely equivalent objection will 

 apply to the elasticity actually produced by a gyrostatic distribution 

 of momentum in an ordinary solid medium, the only difference in 

 the circumstances being that in the latter case the rotational elas- 

 ticity is proportional to the angular velocity and not to the angular 

 displacement ;f and this remark suggests that there must be some 

 way out of the difficulty. If we consider the laws of motion, stated 

 in Newton's manner with reference to absolute space and absolute 

 time, as fundamental principles, then it is also a fundamental prin- 

 ciple that the energy of a spinning gyrostat has reference to absolute 

 space, and is not relative to the material system which contains it. 

 The gyrostat may be considered as a kind of connexion binding that 

 system to absolute immovable space by means of the forcive which it 

 opposes to rotation ; and this is the reason why the element of mass 

 in a gyrostatic medium remains in equilibrium with its translational 

 kinetic reactions, although the tractions of the surrounding parts on 

 its surface are unbalanced and result in a couple. If this mode of 

 viewing the subject is regarded as incongruous, then we must discard 

 from dynamics the notion of absolute space, and we must set out in 

 quest of some transcendental explanation of the directional forcives 

 in rotational systems. In any case the general Lagrangian dynamical 

 procedure applies precisely to the gyrostatic medium we have here 

 taken as an illustration : nor, probably, would its application to 

 MacCullagh's aether be questioned, once the preliminary objection 

 was removed. 



* [I ain informed by Sir George Stokes that in the above criticism he con- 

 templated only media of which the elements are self-contained, and devoid of 

 internal motions.] 



t For a detailed discussion of equilibrium and wave-propagation in such a 

 medium, see ' Proc. Lond. Math. Soc.,' 1890. 



