268 REPORT—1862. 
independently of, and in a different manner from Green, precisely Fresnel’s 
laws of double refraction and the accompanying polarization, on the condition, 
however, that in polarized light the vibrations are parallel to the plane of 
polarization. 
It is remarkable that in the previous year MacCullagh, in a letter to 
Sir David Brewster *, published expressions for the internal pressures identical 
with those which result from Green’s first theory, provided that in the latter 
the terms be omitted which arise from that term in ¢ which contains yp, a 
term which vanishes in the case of transversal vibrations propagated within 
a crystal. It does not appear how these expressions were obtained by 
MacCullagh ; it was probably by a tentative process. 
The various theories which have just been reviewed have this one feature 
in common, that in all, the direct action of the ponderable molecules is 
neglected, and the ether treated as a single vibrating medium. It was, 
doubtless, the extreme difficulty of determining the motion of one of two 
mutually penetrating media that led mathematicians to adopt this, at first 
- sight, unnatural supposition ; but the conviction seems by some to have been 
entertained from the first, and to have forced itself upon the minds of others, 
that the ponderable molecules must be taken into account in a far more direct 
manner. Some investigations were made in this direction by Dr. Lloyd as long 
as twenty-five years ago}. Cauchy’s later papers show that he was dissatisfied 
with the method, adopted in his earlier ones, of treating the ether within a 
ponderable body as a single vibrating medium}; but he does not seem to 
have advanced beyond a few barren generalities, towards a theory of double 
refraction founded on a calculation of the vibrations of one of two mutually 
penetrating media. In the theory of double refraction advanced by Professor 
Challis$, the ether is assimilated to an ordinary elastic fluid, the vibrations of 
which are modified by resisting masses; and his theory leads him at once to 
Fresnel’s elegant construction of the wave surface by points. The theory, 
however, rests upon principles which have not received the general assent of 
mathematicians. In a work entitled “ Light explained on the Hypothesis of 
the Ethereal Medium being a Viscous Fluid”||, Mr. Moon has put in a clear 
form some of the more serious objections which may be raised against Fresnel’s 
theory ; but that which he has substituted is itself open to formidable objec- 
tions, some of which the author himself seems to have perceived. 
In concluding this part of the subject, I may perhaps be permitted to 
express my own belief that the true dynamical theory of double refraction 
has yet to be found. ; 
In the present state of the theory of double refraction, it appears to be of 
especial importance to attend to a rigorous comparison of its laws with actual 
observation. I have not now in view the two great laws giving the planes 
of polarization, and the difference of the squared velocities of propagation, of 
the two waves which can be propagated independently of each other in any 
given direction within a crystul. These laws, or at least laws differing from 
them only by quantities which may be deemed negligible in observation, had 
previously been discovered by experiment; and the deduction of these laws 
by Fresnel from his theory, combined with the verification of the law, which 
his theory, correcting in this respect previous notions, first pointed out, that 
* Philosophical Magazine for 1836, vol. viii. p. 103. 
+ Proceedings of the Royal Irish Academy, vol. i. p. 10. 
t See his optical memoirs published in the 22nd volume of the ‘Mémoires de l’ Académie.” 
§ Cambridge Philosophical Transactions, vol, vill. p, 524. 
|| Macmillan & Co., Cambridge, 1853. 
