VAUIATLON OF TERRESTRIAL MAGNETlSxM. 
477 
Curves were now carefully drawn for each of the eight coefficients, making them fit 
in as well as possible with the ordinates and the direction of their tangents, as given 
in Tables III. and V. 
The values of Y were then read off foi’ each 7°‘5 of colatitude, and a fresh table 
was formed (Table VI.). 
From this point onwards we have to carry on the calculations separately for each 
type of the variation. 
Table VI. 
Coefficients in the series Y = cos t sin t + a., cos 2t sin 2t Vc. for 
different degrees of colatitude, the unit of force being C.G.S. X 10“''. 
Colatitude. 
K 
a_. 
h,. 
a j. 
h- 
a^. 
■i' 
i 
O 
1 0 
+ 
10 
0 
0 
0 
0 
( + 
48) 
( 
0) 
( 
i 
0) 
7-5 
-f 
32 
+ 
97 
+ 
42 
+ 
9 
(+ 
12) 
( + 
51) 
( + 
1) 
( + 
3) ' 
15-0 
+ 
52 
+ 
158 
+ 
76 
+ 
22 
(+ 
24) 
( + 
53) 
( + 
■ 1) 
( + 
6) ' 
22-5 
+ 
71 
+ 
196 
+ 
91 
+ 
48 
+ 
39 
+ 
54 
+ 
1 
+ 
7 
30-0 
+ 
85 
+ 
215 
+ 
90 
+ 
101 
+ 
56 
+ 
54 
+ 
2 
+ 
11 
37-5 
+ 
96 
+ 
231 
+ 
89 
+ 
143 
+ 
73 
+ 
55 
+ 
11 
+ 
18 
4.5-0 
+ 
92 
+ 
243 
+ 
96 
+ 
160 
+ 
99 
+ 
61 
+ 
16 
— 
3 
52-5 
+ 
85 
+ 
247 
+ 
90 
+ 
168 
+ 
98 
58 
+ 
22 
— 
21 
60-0 
+ 
74 
+ 
205 
+ 
83 
+ 
165 
+ 
91 
+ 
54 
+ 
20 
— 
24 
67-5 
-t- 
65 
+ 
144 
+ 
131 
+ 
83 
+ 
89 
+ 
28 
+ 
11 
— 
20 
75-0 
+ 
63 
+ 
87 
+ 
127 
37 
+ 
69 
+ 
10 
+ 
2 
— 
15 
82-5 
+ 
58 
+ 
58 
+ 
117 
+ 
15 
+ 
46 
— 
3 
— 
6 
— 
11 
90-0 
+ 
37 
+ 
42 
+ 
82 
-J- 
7 
+ 
25 
— 
2 
— 
14 
+ 
6 
97-0 
+ 
10 
+ 
21 
+ 
15 
+ 
1 
+ 
3 
-1- 
1 
— 
20 
+ 
18 
105-0 
— 
3 
— 
7 
— 
4 
— 
17 
— 
16 
— 
6 
— 
27 
13 
112-5 
+ 
3 
— 
56 
— 
3 
— 
48 
— 
36 
— 
23 
— 
40 
0 ' 
120-0 
0 
— 
105 
— 
4 
— 
102 
— 
47 
— 
45 
— 
43 
— 
23 
127-5 
— 
50 
— 
120 
— 
15 
— 
118 
— 
53 
— 
50 
— 
35 
— 
26 
135-0 
— 
78 
— 
113 
— 
16 
— 
106 
— 
54 
— 
46 
— 
31 
— 
25 
i 142-5 
— 
97 
— 
100 
+ 
10 
— 
85 
— 
47 
— 
37 
— 
24 
— 
24 
150-0 
— 
121 
— 
85 
+ 
6 
— 
65 
— 
38 
— 
30 
— 
12 
— 
14 
157-5 
— 
140 
— 
75 
+ 
2 
— 
46 
— 
22 
— 
21 
— 
5 
— 
13 
^ 165-0 
— 
154 
— 
61 
+ 
1 
— 
30 
(- 
9 ) 
14) 
(- 
3) 
(- 
9) 
172-5 
— 
162 
— 
36 
0 
— 
14 
(- 
2) 
(- 
6) 
(- 
2) 
4) 1 
180-0 
165 
0 
0 
0 
( 
0 ) 
( 
0 ) 
( 
0 ) 
( 
0) 1 
The quantities a^, by were expressed in the usual way in terms of the multiples of 
the cosines of the colatitude, and two equations obtained which can be shown to 
represent with sufficient accuracy the force of the first type towards the geogTaphical 
West. 
ay= — 5 + 106'7 cos u — 50'6 cos 2u =- 1’7 cos Su — 14'6 cos -in 
— 8’9 cos 5u — 2'0 cos 6u, 
by — 49'4 + lofffi cos u — 0‘4 cos 2u — 76'0 cos 3w — 18’i cos 4w 
— 31'3 cos 5u — 9'2 cos 6u. 
If, now, cos ic, cos 2m, cos 3m, &c., be expressed in terms of dVyjdjx, d^Jd^iy, dV.JdyL, 
