MR. G. A. SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT. 82.5 
‘Wted. Ann./ 40), as according with experiment for heterogeneous media in the 
absence of free electricity. 
But following Lord Rayleigh (“ Electromagnetic Theory of Light,” ‘Phil. Mag.,’ 
1881), I have put the magnetic permeability = 1 in Hertz’s equations, so as to 
make them give results agreeing with experiments on reflection of light and on the 
scattering of light by small particles. There are also electrical experiments to justify 
this course, due to Hertz, and showing that the phenomena of, at any rate, quick 
vibrations, are independent of the magnetic permeability of the medium. 
Elastic Solid Theory .—Let represent components of displace¬ 
ment at the point of the medium, where the effective density is p, the rigidity 
is n, and the bulk-modulus is L Following Lord Rayleigh (“On the Scattering of 
Light by Small Particles,” ‘Phil. Mag.,’ 1871), we shall suppose n the same in all 
bodies, and therefore constant throughout the variable medium considered. Then 
the equations of vibration in Lame’s form are 
B.r 
(^' -f- 
4 
3 
dv I \ 1 I 9 \ 
dy 9-2 / J \32/ 
q- pphi = 0 (and two others) 
These equations include the results of the more general theories of Voigt and of 
K. Pearson. 
Voigt (“ Theorie des Lichtes fur durchsichtige Medien,” ‘ Wied. Ann.,’ 19, p. 873) 
neglects the first pressural term, and replaces n, pp^ respectively by e + a — and 
[m-\-r) p^ — n, that is, makes the effective density and rigidity depend on the period. 
K. Pearson (“ Generalized Equations of Elasticity,” ‘ Proc. Lond. Math. Soc.’, 
vol. 20, p. 291) replaces n, and pp^ by X + 2/x + (X'-f 2p,')p^ + (P'" + i y) 
and by [p — k) p®. 
Thus, in the general case, k, n, p are functions of the period. 
There are two principal forms of elastic solid theory— 
First. — Green’s Theory —which attempts to get rid of the longitudinal (pressural) 
waves by a kind of total reflection at all but very small angles of incidence, whilst at 
nearly normal incidence their effect is inappreciable owing to the smallness of the 
normal component. 
du , dv . dw. ,, 
X—Lx-h ^ IS very small, 
ox cy o.z 
the pressure is finite—it is not necessary that k be greater than lOOn to make the 
effect of the longitudinal wave inappreciable. (Glazebrook, ‘ B.A. Report on Optics,’ 
1885, p. 192.) 
Secondly. —Lord Kelvin’s Contractile Ether Theory — k + is made zero, so that 
the longitudinal wave is not propagated from any place where it may arise. Putting 
zero for k -}- in equations (IL), they become of exactly the same form as 
MDCCCXCIV.—A. 5 N 
ihe bulk-modulus k is made very large, the expansion 
