MAGNETIC VARIATION AT TORONTO. 
501 
or the more convenient equivalent expression, 
A^=+-05 + -215 sin (a+353°-6)+-3324 sin (2a+ 13°-5), 
the coefficients being decimals of a scale-division, and a reckoned in liours, multi- 
plied by 15°, from the time of the Moon’s superior culmination. By this formula is 
obtained the curve which is shown by the stronger line in fig. 1 of the accompanying 
Plate XIX.; and for the purpose of showing the degree of confidence to which this 
curve is entitled, as an approximate representation of the variation produced in the hori- 
zontal force by the moon in the course of a lunar day, the variation in the different 
years in columns 2 to 6 of Table I. have been so combined as to form two separate 
means, one representing the columns headed 1844, 1845 and 1 846, and a second repre- 
senting the columns headed 1846, 1847 and 1848; the years 1844 and 1845 having 
double weight assigned to them in the first mean, and 1847 and 1848 double weight 
in the second mean. The formulae representing these separate means are, — 
for 1844 to 1846, A^= -h'088 + -243 sin (rt-i-347°'6)-l-'277 sin (2a-l-4°-4), 
for 1846 to 1848, A^=+'013 + -J92 sin (rt-|-355°-0)-h-395 sin (2a-l- 19°-2). 
The curves respectively computed by these formulae are shown by the fainter lines 
in fig. ], in which the stronger line has been already noticed as derived from the 
mean of the five years. 
Vertical Force. — Table II. exhibits in columns 2 to 6 the mean horary variation of 
the Vertical Force at the different lunar hours in each of the five years ending June 30 ; 
and in column 7, the mean variation in the five years. 
Table II. 
Lunar 
hours. 
III the year ending June 30. 
! 
Mean of the 
1 five years. 
Lunar 
hours. 
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 
- I - 0-08 
+ 0-02 
— 0-02 
- 0-03 
+ 0-03 
+ 0-02 
0 
1 
+ 0-09 
— 0-03 
+ 0-06 
0-00 
+ 0-02 
+ 0-03 
1 
2 
+ 0-02 
— 0-07 
- 0-16 
- 0-09 
— 0-18 
— 0-10 
2 
3 
— 0-11 
0-00 
- 0-07 
+ 0-18 
— 006 
+ 0-01 
3 
4 
- 0*09 
— 0-01 
— 0-01 
+ 0-13 
+ 0-08 
+ 0-02 
4 
5 
+ 0-01 
— 0-02 
- 0-09 
+ 0-07 
+ 0-02 
0-00 
5 
6 
— 0-12 
— 0-12 
+ 0-09 
+ 0-01 
- 0-05 
- 0-04 
6 
7 
— 0-06 
— 0-24 
+ 0-08 
— 0-18 
— 0-02 
— 0-08 
7 
8 
- I - 0-03 
— 0-22 
+ 0-03 
— 0-15 
— 0-17 
— 0-10 
8 
9 
— 0*04 
— 0-10 
- 0-10 
+ 0-02 
- 0-07 
— 0-06 
9 i 
10 
— 0-13 
- 0-10 
- 0-10 
+ 0-08 
- 0-11 
- 0-07 
10 1 
11 
— 0-14 
+ 0-03 
— 0-03 
+ 0-02 
- 0-14 
- 0-05 
11 I 
12 
- 0-08 
+ 0-12 
- 0-10 
+ 0-01 
— 0-20 
— 0-05 
12 
13 
- I - 0-14 
+ 0-03 
+ 0-08 
+ 0-10 
- 0-16 
+ 0-04 
13 i 
14 
4 - 0-03 
+ 0-10 
+ 0-04 
+ 0-03 
- 0-09 
4 - 0-02 
14 
15 
4 - 0-08 
+ 0-15 
+ 0-06 
+ 0-02 
+ 0-04 
+ 0-07 
15 : 
16 
4 - 0-11 
+ 0-18 
+ 0-08 
+ 0-12 
+ 0-06 
+ 0-11 
16 1 
17 
+ 0-17 
+ 0-09 . 
4 - 0-04 
+ 0-04 
+ 0-12 
+ 0-09 
17 
18 
+ 0-19 
+ 0-09 
+ 0-18 
- 0-03 
+ 0-02 
+ 0-09 
18 
19 
+ 0-11 
+ 0-05 
0-00 
0-00 
+ 0-12 
+ 0-06 
19 
20 
+ 0-14 
+ 0-01 
+ 0-01 
- 0-14 
+ 0-08 
+ 0-02 
20 
21 
+ 0-11 
- 0-07 
- 0-17 
— 0-13 
+ 0-05 
- 0-04 
21 
22 
+ 0-08 
+ 0-04 
— 0-21 
— 0-07 
+ 0-07 
- 0-02 
22 
23 
+ 0-11 
+ 0-04 
- 0-18 
— 0-13 
- 0-03 
— 0-06 
23 
3 u 2 
