MR. G. A. SCHOTT ON THE REELECTION AN[) REFRACTION OF LIGHT. 
861 
and here we may, in the coefficients, replace Sg, /8 q, by S', /3' wherever convenient, 
thus find 
E _ _ Eg slid B' 
® \9Fq/ sin- {q cos Iq ’ 
We 
sin 5' cos S', 
2 coffi a . 
'9/5o\_^ _„.2 O' % sffi h cos % cos h cos + h) 
Mo/ - ^ ^ 
.T 4.0 / 9 /Sn\ , O' 3 0' sin^ i sild h cos ^ cos h 
2 cot- a. I ) = cot p . cos- p . -^- 
SB, 
COS^ (tg — h) 
This is the method used in most cases, but in the more inaccurate experiments it 
was easier to find the sums of the squares of the errors for several pairs of values 
of the constants, and thence, by a kind of interpolation, to find the best values of 
the constants. 
Since the values of E, B are determined independently, the nearness with which 
they satisfy the relation E- = — B will serve in some measure as a test of the 
formulae. 
I have for comparison given the deviations from Cauchy’s formulae, calculated with 
the given value of e by the experimenter himself. These run roughly parallel 
with the deviations from the theoretical values, and where there seemed any very 
great deviation from parallelism, I have recalculated the results of Cauchy’s 
formula. For instance, Jamin, for fire-opal, gives incorrect values for RJL/RII 
(his J/T). On recalculating from the given values of y8, some of his values are found 
to be the square roots of what they should be. 
As an index of the accuracy of agreement, I have given the probable error of a 
single observation, as calculated by the formula ’6745 ^/(S/n — 1), where n is the 
number of observations, S the sum of the squares of the errors. 
