ON OPTICAL THEORIES. 167 
§ 2. Terms of asimilar kind were first applied by Airy ! to explain 
the magnetic rotation of the plane of polarisation discovered by Faraday. 
Airy starts by calling attention to the fundamental difference between 
the rotation produced by quartz and that due to magnetic action. In 
quartz, sugar, etc., by reflecting the ray back along its original path the 
rotation is reversed, so that the ray emerges with its plane of polarisation 
unaltered, while in bodies under magnetic action the rotation is doubled 
by the same process. It is as if the former effect were due to a heliacal 
arrangement of the molecules, the latter to a continuous rotation of them 
round the lines of force. Airy shows that the effects produced can be 
accounted for by the introduction into the equation for w of terms 
involving odd differential coefficients of v with respect to the time, and 
he works out the case in which the equations are 
d?u du rou v 
dt? dz? dt 
(17) 
The two possible velocities for a wave of period r are given by 
f=, t= = 
Te RUT 5 Pet yy 
us or 
dv d3y 
aed ae would also 
lead to the effect observed; though they would differ in the law, express- 
ing the relation between the velocity and the wave length. Airy 
remarks that ‘the equations are given, not as offering a mechanical 
explanation of the phenomena, but as showing that they may be ex- 
plained by equations, which equations appear such as might be intro- 
duced by some plausible mechanical assumption.’ 
§ 3. The attempt to estimate the relative value of the theories of 
reflexion and refraction just developed is rendered easier if we consider 
the physical meaning of the two constants involved. The importance of 
this has been continually insisted upon by Sir Wm. Thomson? in his 
numerous writings on the subject of elasticity, which have done so much 
to clear away difficulties and obscurities; and though these writings 
belong to the later period of our subject, we shall consider here some of 
the results they lead to. 
It is pointed out also that terms such as 
__ To Green, Cauchy, and MacCullagh, A and B are constants, appearing 
in the most general form of the equations, and on which the rate of propa- 
gation of waves depends; their connection with the other physical pro- 
perties of the solids is not considered. Now an isotropic ‘elastic solid is 
one which possesses the power of opposing resistance (1) to change of 
shape, (2) to change of volume, and has in consequence only two prin- 
cipal moduluses of elasticity. 
__} Airy, ‘On the Equations applying to Light under the Action of Magnetism,’ 
Phil. Mag. (3), vol. xxviii. p. 469. 
? See especially, Thomson, ‘Elements of a Mathematical Theory of Elasticity,’ 
Phil. Trans. 1856, p. 481; Thomson and Tait, A Treatise on Natural Philosophy, 
vol. i. ; Thomson, article ‘ Elasticity,’ Encyclopedia Britannica, ninth edition, 1880. 
