MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 877 
The expressions for A, B, D, E are given on p. 856. Considering the values of A, 
B — c, G, J, given on the same page, we see that A, G do not change when the 
two media on either side of the variable layer are interchanged, b — c merely 
changes sign, and J does the same—this is evident from the physical meaning of J ; 
we have to take an element P and another element Q, form the expression 
2 2 
^ ^ 5 multiply by the product of the elements, and then sum, first, for all 
Mq" p“ 
elements Q on that side of P from which the light comes, and, lastly, for all the 
elements P of the film; calling the result j, j', according as the light comes from one 
or the other side of the layer, clearly in forming the sum J + j' we must sum 
2 2 
^ for all elements Q and for all elements P, hence J + j' vanishes, since the 
/iQ- /ip- 
two elements of the integral for any two points P, Q destroy each other. 
An inspection of the values of A, B shows that they should have the same values, 
whether the light comes from one side or the other—provided, of course, the layer 
remains the same. 
As for D, E — D becomes + 2a, ~E becomes 
A'-r A'-o" ^ 
, A — 27rf? 
+ -kl-^ * 
It has already been stated that B, E are not independent constants; by theory we 
have B = • Eb 
M'i) 
A comparison of the values of B and p,E^, as given in the table, p. 876, shows that 
this last condition is, with few exceptions, very nearly fulfilled. The chief exception 
is in the case of essence of lavender, where B is ’000027, whilst jU.E^ is ’000065, but 
this is sufficiently accounted for by the smallness of B, and the consequent smallness 
of zu and which makes a small error in the determination of jS important relatively 
to the magnitude of B. The large differences in the last four pairs in the table on 
p. 876 may be due to terms of the third order in E, but these sets of experiments are 
not very accurate, the contact of liquids and solids being irregular in character. Of 
the two constants, E is determinable with much the greater accuracy, since the 
variations from Ebesnel’s formulae, which are given by all the constants = zero, are 
much greater for the phases than for the intensities, but it is not easy to say what 
weight should be attached to each determination. I myself should j)refer to rely 
solely on the value of E, and thence calculate B; this will not very much alter the 
values of tan^ cr, which are chiefly determined by the values of ’ This is 
confirmed by the experiments of Kuez on flint-glass in air (p. 871), where Feesnels 
formula is seen to give nearly as good a representation of the intensities as the 
theoretical formula and that of Cauchy. 
