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MR. J. LARMOR ON A DYNAMICAL THEORY OF 
of bodies^ are utterly unknown. The peculiar mechanism of light is a secret which 
we have not yet been able to penetrate . , . but perhaps something might be done by 
pursuing a contrary course; by taking these laws for granted, and endeavom^ing to 
proceed upwards from them to higher principles ...” He then allows himself to 
give a pui’e mechanical interpretation to his formal results, taking his displacement to 
be linear, and he derives the conclusion that the effective density of the aether is the 
same in all bodies. 
13. In the notes appended to this purely formal paper MacCullagh ‘‘afterwards 
proved tliat the laws of reflexion at the surface of a crystal are connected, in a very 
singular way, with the laws of double refraction, or of propagation in its interior;” 
he was led to infer that “ all these laws and hypotheses have a common source in 
other and more intimate law^s that remain to be discovered ; and that the next step 
in physical optics would probably lead to those higher and more elementary principles 
by wdiich the laws of reflexion and the laws of propagation are linked together as 
parts of the same system.” And in the following memoir* he takes this step by 
developing his dynamical theory. His analysis is based on the hypothesis of constant 
density of the sether, and on the principle of rectilinear vibrations in crystalline 
media, substances like quartz being excepted. “ Concerning the peculiar constitution 
of the ether we know nothing, and shall assume nothing, except what is involved in 
the foregoing assumptions,” and that it may be taken as homogeneous for the 
problem in hand. 
In Section HI. of this paper MacCullagh proceeds to determine the potential- 
energy function on which the transverse rectilinear vibrations propagated through 
the aether must depend. He observes that such vibrations involve no condensation ; 
and as in a plane wave all the points in the medium move in parallel directions, the 
effective strain produced in it may be taken to be specified by the rotation of the 
element, wdiich is round a line in the plane of the 'wave-front and at right angles to 
the line of the displacement, this rotation being proportional to the rate of change of 
the displacement in the direction of propagation. Having previously shown, probably 
for the first time, that the expression now interpreted as representing the elementary 
rotation in the displacement of a medium by strain, enjoys the invariant properties 
of a vector, he at once seizes upon it as the very thing he wants, as it has a meaning 
independent of any particular system of axes to which the motion is referred; and 
he makes the potential energy of the medium a quadratic function of the components 
of this elementary rotation. As pointed out by StokesI, the possible forms of the 
effective strain and therefore of the energy-function are by no means thus restricted : 
in fact Green had a short time previously established another form, in which the 
* MacCullagh, “An Essay towards a Dynamical Theory of Crystalline Reflexion and Refraction,’’ 
‘Trans. R.l.A.,’ 21, Dec. 9, 1839. 
t Sir G. G. Stokes, “ Report on Donble Refraction,” ‘ Brit. Assoc.,’ 1862. MacCullagh possibly 
, perceived this afterwards himself; of. note at the end of his memoir. 
