DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 273 



Now in the experiments y < T^ an( l the iimximum variation in \ for rays passing 

 through the slabs amounts only to 5 J fl . 

 But from (10) 



A(tan x -tan^) = y sec x { /i V+^ t -l]tan > x )-^-l}. . . (11). 

 a \ 



Accordingly the greatest variation in tan X tan <f> for the rays passing through 

 the slahs is less than 



)-*--!} ..... (12). 



To compute the order of this expression take p. = 1'5 and x = 30, which last is an 

 extreme estimate. (12) gives 



8 (tan x- tan <) = -0-000033, 

 that is, 



S(x-<) = -0-000033 cos* x = -0-000025 about. 



The change in relative level of the points P,, P, of fig. 1 due to the above amounts 

 to (0-000025) I, and in the experiments I 18 centims. roughly. Thus the change in 

 relative level = 0'00045 centim. The proportional change in the total effective 

 stress = change of relative level -f- semi-height of slab = 0'0009, and this will 

 produce a negligible error in the stress-optical coefficient. Accordingly for mono- 

 chromatic light the effect is to increase the obliquity of all rays by a small constant 

 amount, or to change the effective height k of the slit. As the absolute value of h is 

 not known, and will be found not to enter into the calculations, the presence ot the 

 Nicol will not affect the observations for monochromatic light. 



Kin- white light, however, it may do so if the quantity tan <j> tan x vary sensibly 

 with the colour of the light used, other things remaining the same. 



From (10) 



8 (tan x~ tan <f>) = /ny8/i sin x (/*' 8 i n * x)~*" 



Now for calcite 



X = 6708, jt. = 1-484, /x, = 1'653, 

 X = 5350, p.. = 1-488, p. = T658, 



8/x. = 0-004, 8/io = 0-005. 



Taking the ordinary index as the basis of computation and x = 30 as before, 



8 (tan x- tan <f>) = -0'000026 nearly. 



The proportional error in C deduced from this is obtained by multiplying by 

 /^ t-e., by 27. It is therefore 0-00070. This error corresponds only to the 

 VOL. ocvn. A. 2 N 



