ON OPTICAL’ THEORIES. 213 
by the reaction of the material particles of the medium through which 
the light was being propagated. According to Fresnel the density of the 
ether is affected, while according to Neumann and MacCullagh it is to 
changes in the rigidity that the effects are due. 
In both cases the direct effects of the communication of momentum 
from the ether to the material particles of the transparent medium is not 
considered. Fresnel,! it is true, thought it ‘ probable’ that the molecules 
of ponderable matter should partake of the movement of the ‘ether 
which surrounds them on all sides,’ and Cauchy,” in one memoir, deals 
with the motion of two mutually interpenetrating systems of molecules, 
but without arriving at any specially important result. Voigt? states 
that about 1865 F. Neumann was in the habit of treating, in his lectures, 
the system of simultaneous equations relating to the motion of ether and 
matter. SBriot,‘ in his work on dispersion, considers the direct reaction 
between matter and ether particles, but in his final result equates, as we 
have seen,” the term expressing it to zero. 
§ 2. In 1867 a paper was presented to the French Academy by 
M. Boussinesq® on the ‘Théorie nouvelle des ondes lumineuses.’ In 
this paper the dynamical effects of momentum communicated by the 
ether to the molecules of ponderable matter are considered as the cause 
of reflexion, refraction, polarisation, dispersion, &c. 
The ether is treated as homogeneous, and of the same density and 
rigidity in all bodies, and it is supposed that when light enters a trans- 
parent medium the molecules of that medium may be set in vibration 
isochronously with those of the ether. We have thus to consider the 
forces acting on such a medium, and these may be divided into three 
parts: (1) those which arise from the elastic reactions of the ether, 
(2) those arising from the elastic reactions of the matter, and (3) those 
arising from the mutual action between matter and ether. 
Now let us consider a small element of volume, containing both matter 
andether. Let m be the density of the ether, » of the matter, u, v, w the dis- 
placements of the ether in the element, U,V, W those of the matter. 
Then, using Green’s notation, the force, measured parallel to the axis of «, 
arising from (1) will be per unit of voluame— 
10 
(A—B) 5 +Byv%, 
dud v dw 
where =de d y | da" 
ae 5 P 
For the forces arising under (2) we have to consider that m ae and 
au Ss : : 
Pap will be quantities of the same order; but p» is very great indeed 
compared with m, and hence U is very small compared with uw. The 
' «Premier Mémoire sur la double réfraction,’ Quvres completes, t. ii. p. 278. 
2 Exercices d Analyse, t. i. p. 33. 
3 Wied. Ann. t. xvii. p. 473. 
4 Essais sur la théorie mathématique de la lumiere. Paris: 1865. 
5 See p. 181. 
6 C. R. t. [xv. p. 235; Liowville’s Journal, s. ii. t. xiii. p. 313. A most clear ac- 
count of this theory is given by M. de St. Venant in the article already quoted, 
“Théorie des ondes lumineuses,’ Ann. de Chim. s. ix. t. xxv. p. 368 seq. 
