384 
MR. CHRISTIE ON THE MAGNETICAL OBSERVATIONS 
tan (S - &) = \/|^zrr| ......... (10.)* 
TSie equation (5.) gives 
cot (y D) = p qj _ j j - • • • • • • * • • (1 1 •); 
or, putting P ( = — and Q y = -q, 
cot(y-D) = \/{r=^7 } * * ( n r) 
Assuming that the values of M deduced from the time of vibration of the needle at 
the several stations are the correct values, and substituting them in the equation (10.), 
I have computed the values of S — 5, y — D, and thence determined the dip and the 
angle y at these stations. The results are arranged in the following Table. 
Place of observation. 
Value of M 
deduced from 
the time of 
vibration of the 
needle No. II. 
Value of y— D 
deduced from 
the foregoing 
value of M. 
Value of S - 5 
deduced from 
the foregoing 
value of M. 
Resulting 
value of y. 
Resulting 
value of 3. 
Value of £ 
deduced 
from the 
constant value 
^=16 29' 19'/. 
Difference 
between the two 
values of J. 
New York 
8-140936 
0 
3 
21 
55 
o 
2 
1 
// 
37 
o 
3 
45 
// 
40 
o 
71 
12 
// 
29 
o 
72 
49 
// 
18 
o 
+ i 
36 
49 
Montreal 
8-3 ? 
7 
43 
10 
1 
26 
41 
8 
37 
34 
76 
21 
55 
77 
6 
27 
+ o 
44 
32 
Fort Alexander 
8-569610 
5 
46 
7 
1 
13 
54 
6 
25 
45 
78 
6 
3 
78 
53 
37 
+ 0 
47 34 
Cumberland House 
8-409142 
18 
1 
36 
1 
2 
7 
20 
6 
31 
79 
46 
34 
79 
29 
59 
-0 
16 
35 
Isle a la Crosse 
8-278406 
15 
0 
21 
1 
5 
37 
16 
46 
28 
79 
29 
45 
79 
28 
24 
— 0 
1 
21 
Fort Chipewyan 
8-324042 
13 
24 
54 
0 
56 
54 
14 
59 
47 
80 
54 
44 
81 
00 
39 
+ 0 
5 
55 
Fort Resolution 
8-612853 
19 
43 
10 
0 
45 
6 
21 
56 
55 
82 
21 
39 
82 
3 
9 
-0 
18 
30 
Fort Reliance, October 9, f 
8-267020 
14 
44 
0 
0 
37 
34 
16 
29 
19 
84 
1 
0 
84 
1 
0 
0 
0 
0 
1833,andMay 21, 1834 / 
Musk-Ox Rapid 
8-169870 
11 
26 
22 
0 
27 
16 
12 
49 
39 
85 
45 
24 
85 
53 
32 
+ 0 
8 
8 
Rock Rapid 
8-327742 
14 
56 
30 
0 
14 
35 
16 
42 
53 
87 
39 
48 
87 
39 
34 
-0 
0 
14 
Point Beaufort 
8-041422 
11 
5 
49 
0 
13 
5 
12 
28 
4 
87 
59 
40 
88 
3 
15 
+ 0 
3 
35 
Montreal Island 
8-154152 
8 
26 
47 
0 
16 
25 
9 
55 
17 
87 
27 
13 
87 
35 
49 
+ 0 
8 
36 
Point Ogle 
8-277498 
7 
35 
38 
0 
4 
3 
8 
30 
31 
89 
22 
5 
89 
24 
12 
+ 0 
2 
7 
Fort Reliance, Oct. 9, 1834 
8-269714 
12 
20 
15 
0 
35 
23 
13 
48 
45 
84 
24 
52 
84 
31 
24 
+ 0 
6 
32 
The differences between the values of y in the above Table, deduced from the 
equation (11.), and its assumed value, are certainly in many cases considerable; and 
the dip also, in some, differs considerably from that previously deduced. It is, how- 
ever, to be remarked with regard to these differences, that the above values of y are 
deduced from the assumption that no other sources of error existed in the instrument 
than the want of permanence in the axis of the needle itself. Those who have been 
most in the habit of making observations for determining the dip, will be best able 
* Either of the equations (8.) or (9.) gives a convenient expression for the calculation of S — 8, viz. 
sin 2 S / 1 — P 2 ^ sin 2 S / Q, 2 — 1 
sin (S — S) = 
2 M 
5 / 1 - I 
y sin '0 si 
P 2 , a sin 2 S 
- — or cos (b — o) = 
sin,0 v 1 2 M 
V= 
; but the equation (10.) is even 
more so. It might appear that the equation (10.) would be better adapted for logarithmic computation, if 
put in the form tan (S 
(1 + P) ■ (! -P) 
(Q + 1) . (Q - 1) 
but this is not the case, since the computation which 
would determine P determines P 2 by simply doubling the logarithm ; and besides this, the same opening of 
the table by which Q 2 would be found, gives the logarithm of Q 2 — 1. 
