824 ME. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
which are incomplete, taking no account of other terms of the same order involving 
B — C (see p. 849, seq.). 
P. Deude treats the subject from the standpoint of Voigt’s elastic solid theoiy, 
and obtains analogous formulse. He uses Kirchhoff’s boundary conditions, and since 
these are at best hypothetical, his method is not perfectly satisfactory. 
In the following paper the employment of more or less hypothetical boundary 
conditions is avoided by supposing the medium continuous, the transition taking place 
in a variable layer of small but finite thickness, and solutions of the equations of 
vibration are obtained in ascending powers of the thickness, which expressions are at 
least as convergent as the geometric progression whose ratio is 
''2'ir d —\2 
W'here d is 
tlie thickness of the varial)le layer, p, is the greatest value of the refractive index 
occurring in it, and X is the wave-length of light. Exjiressions are then found for 
the intensities and phases of the reflected and refracted light, taking into account 
terms of order d^. 
The consequences are examined both of a rigid elastic solid theory, which includes 
tlie theories of Voigt and K. Pearson, and of the electromagnetic theory and 
Lord Kelvin’s contractile ether theory, which lead to the same result. 
The elastic solid theory gives modifications of Green’s expressions, even wheo the 
refractive index of the pressural wave differs from that of light, and cannot be made 
to agree with experiment. 
The electromagnetic and contractile ether theories lead to Cauchy’s type of 
expression, the ellipticity being variable, and these agree very well with experiment. 
§ 1. General Equations of Vibration. 
It will be well briefly to recapitulate the systems of equations which have been 
proposed to represent the periodic disturbances to which light is due. 
Electromagnetic Theory .—Let represent the 
components of electric and magnetic force for a periodic disturbance at the point {xyz) 
of the medium, where its specific inductive capacity is K—the real parts of the 
complex expressions being taken in the usual way. Also let the velocity of propaga¬ 
tion of electromagnetic disturbance in vacuo be 1/A. Then the equations of vibration 
are 
whence 
Kqo. X = 
in 
Al]) . = 
d/x 
& 
0^. 
37 
(and two similar pairs). 
_3_ I 7 /_3f 
dif \dy dr) dz yd' 
-f- A"Ky)~^ = 0 (and two others) . , (I.). 
OX y 
These are given by Hertz (“ Ueber die Grundgleichungen der Elektrodynamik,” 
