400 MESSES. C. AND F. CHAMBERS ON THE MATHEMATICAL EXPRESSION 
Specimen Calculation of Bessel’s Coefficients, for variation of Aggregate 
Successive "1 
months. J 
0 
1 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
Twenty-sixths 
of the sidereal 
0 
9 
18 
1 
10 
19 
2 
11 
20 
3 
12 
21 
4 
period of Mer- 
cury 
Cosine 
+ 1000 
-•567 
-■355 
+ ■971 
-•749 
-•120 
+ •885 
-•885 
+•120 
+ 749 
-•971 
+•355 
+ ■568 
Sine 
0000 
+■823 
-•935 
+•239 
+•663 
-•993 
+•465 
+■465 
-•993 
+•663 
+ •239 
-•935 
+•823 
Monthly Aggregates 
| 
1st 9 period* 
53-343 
81-730 
52675 
31-843 
41-527 
69-892 
153-729 
108-458 
67142 
210-564 
52-444 
82-755 
84-714 
2nd 
16-206 
16-850 
18-278 
32 054 
19-469 
53-973 
92-298 
20-561 
28-997 
28-544 
34-003 
15 067 
18-623 
3rd 
35-098 
21-894 
90-523 
49-580 
18-995 
72240 
53-346 
129-985 
24127 
74-522 
126-439 
14-392 
18-704 
4th „ 
94-948 
19-424 
17374 
38-480 
50-902 
64-843 
56-504 
43-466 
10-708 
22-208 
31-258 
10-283 
22-554 
5th „ 
14-734 
14-338 
8054 
14-978 
10 926 
13-924 
1-665 
12-098 
5 052 
9554 
21-379 
15-433 
0-000 
6th 
49-958 
39181 
64-664 
111087 
18-894 
25-834 
77-967 
30-488 
43-782 
44-923 
27-337 
15 034 
57-819 
7th „ 
103-117 
37-567 
17-695 
38-733 
140-932 
221-409 
64-623 
63-580 
11-436 
38-406 
60-495 
56-850- 
37678 
8th „ 
27-592 
21-266 
51-978 
81-257 
55-343 
163-152 
13-866 
55-289 
62-003 
39-771 
60-408 
56-068 
56448 
9th 
57-361 
40140 
39-891 
20-698 
5 020 
20-390 
52-565 
27-247 
9-906 
39-858 
27-21 1 
25-372 
53231 
10th „ 
12-088 
31-926 
32-221 
8047 
30-424 
15-881 
4-994 
2-875 
14 832 
11-655 
16-841 
25-108 
21-224 
1 1th 
7-087 
6-428 
55-697 
43-308 
60-588 
75-824 
67852 
52-912 
17095 
30-644 
116-304 
50-840 
17692 
Sums 
471532 
330-744 
449-050 
470065 
453020 
797-362 
639-409 
546-959 
295 080 
550-649 
574 119 
367-202 
388-687 
Means 
42-867 
30-068 
40-823 
42'733 
41-184 
72-487 
58128 
49-724 
26-825 
50059 
52-193 
33-382 
35-335 
Variations 
1 -0-313 
-13 112 
-2-357 
-0-447 
-1-996 
+29307 
+ 14-948 
+6-544 
- 16-355 
+6-879 
+9-013 
-9-798 
-7-845 
* Commencing with March 1847. 
