THE INTERFERENCE OF LIGHT. 
225 
and v' =-\/ a- cos- i' + si n^ i\ 
and if V be the velocity in air, so that — =fh, and we take ~=^, then —t=^ ; 
and M being- the retardation expressed by the number of waves’ lengths, we get 
M= ■ ^ cos (/— i')Y 
Also i' is found to differ but little from 30° (about 30' for the extreme rays) and 
cos (i— i') = '9999, which may be put =1. Thus 
T 
M= - sec i {k — !«/). 
For the ordinary ray we have simply 
. /i . . 
sin ^ — sin i 
{^o 
and M= - sec /'(/T/ q— |!a). 
(44.) In this way the following results are obtained, r=:T5 inch. 
Ray. 
Quartz 
/^PQ- 
Oil of Sas- 
safras, 
X 
Position 
vertical 
diif. = «. 
M = M' sec i. 
Position 1. 
DitF.=+. 
B. 
1-5409 
1-5257 
-f-0152 
+ 598 
+ 89-7 
+ 103-4 
D. 
1-5441 
1-5321 
-f-0120 
+ 552 
+ 82-8 
- 7 
+ 95-7 
- 7 
E. 
1-5471 
1-5387 
i--0084 
+ 432 
+ 64 
— 18 
+ 73-9 
- 22 
F. 
1-5496 
1-5448 
-f -0048 
+ 267 
+ 40 
- 24 
+ 46 
— 28 
G. 
1-5542 
1-5575 
— -0033 
-208 
— 31 
- 71 
- 35-8 
- 82 
H. 
1-5582 
1-5693 
— -0111 
— 758 
— 113 
— 82 
-131 
95 
202 
234 
(45.) For the extraordinary ray Mr. Stokes has made a calculation, of which the 
following are the principal steps and results. From the expression above. 
and assuming 
v' = a cos i' 
^ tan2 r ; 
tan 6—- tan i tan T, 
v'=:a cos r sec d, 
whence 
