222 
Abstracts of the Makerstoun Observations, 1843. 
TABLE II. — Mean Variations of Westerly Declination, after Eliminating the Secular Change, with 
Reference to the Moon's Age, Declination, and Distance from the Earth, for 1843. 
Variations 
Variations 
After 
Variations 
After 
Variations 
Before 
Variations 
Before 
Variations 
Moon's 
of West 
Moon's 
of West 
Moon 
of West 
Moon 
of West 
and 
of West 
and 
of "West 
Age. 
Age. 
Declina- 
farthest 
Declina- 
farthest 
Declina* 
Declina* 
after 
Decli na- 
tion. 
tion. 
North. 
tion. 
North. 
tion. 
Perigee. 
tion. 
Apogee. 
tion. 
Day. 
' 
Day. 
' 
Day. 
' 
Day. 
' 
Day. 
' 
Day. 
• 
15 
0-85 
0 
0-19 
0 
1-05 
14 
1-28 
7 
0-72 
7 
0-88 
16 
0-94 
1 
0-30 
1 
080 
15 
0-64 
6 
0-00 
6 
0-93 
1 / 
U*UU 
o 
Z 
i /in 
1 ft 
ID 
n qa 
U'O'i 
D 
1 AO 
D 
U-D4 
18 
1-04 
3 
0-43 
3 
0-69 
17 
1-16 
4 
0-40 
4 
0-18 
19 
1-10 
4 
0-71 
4 
0-96 
18 
0-47 
3 
0-23 
3 
0-19 
20 
0-89 
5 
0-96 
5 
0-66 
19 
025 
2 
0-62 
2 
0-08 
21 
0-35 
6 
0-88 
6 
0-53 
20 
0-00 
1 
0-35 
1 
0-03 
22 
0-32 
7 
0-71 
7 
0-89 
21 
013 
P 
0-40 
A 
0-01 
23 
0-11 
8 
0-71 
8 
1-02 
22 
0-40 
1 
0-60 
1 
0-40 
24 
0-25 
9 
0-14 
9 
0-99 
23 
0-76 
2 
0-64 
2 
0-24 
25 
0-66 
10 
0-32 
10 
0-40 
24 
0-30 
3 
0-66 
3 
0-42 
i 26 
0-84 
11 
0-96 
11 
0-64 
25 
1-19 
4; 
0-85 
4 
1-23 
27 
0-06 
12 
0-92 
12 
1-42 
26 
111 
5 
0-82 
5 
0-89 
28 
0-30 
13 
1-04 
13 
1-03 
27 
1-24 
6 
0-75 
6 
0-67 
29 
0-32 
14 
0-73 
7 
0-60 
7 
0-80 
The above Table was formed from the daily means in Table I. in the following manner : — The mean westerly 
declination on the 12 days, between January 15. 1843 and January 4. 1844, on which the moon's age was 15 days, 
were summed together, similarly for 16 days old, 17 days old, . . . the means of these sums were then tahen, and 
the differences from the lowest mean are given in the above Table. In these summations the approximate means 
for Sundays were used, as it was conceived that the want of any means on these days would affect the results more 
seriously than the use of the approximations. As in some lunations the 29th day was awanting, the mean of the 
declinations on the 28 day and the day of new moon was summed instead. 
For the variations of westerly declination with reference to the moon's meridian altitude, the day on which 
the moon was farthest north was numbered 0, and the days after this were numbered up to 26 or 27, the day before 
the moon again attained its greatest north declination ; if there were only 26 days the mean of the declinations on 
the 26th and Oth day was substituted for the mean on the 27th day ; the mean westerly declination was then ob- 
tained for all the days of the same number from January 13. 1843 till January 3. 1844, each mean being the 
mean of the westerly declinations on 1 3 days ; the differences from the lowest were then taken, and are inserted above. 
For the variation of westerly declination with respect to the moon's distance from the earth, it will be seen in 
the foregoing Table that the days before and after apogee and perigee are numbered from 1 up to 7 ; in some 
instances there are only 5 days before apogee and 5 days after perigee, or before perigee and after apogee ; in these 
cases, for example, the 5th day before apogee has been numbered also as the 6th and 7th after perigee, and the 
5th after perigee as the 6th and 7th before apogee ; when there are 1 1 days between apogee and perigee, or perigee 
and apogee, the 6th is counted as the 6th and 7th before and after ; when there are 12 days between, the 6th 
before apogee is counted as the 7th after perigee, and vice versa; when there are 13 days, the 7th day is counted 
as the 7th before and after, and when there are 15 or 16 days, the mean of the declinations for the 7th and 8th 
days is used as the mean for the 7th. The mean westerly declinations for the days with similar numbers, between 
January 12. 1843 and January 5. 1844, were then obtained as in the previous cases, and the differences from the 
lowest moan aro given in Table II. ; each number is the mean of 13. It would have simplified the summations, 
and this statement of them, to have rejected the means on the 8th, 7th, and 6th days (of themselves they would 
have been useless), but it seemed better to combine them with other means nearly similarly related to the distance 
of tho moon than to throw them away. 
After the summations for each of the above cases had been performed, and the means obtained, the secular 
chango was eliminated at the rate of Q'-QlQb per diem. 
Tho abovo statement will apply to the similar summations for the horizontal and vertical components of mag- 
netic force. 
