18 Mr. Mac Cuttacu on the dynamical Theory of 
two sets of laws by means of a very simple theory, depending on certain special 
assumptions, and employing the usual methods of analytical dynamics. 
In this theory, the two kinds of laws, being traced from a common origin, are 
at once connected with each other and severally explained ; and it may be observed, 
that the explanation of each, as well as the source of their connexion, is now 
made known for the first time. For though the laws of crystalline propagation 
have attracted much attention during the period which has elapsed since they 
were discovered by Fresnel,* they have hitherto resisted every attempt that has 
been made to account for them by dynamical reasonings ; and the laws of reflex- 
ion, when recently discovered, were apparently still more difficult to be reached 
by such considerations. Nothing can be easier, however, than the process by 
which both systems of laws are now deduced from the same simple principles. 
The assumptions on which the theory rests are these :—/“rst, that the density 
of the luminiferous ether ‘is a constant quantity; in which it is implied that this 
density is unchanged either by the motions which produce light or by the pre- 
sence of material particles, so that it is the same within all bodies as in free space, 
and remains the same during the most intense vibrations. Second, that the 
vibrations in a plane wave are rectilinear, and that, while the plane of the wave 
moves parallel to itself, the vibrations continue parallel to a fixed right line, the 
direction of this right line and the direction of a normal to the wave being func- 
tions of each other. This supposition holds in all known erystals, except quartz, 
in which the vibrations are elliptical. 
Concerning the peculiar constitution of the ether we know nothing, and shall 
suppose nothing, except what is involved in the foregoing assumptions. But 
with respect to its physical condition generally, we shall admit, as is most natural, 
that a vast number of ethereal particles are contained in the differential element 
of volume ; and, for the present, we shall consider the mutual action of these 
particles to be sensible only at distances which are insensible when compared with 
the length of a wave. 
By putting together the assumptions we have made, it will appear that when 
a system of plane waves disturbs the ether, the vibrations are transversal, or 
parallel to the plane of waves. For all the particles situated in a plane parallel 
to the waves are displaced, from their positions of rest, through equal spaces in 
* These laws were published in his Memoir on Double Refraction.—Mémoires de l'Institut, 
tom. vil. p. 45. 
