226 PROFESSOR POWELL ON A NEW CASE OF THE INTERFERENCE OF LIGHT. 
(46.) To obtain assuming T approximately as differing little from which is near 
enough for this purpose, the following values result : — 
Ray. 
P- 
sin = ^ sin 
Pos. 1. 
Pos. 2. 
l“o- 
P'E’ 
Pos. (I). 
Pos. (2). 
Sassafras. 
<?'■ 
2 = 60 — <p'. 
2 = ip. 
B. 
1-5409 
1-5499 
1-5430 
1-5432 
1-52575 
0 / // 
30 25 
29 35 
0 / // 
30 25 
D. 
1-5442 
1-55.33 
1-5464 
1-5465 
1-53215 
30 16 30 
29 43 30 
30 16 30 
E. 
1-5471 
1-5563 
1-5494 
1-5494 
1-53870 
30 30 80 
29 52 0 
30 30 80 
F. 
1-5496 
1-5589 
1-5519 
1-5519 
1-54485 
30 0 0 
30 0 0 
30 0 0 
G. 
1-5542 
1-56.36 
1-5566 
1-5565 
1-55750 
29 44 0 
30 16 0 
29 44 0 
H. 
1-5582 
1-5677 
1-5607 
1-5605 
1-56935 
29 29 0 
30 31 0 
29 29 0 
(47.) Then with more accurate values of T we obtain, successively, 
Ray. 
sin i = 
i 
LC . 
— Sin i, 
z 
z — 
Z — pc. 
k cos i 
VX cos 2 y 
Diff. 
=+. 
Position 1. 
Position 2. 
Pos. 1 . 
Pos. 2. 
Pos. 1. 
Pos. 2. 
Pos. 1. 
Pos. 2. 
Pos. 1. 
Pos. 2. 
B. 
0 / // 
29 13 0 
0 / 
30 2 
// 
0 
+ -OI73 
+ -OI75 
+ 779 
+ 795 
+ 117 
+ 119 
D. 
29 25 30 
29 58 
0 
+ -0143 
+ -0144 
+ 754 
+ 762 
+ 113 
+ 114 
— 4 
— 5 
E. 
29 38 30 
29 54 
+ -OIO7 
+ •0107 
+ 633 
+ 634 
+ 95 
+ 95 
-18 
-19 
F. 
29 51 
29 51 
+ -OO71 
+ •0071 
+ 451 
+ 451 
+ 68 
+ 68 
-27 
-27 
G. 
30 17 
29 45 
--OOO9 
--0010 
— 65 
- 73 
— 10 
— 11 
-78 
-79 
H. 
30 42 
29 40 
--0086 
— -0088 
-683 
-694 
-102 
— 104 
-92 
-93 
219 
223 
Hence arrangement I. gives bands. 
(48.) For the ordinary ray with the plate vertical, the number of bands agrees well 
with observation as far as it goes. 
It is obvious in general, that if two sets of bands differing in number be super- 
posed, there will be a number of coincidences equal to their difference, separated by 
spaces of pai’tial obliteration, which if the bands be of sensible breadth, will extend 
over several bands. 
On comparing the above values of/> for O and for E in position 1, we find — 
From B to £ . . . 29 — 22= 7j 
From E to H . . . 205 — 197= 8 =number of intervals of indistinctness. 
From B to H =15^ 
From E to H this agrees with observation, and may do so from B to E, occasioning 
a total disappearance of bands. 
Postscript . — At the time the foregoing paper was communicated to the Royal 
Society, I had not seen Mr. Stokes’s paper ; nor in writing his, had he seen mine at 
length ; hence it will be found that there are some repetitions in the latter, of points 
mentioned in mine, but usually put in so much clearer a light that the reader will 
not regret the repetition. 
