4 
MR. AIRY’S SUPPLEMENT TO A PAPER “ ON THE THEORETICAL 
Table of ( s -^) 2 • cos* (w - §). 
Values of w. 
Values of R. 
0° 
60° 
120° 
180° 
240° 
300° 
O 
- 175 
25 
20 
8 
0 
4 
17 
— 165 
229 
230 
123 
17 
17 
123 
- 155 
610 
738 
499 
133 
6 
245 
- 145 
1050 
1553 
1286 
515 
12 
280 
— 135 
1372 
2560 
2560 
1372 
184 
184 
- 125 
1413 
3527 
4261 
2882 
767 
33 
- 115 
1109 
4168 
6l64 
5101 
2043 
47 
- 105 
567 
4231 
7896 
7896 
4231 
567 
- 95 
84 
3618 
9032 
10912 
7378 
1964 
- 85 
104 
2453 
9216 
13631 
11282 
4519 
- 75 
1111 
1111 
8294 
15475 
15475 
8294 
— 65 
3473 
148 
6396 
15970 
19294 
13046 
- 55 
7298 
169 
3962 
14884 
22013 
18221 
- 45 
12346 
1654 
1654 
12346 
23038 
23038 
- 35 
18020 
4796 
204 
8835 
22060 
26652 
- 25 
23474 
9402 
217 
5104 
19175 
28360 
- 15 
27778 
14887 
1994 
1994 
14886 
27778 
- 5 
30154 
20389 
5427 
231 
9996 
24959 
+ 5, 
30154 
24959 
9996 
231 
5427 
20388 
+ 15 
27778 
27778 
14887 
1994 
1994 
14887 
+ 25 
23474 
28360 
19175 
5104 
21-7 
9402 
+ 35 
18020 
26651 
22060 
8835 
204 
4794 
+ 45 
12346 
23038 
23038 
12346 
1654 
1654 
+ 55 
7298 
18220 
22013 
14884 
3962 
169 
+ 65 
3473 
13045 
19294 
15970 
6396 
148 
+ 75 
1111 
8294 
15475 
15475 
8294 
1111 
+ 85 
104 
4519 
11282 
13631 
9216 
2453 
+ 95 
84 
1964 
7378 
10912 
9032 
3618 
+ 105 
567 
567 
4231 
7896 
7896 
4231 
+ 115 
1109 
47 
2043 
5101 
6164 
4168 
+ 125 
1413 
33 
767 
2882 
4261 
3527 
+ 135 
1372 
184 
184 
1372 
2560 
2560 
+ 145 
1050 
279 
12 
515 
1286 
1553 
+ 155 
610 
245 
6 
133 
499 
738 
+ 165 
229 
123 
16 
17 
123 
230 
+ 175 
25 
17 
4 
0 
8 
20 
It has been deemed unnecessary to continue the Table beyond the values of w — 1/5° 
and + 175°, because the values of become very small. The greatest maxi- 
mum of this quantity occurs when w — 0; its value (expressing w in terms of the 
3 7T 
radius) is then = 1 ; the second maximum occurs when w — — nearly; its value is 
then 
/ 2 \ 2 1 
nearly = ^ nearly; the amount of which will probably produce an in- 
considerable influence on the expressions which we are now about to consider. 
The curves in the annexed figure represent, by their ordinates, the values of 
* cos2 i. w ~ y) ’ *he va * ues °f R being continued as far as 720°, in order to 
exhibit more distinctly to the eye the successive displacements of the principal bows 
