ON OPTICAL THEORIES. 163 
ment tells us, to a high degree of approximation, that the whole of the 
energy of the incident light appears in the reflected and refracted light. 
Weare therefore forced to suppose not merely that the longitudinal wave 
does not affect our eyes as light, but also that it does not absorb any 
material part of the incident energy. This conclusion is confirmed when 
we recollect that on arriving at a second refracting surface this longi- 
tudinal wave would, if it existed, set up transverse vibrations which 
would be visible, so that on passing through a prism, for example, there 
would always be two emergent rays. 
Now, Green shows that very little energy will be absorbed by the 
longitudinal vibrations, provided that the ratio A/B be very small or 
very great; and, further, that the condition of stability of the medinm 
requires that A/B should be greater than 4/3. He therefore concludes 
that A/B is very great—practically infinite, or that the wave of longi- 
tudinal vibrations travels with a velocity enormously greater than that of 
light. 
; The equations are then solved, assuming that B=B, and A= A,,* by 
the substitutions— 
dx dy 
(12) 
y = _o 
dy dx 
The symbol ¢ represents the longitudinal or, as Sir Wm. Thomson 
has called it, the pressural wave, and W the transverse or light wave. 
It is shown that by the reflexion a difference of phase is produced 
between the reflected and incident and the refracted and incident waves, 
and expressions are found for the intensities of the reflected and refracted 
waves in terms of that of the incident. According to these expressions, 
the intensity of the reflected wave never vanishes, but reaches a minimum 
when 9 + ¢'= 90°. The minimum value of the ratio of the two intensi- 
ties will be for air and water about 1 /151, while for a diamond or other 
substance of great refractive index it would be much greater still. 
§ 3. This result, then, of the theory is in direct antagonism to the fact 
that light is very nearly completely polarised by reflexion from most 
transparent surfaces at the polarising angle, while the values found for 
the change of phase do not agree with the experiments of Jamin,! 
Quincke, and-others, and the theory as left by Green is certainly incorrect. 
We shall, however, return to this point later. 
Green does not apply his equations to the problem of crystalline 
reflexion, and, indeed, his theories of reflexion and of double refraction are 
entirely inconsistent, for the former supposes the ether to have the same 
rigidity in all bodies, while the latter attempts to explain double refrac- 
ie by making the rigidity of a crystal a function of the direction of the 
strain. 
* This last equation, as we shall see later, is not necessary. 
_ ' Jamin, Ann. de Chimie (3), t. xxix. p. 263 ; Quincke, ‘Experimentelle optische 
Untersuchungen,’ Pogg. Ann. See also Haughton, Phil. Mag. (4), vol. vi. p. 81. 
? See p. 192. 
M 2 
