504 
MAJOR-GENERAL SABINE ON THE LUNAR-DIURNAI 
Table V. 
Arguments ... 
Constant 
cos a 
sin a 
cos 2a 
sin 2a 
cos 3a 
sin 3a 
cos 4a 
sin 4 a 
cos 5a 
sin 5a 
cos 6a 
sin 6a 
f 
Ao = 
Ai = 
Bi = 
k^ = 
B2 = 
Ag^ 
B3 = 
A4 = 
B4 = 
A5 = 
B5 = 
Be = 
Coefficients .i 
// 
00 
4 0-20 
// 
-1-03 
-19-18 
+0-45 
// 
+ 1-84 
it 
-0-32 
// 
+ 1-21 
+0-59 
+0-61 
-0-48 
// 
-0-22 
+0-57 
Arguments ... 
cos 7a 
sin 7a 
cos 8a 
sin 8a 
cos 9a 
sin 9a 
cos 10a 
sin 10a 
cos 11a 
sin 11a 
cos 12a 
1 
A; = 
B; = 
^8 = 
B8 = 
Ag = 
B9 = 
Aio= 
Bio= 
kii — 
B„ = 
Ai2 = 
Coefficients < 
-0-56 
+0-08 
+0-16 
-0-03 
-0-91 
-0-39 
-0-50 
// 
-0-42 
+0-49 
+0-28 
-0-29 
The coefficient of principal magnitude is A 2 = — 19"’18, whose argument is cos a. 
The same coefficient, calculated for the different years, is as follows; — 
Year ending June 30, 1843 — 19'35 
Year ending June 30, 1844 — 17‘61 
Year ending June 30, 1845 — 21'05 
Year ending June 30, 1846 — 20’22 
Year ending June 30, 1847 — 19‘04 
Year ending June 30, 1848 — 18'53 
And from the tnean of the six years . . . —19’ 18 
Whence we obtain the probable error of — 19"'18, being the value of A 2 derived from 
the mean of the six years= + 0"‘34. 
With the two first terms of this formula, viz. 
A^=0"'0-|-0"‘20 cos a— 1"'03 sin a— 19"* 18 cos 2a+0"‘45 sin 2a, 
or its more convenient equivalent, 
A,=0"-0-l"-05 sin (a-f348° 52')-f 19"-186 sin (2a+271° 21'), 
we obtain the deflections of the north end of the magnet at the several lunar hours 
as follows : — 
Table VI. 
Lunar 
hours. 
Deflections. 
Lunar 
hours. 
Deflections. 
Lunar 
hours. 
Deflections. 
Lunar- 
hours. 
Deflections. 
22 
9’29 to the East 
4 
9'19 to the West 
10 
10-67 to the East 
16 
10-77 to the West 
23 
15-92 
5 
15-89 
11 
17-30 
17 
17-78 
0 
18-95 
6 
18-14 
12 
19-38 
18 
20-21 
1 
16-46 
7 
15-34 
13 
16-31 
19 
17-43 
2 
9-54 
8 
8-20 
14 
8-86 
20 
10-19 
3 
0-14 
9 
0-42 to the East 
15 
1-04 to the West 
21 
0-42 
Comparing these values with the actual deflections, we find the probable error at 
each observation hour +l"-37. 
