878 MR- G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
The only experiments bearing on the relations between the constants for reflection 
from either of several j^airs of media are those of Quincke for flint-glass—air, flint- 
glass—water, and crown-glass—air. These experiments are very irregular, as shown 
by the very large “ probable errors ” occurring in all except the first. Quincke 
himself admits that he could not attain to the accuracy of Jamin and even of Kuez, 
and, as already stated, in order to make Cauchy’s formulae fit at all, he has to use a 
different value of p, from that which is determined in the ordinary w'ay. For 
instance, for flint-glass—air he uses 1’609 in place of I'6160, for flint-glass—water 
1'23I2 in place of 1'20!)6, and for crown-glass—air l’5f0 instead of 1‘5I5. He gives 
several other sets of experiments in addition to these, but they consist of few 
observations and are very much more unreliable still. 
As stated above (p. 877) A, B should be the same for the two sets of experiments 
on each pair. In the case of A this is certainly not true. For flint-glass—air and 
flint-glass—water they are of opposite sign. The determination of A depends almost 
entirely on the extreme terms of the series of observations, for it is multiplied by 
cos -f- Q), which is very small for the middle terms. Now the extreme observations 
in these experiments of Quincke’s show very large errors indeed, in some cases of 
more than a degree in nr, and are not to be much relied upon. The entire extinction 
of A wmuld not make a difference of more tlian a few minutes, and if we decide to 
retain it, little stress can be laid on its not satisfying the theoretical conditions."^' 
The case of B and E is much more important, as the deviations from Fresnel’s 
formulae depend on them to a first approximation. 
* On the Accuracy ivitli which the Constants are determined. 
Tlie expressions on p. 860 give 
'dvT _ sin I’o sin p cos cos p 
0A 
aF^ 
2 cos^ (ty — ii) 
drr- sin-L sin^L cos A cos i^ c , 
■ cos- tr, . - = - i cos- 3^ . cot 3-, 
0B 2 cos^ (t, — h) 
sin- 0 
0c 
sin^'t, cosz'q 0E 
sin 2^ 
2E 
Let ns consider tlie effect of small eri'ors of 10' in w, and of i/\ in r, say for a glass sucff as tliat iised 
by Kuez (p. 871) at an aiig-le of incidence of 60°. For this angle zr is about 4°, r is about oi’ I50°- 
We find 
5-A=:-12o. t"=’9I5, |f = --667, = -5-85, 
0A ' 0B 0F 0E 
dzr, dc being measured in radians. 
The circular incasure of d-ur — 10' — is ‘0029, that of do — UIO of ^ or 1° 8' — is '0200. 
Thus, 
and 
Thus, 
dw = 10' could be i^roduced by dK = ■023, or by dli — 'OOo'l, 
do = of y\ could be produced by dF = — '080, or b}^ (ZE = — '0035. 
