500 
MAJOR-GENEHAL SAJBINE ON THE LUNAR-DIURNAL 
nearly corresponded was marked by myself, and the differences from the normals and 
their arrangement in tables exhibiting the lunar-diurnal influence were prepared, 
under the superintendence of Mr. Magrath, by the Non-commissioned Officers of the 
Royal Artillery employed in the Woolwich Office. The total number of observations 
in the five years, after the separation of the larger disturbances, was, — of the Bifilar, 
34303 ; and of the Vertical Force Magnetometer, 31773. The lunar influence at the 
different lunar hours is shown in the tables in decimals of a scale division; the value 
of a scale division of the Bifilar being *000087 parts of the horizontal force, and of the 
vertical force magnetometer *000065 parts of the vertical force. 
Horizontal Force . — Table I. exhibits, in columns 2 to 6, the mean horary variation 
of the horizontal force at the different lunar hours in each of the five years ending 
June 30 ; and in column 7? the mean of the five years. 
Table I. 
Lunar 
hours. 
111 the year ending 30th June. 
Mean of the 
five years. 
Lunar 
lioiirs. 
1844. 
1845. 
1846. 
1847. 
1848. 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
sc. div. 
sc. div. 
sc. div. 
sc. div. 
sc. div. 
sc. div. 
0 
-(-0-44 
— 0-05 
-I-O-IO 
+ 0-70 
-0-07 
+ 0'22 
0 
1 
+ 0-48 
+ 0-01 
-|-0'09 
-I-0-70 
+ 0-68 
+ 0-39 
1 
2 
+ 0-68 
+ 0-59 
-l-O-ll 
+ 0-29 
-I-0-42 
+ 0-42 
2 
3 
-i-0'42 
+ 0-48 
+ 0-71 
+ 0-30 
-I-0-08 
-f-0-44 
3 
4 
-I-0-58 
-f 0-28 
-t-O-22 
+ 0-09 
+ 0-19 
+ 0-27 
4 
5 
+ 0-16 
+ 0-68 
+ 0-21 
+ 0-43 
-hO-74 
-I-0-44 
3 
6 
— 0-23 
+ M1 
— 0-03 
+ 0-09 
-hO-43 
-I-0-27 
6 
7 
-0-13 
+ 0-72 
-0-20 
-0-23 
+ 0*21 
+ 0-07 
7 
8 
-0-16 
+ 0-59 
— 0*31 
—0-24 
-0*19 
-0-06 
8 
9 
-0-12 
+ 0-28 
-0-23 
-0-79 
-I-0-24 
— 0-12 
9 
10 1 
— 0-43 
+ 0-20 
— 0-10 
-0*62 
+ 0*23 
— 0-14 
10 
11 
— 0”02 
+ 0-32 
-1-0-36 
+ 0-39 
— 0-22 
+ 0-17 
11 
12 
-0-28 
+ 0-37 
+ 0-15 
— 0-03 
— 0*31 
— 0‘02 
12 
13 
-)-0-ll 
+ 0-64 
+ 0-11 
+ 0-23 
+ 0-47 
+ 0-31 
13 
14 
-I-0-06 
+ 0-84 
-l-0']8 
-0-09 
-HO-40 
-I-0-28 
14 
13 
-LO-06 
+ 0-04 
+ 0*23 
— 0-06 
+ 0-73 
+ 0-20 
15 
16 
0-00 
-0-01 
-hO-13 
-i- 0-32 
-I-0-28 
+ 0-14 
16 
17 
— 0-17 
-I-0-48 
-0-47 
0-00 
+ 0-33 
+ 0-03 
17 
18 
— 0*08 
-0-19 
— 0-13 
-0-24 
— 0-47 
— 0-22 
18 
19 
-0*21 
— 0-13 
— 0-33 
— 0-34 
-0-80 
— 0-40 
19 
20 
-0-19 
— 0-70 
— 0-11 
— 0-33 
— 1-33 
-0*38 
20 
21 
-0-19 
— 0-82 
— 0-31 
-0-09 
-1-07 
— 0-30 
21 
22 
— 0-28 
— 0-44 
-0-22 
+ 0-09 
-0-63 
-0*30 
22 
23 
— 0-08 
— 0-46 
-0-15 
+ 0-34 
— 0-18 
— 0-11 
23 
We may represent the values in column 7 of this Table (or the variation of the 
horizontal force at the several lunar hours on the average of the five years of observa- 
tion) by the first terms of the usual formula for periodical functions, viz. 
A^=Ao-l-Ai cos a+Bi sin a-{- Ag cos 2a-}- Ba sin 2a. 
By substituting in this formula the numerical values of the coefficients obtained from 
the numbers in eolumn 7, it becomes 
A^= -l-*05 — *024 cos a-|-'214 sin a-l-'0775 cos 2a-l-*323 sin 2a, 
