ON DOUBLE REFRACTION. 2538 
Report on Double Refraction. By G.G.Stoxss, M.A., D.C.L.,Sec.R.S., 
Lucasian Professor of Mathematics in the University of Cambridge. 
I recrer to say that in consequence of other occupations the materials for a 
complete report on Physical Optics, which the British Association have re- 
quested me to prepare, are not yet collected and digested. Meanwhile, instead 
of requesting longer time for preparation, I have thought it would be well to 
take up a single branch of the subject, and offer a report on that alone. I 
have accordingly taken the subject of double refraction, having mainly in 
view a consideration of the various dynamical theories which have been 
adyanced to account for the phenomenon on the principle of transversal vibra- 
tions, and an indication of the experimental measurements which seem to me 
most needed to advance this branch of optical science. As the greater part 
of what has been done towards placing the theory of double refraction on a 
rigorous dynamical basis is subsequent to the date of Dr. Lloyd’s admirable 
report on ‘ Physical Optics,” I have thought it best to take a review of the 
whole subject, though at the risk of repeating a little of what is already con- 
tained in that report. 
The celebrated theory of Fresnel was defective in rigour in two respects, 
as Fresnel himself clearly perceived. The first is that the expression for the 
force of restitution is obtained on the supposition of the absolute displacement 
of a molecule, whereas in undulations of all kinds the forces of restitution 
with which we are concerned are those due to relative displacements. Fresnel 
endeayoured to show, by reasoning professedly only probable, that while the 
magnitude of the force of restitution is altered in passing from absolute to rela- 
tive displacements, the Jaw of the force as to its dependence on the direction of 
vibration remains the same. The other point relates to the neglect of the com- 
ponent of the force in a direction perpendicular to the front of a wave. In the 
state of things supposed in the calculation of the forces of restitution called 
into play by absolute displacements, there is no immediate recognition of a 
wave at all, and a molecule is supposed to be as free to move in one direction 
as in another. But a displacement in a direction perpendicular to the front 
of a wave would callinto play new forces of restitution having a resultant not 
in general in the direction of displacement; so that even the component of 
the force of restitution in a direction parallel to the front of a wave would 
haye an expression altogether different from that determined by the theory 
of Fresnel. But the absolute displacements are only considered for the sake 
of obtaining results to be afterwards applied to relative displacements; and 
Fresnel distinctly makes the supposition that the ether is incompressible, or 
at least is sensibly so under the action of forces comparable with those with 
which we are concerned in the propagation of light. This supposition re- 
moves the difficulty ; and though it increases the number of hypotheses as to 
the existing state of things, it cannot be objected to in point of rigour, unless 
it be that a demonstration might be required that incompressibility is not in- 
consistent with the assumed constitution of the ether, according to which it 
is regarded as consisting of distinct material points, symmetrically arranged, 
and acting on one another with forces depending, for a given pair, only on 
the distance. Hence the neglect of the force perpendicular to the fronts of 
the waves is not so much a new defect of rigour, as the former defect appear- 
ing under a new aspect. 
Lhave mentioned these points because sometimes they are slurred over, 
and Fresnel’s theory spoken of as if it had been rigorous throughout, to the 
injury of students and the retardation of the real progress of science ; and 
