882 
MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
It lias already been pointed out (p. 858) that tlie above supposition would give 
a value of d less than that for tlie red of the first order of thin plates, so that 
no colours of thin plates are to be expected. The constants A, . . . , of course vary 
with the colour, but tlieir effect, in any case, would not equal that due to variation of 
q, and therefore of cos (^Q + ^\) and cos [Iq — q). 
[Owing to the secondary importance of the constants A, D, F, and the impossibility 
of measuring them accurately, it will be necessary to take account only of E in dis¬ 
cussing the limitations to which any law of variation of the refractive index /x in the 
variable layer is subject. In any particular case, the law must be such as to make [jd 
continuous in value throughout the layer and equal to /xy and /xp at the two 
boundaries ; and to give to E its experimental value by a sufficiently small choice of 
the thickness of d of the layer to ensure convergence of the series for the displacements. 
Besides, yd must nowhere be less than l,and nowhere greater than about 10, this last 
representing the greatest value of yd known to exist for a transparent substance. 
The law of variation must involve at least two disposable constants in addition 
to d. 
If the law is to be a general law, so as to include every known case, then it must 
be capable of making E positive and negative, corresponding to positive and negative 
reflection. That is, jx^ must be capable of maxima or minima. For example, the law 
of variation discussed b}^ Lord Bayleigii (‘Proc. Loud. Math. Soc.,’ XI., p. 51) will 
not satisfy this condition. In this case, we have fx — , x being the distance 
a 
/^1 — 17 4 Svrd 
, E = 3/Xo —--. —, 
which is always positive when the second medium is the more refractive. Hence, 
Lord Rayleigh’s law will only explain positive reflection. 
If the first medium have a refractive index 1, then yd must have a maximum to 
give negative reflection. 
If the second medium have a refractive index equal to the upper limit, that is 
3 or so, then yd must have a minimum in order to give negative reflection. 
In addition tlie general law must make E vanish, that is, jxd -fi /xy = a + /XqVi" 
when y.Q = 1, = IMG or so, in order to explain Jamin’s results. 
It follows from Gladstone and Dale’s experiments, and others of the same kind, 
that the law of variation of yd may be of the same form as that of the density. The 
eftect of capillary forces will be to make the density vary near the surface of a liquid, 
possibly also of a solid. A somewhat problematical investigation of the law of 
variation of the density in the transition film between a liquid and its vajiour is 
given by J. Clerk Maxwell, in his article on Capillary Action, in the ‘Encyclopedia 
Britannica’ (9th Ed.), which gives the density of the variable portion an exponential 
function of the distance from the sui'face. If such a law represent the actual 
circumstances, then negative reflection must be ascribed to adventitious films of dust 
from the first face of the variable layer ; this gives 
