880 MR. G. A. SCHOTT OH THE REFLECTIOH AHD REERACTIOH OF LIGHT. 
far from being the case. In so far as no such relation exists for our theory, it has the 
advantage over Cauchy’s. 
Let us now consider the values of D, E in greater detail; by p. 836 the values of 
these constants are, leaving out of account terms in (27r(://X)^, 
D = 2/Zy. 
AC-A 
0 0 
lirrl 
A 
E = — 2/^0 
A O o , 0 o 
- /^o~ - /^i' + 
o o 
ay - /xy 
27r'/ 
A 
where A, G are the mean values of fj}, for the variable layer respectively. 
A” 
We have 
A - fiQ- - -I- 
.'O '. A / \ H- / 
uji— — ] (h — - ” j vanishes, when /x = p,j or (of course values of /x < + 1 do 
not occur), it has an algebraic minimum — (/Xj — jj^qY for the value of /x = •v/(p,i/ro), 
is negative for values of [x between /Xq and /x^, is positive for values either less or 
greater than both /Xq and 
Hence if jx for the variable layer lie between /x^ and A ~ — fx^ -f GpoVi^ 
is certainly negative, if outside those limits, certainly positive. In any other case 
nothing can be said cl priori as to its sign, unless indeed the law of variation of p in 
the v.ariable layer be given. 
If then p lie between Pq and p^, E will be positive or negative—and the same will 
be the character of the reflection in Jamin’s sense—according as the first medium is 
the more refractive or the less. And the reverse holds when p is outside the given 
limits. 
Now Jamin’s and the other experiments show that the reflection is in most cases 
(but not in all) positive or negative according as P]/po is greater or less than 1‘46. 
In these cases, we are at liberty to suppose that for positive reflection, that is, 
when pi/po > 1‘46, p for the film < p^, and that, for negative reflection, when 
Pj/po < 1’46 (but > 1) p for the film > p^. This shows that w-hen the second 
medium is air (as is tacitly assumed by Jamin, otherwise the critical value might be 
different), the refractive index of the films is, for some parts at least, > 1'46, and 
less than 2'5 or so, or perhaps we ought more properl}?- to say that the average 
refractive index is between those limits. Kundt has shown that the refractive 
index of colcothar, or red oxide of iron, which is a common polishing material, is 
about 2'G6 ; that of chalk, I suppose, would be of the same order of magnitude as 
for calc-spar and arragonite, that is, about 1’5—1‘6. .A. glass surface, with lumps 
of such polishing material embedded in it, might be expected to behave as if coated 
with a film of average refractive index between 1'5 and 2‘5, and thus certainly give 
positive reflection. Of course it has not been proved that p for every part of the 
