ON OPTICAL THEORIES. Ka 
2 
periodic coefficient was attached to the first term, p aS etc., and he states 
2 
that the development of the equations —— .... leads to different 
2 
results. Sarrau,' in reply, points out that this depends on the relative 
magnitudes of the quantities a, /3, y, o®, and the other parameters; on 
making the same suppositions in the two cases the results, he shows, are 
identical. One may, however, start from the general equations of an elastic 
solid with two coefficients, and, by supposing the coefficients to be periodic, 
arrive at the general equations already found. 
M. de St. Venant finds a difficulty in explaining dispersion, for in an 
isotropic medium the periodicity of the coefficients vanishes. This may 
be true, and yet the equations contain differential coefficients above the 
second. 
§ 11. The theory advanced by Von Lang? might perhaps more strictly 
be considered under the next section: ‘Theories based on the mutual 
action between matter and the ether.’ The theory is, however, so slight 
a modification of the ordinary elastic solid theory that it will be more 
convenient to deal with it now. 
Von Lang supposes that the displacements which come into the 
ordinary elastic solid theory are displacements of the ether relative 
to the molecules of the matter. He assumes that the ratio of the 
matter displacement to that of the ether is in general a function of the 
direction, but that for three directions we may write 
U=a*u, V=b?7, W=c?w, 
U, V, W being displacements of matter, w, v, w of ether. 
He then forms the equations of motion, and, equating the velocity of 
the quasi-longitudinal wave to zero, arrives at Fresnel’s wave surface. 
The theory cannot be regarded as having any real physical signification, 
for the elastic forces produced in the ether will depend on the real dis- 
placements of the ether particles, not on the displacements relatively to 
the matter, and the velocity of the normal wave cannot vanish, for if it 
does the medium becomes unstable. 
© § 12. Von Lang? has also given a theory of circular polarisation, 
which consists in adding to the ordinary equations terms such as 
sofdv dw 
?( ——_—_ }, 
t dy 
From this it follows that the velocity in a medium such as sugar is 
given by 
L being the wave length in air; while in quartz 
Bos 19 
w= @?— 7 ~~ ginrg 1 { (a? — c)? sin4d 
2 2 
2 oy 
+ a2 008 i) a LAG} 
Sarrau, ‘ Observations relatives a Yanalyse faite par M. de St. Venant,’ Ann. de 
Chim. (4), t. xxvii. p. 266. 
* Von Lang, ‘Zur Theorie der Doppel-Brechung,’ Wied. Ann. t. clix, p. 168. 
* Von Lang, ‘ Zur Theorie der Circular-Polarisation,’ Pogg. Ann. t. cxix. p. 74. 
1885. N 
