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MR. J. LARMOR ON A DYNAMICAL THEORY OF 
with the ordinary manifestations of energy as exemplified in material structures. We 
shall find that such difficulties are now removed by aid of the mechanical example 
of a gyratory mther, which has been imagined by Lord Kelvix to illustrate the 
properties of the luminiferous and electric medium. The aether whose properties 
are here to be examined is not a simple gyrostatic oneit is rather the analogue of a 
medium filled with magnetic molecules which are under the action, from a distance, 
of a magnetic system. But the same peculiarities that were supposed to fatally 
beset MacCullagh’s medium and render it inconceivable, are present in an actual 
mechanical medium dominated by gyrostatic momentum. 
2. The general dynamical principle which determines the motion of everv material 
system is the Law of Least Action, expressible in the form that 8J(T — MV)dt = 0, 
where T denotes the kinetic energy and W the potential energy of the system, each 
formulated in terms of any co-ordinates that are ’sufficient to specify the configuration 
and motion in accordance with its known properties and connexions ; and where the 
variation refers to a fixed time of passage of the system from the initial to the final 
configuration considered. The power of this formula lies in the fact that once the 
energy-function is expressed in terms of any measurements of the system that are 
convenient and sufficient for the purpose in view, the remainder of the investigation 
involves only the exact processes of mathematical analysis. It is to be observed that 
forces which can do no work by reason of constraints of the system tacitly assumed 
in this specification, but wdiich nevertheless may exist, do not enter at all into the 
analysis. Thus in the dynamics of an incompressible medium, the pressure in the 
medium will not appear in the equations, unless the absence of compression is 
explicitly recognised in the form of an equation of condition between co-ordinates 
otherwise redundant, which is combined into the variation in Lagraxge’s manner; 
in certain cases {e.g. magnetic reflexion of light, infra) we are in fact driven to the 
explicit recognition of such a pressure in order that it may be possible to satisfy all 
the necessary stress-conditions of the problem, while in other cases [e.g. ordinary 
reflexion of light) the pressure is not operative in the phenomena. There is also a 
class of cases at the other extreme—typified by a medium such as Lord Kelvin’s 
labile sether which opposes no resistance to laminar compression,—where a certain 
co-ordinate does not enter into the energy-function because its alteration is not 
opposed and so involves no work ; in these cases there is solution of a constraint 
which reduces by one the number of kinematic conditions to be satisfied. In 
intermediate cases the energy corresponding to the co-ordinate will enter into the 
function in the ordinary manner. 
3. It is to be assumed as a general principle, that all the conditions necessaiy to 
be satisfied in any dynamical problem are those which arise from the variation of the 
* A medium has however been invented by Lord Kelvix, containing gyrostatic cells composed of 
arrangements of Foucault gyrostats whose cases are imbedded in it, such as give precisely the rotational 
elasticity of the asther. 
