860 MR. G. A. SCHOTT OH THE REFLECTION AND REFRACTION OF LIGHT. 
In combining the experiments I have assumed as a first approximation that the 
accuracy is the same for all values of 8 , the difference of phase, and likewise for all 
values of In strictness this is not true, since the accuracy of the readings is 
greater the more nearly equal are the intensities of the two components of the 
reflected light. But as /8 in most cases ranges from above to below^ 45°, the 
assumption will be sufficiently true to give values of the constants not far removed 
from their most probable values. 
The sets of constants A and B, and F and E have in each case been determined 
independently by making the sum of the squares of the errors in a and / 8 , 
respectively, a minimum. 
We have by (XL) 
, r. E sill" L cos L 
tan h — -^’ 
cos (^o — q) cos (^0 + ^l) + F 
COS" (^o-q) 
sin f,, sin q cos \ cos i, cos (fo-t b) -d h\ h b b 
-=H-—- 
cos'^ (b-b) 
cos'*' (b“b) 
tan- 
Let 8 , y 8 be the true, 8 ', /3' the observed values, and let 8 q, be approximate 
values, given tentative values Aq, Bq, Fq, Eq of the constants. 
Let A = Aq + o, B = Bg + F = Fg + y’ E = Eg + e, a, h, f, e being small 
quantities to be determined by the conditions 
t ( 8 ' — 8 )^ = minimum, S {^' — /3)^ = minimum. 
Tlien, substituting for 8 , yS their values 80 +/" + e /3 q + "I" ^ ^ > 
2(8'-S)®b=0. S( 8 '-S)|^ = 0 , S(^'-/3).| = 0 , 2(^'-^)| = 0 , 
in the equations 
9 / 
and measuring 
quantities— 
8 ' — 8 / 3 ' — yS in degrees, we obtain, neglecting squares of small 
/S 
j /9 8o\ /9 8o\ ^ (9' - 9o) /9 8A 
+ 180 ■■■■•W 
^ TT (3' - Bq) /^o\ 
^ 180 ' V3Eo/ 
^ TT { 0 ' — A)) /^o\ 
180 \9«o/ 
TT (/S' - ySo) /a^o\ 
^ 180 \0Bo/ ’ 
