MADE BY CAPTAIN BACK DURING HIS LATE ARCTIC EXPEDITION. 
383 
Place of observation. 
Relative intensity 
COS (V — y) 
JV1 — ' f i or 
sin (V — S) 
lvr — sln S.sin (y — D) 
sin D cos (S — 5) 
Relative intensity, or 
value of M deduced from 
the time of vibration of 
the needle No. 11. 
New York 
38-41 
8-140936 
Montreal 
16-60 
8-3 ? 
Fort Alexander 
23-25 
8-569610 
Cumberland House 
6-76 
8-409142 
Isle a la Crosse 
8-12 
8-278406 
Fort Chipewyan 
9-23 
8-324042 
Fort Resolution 
6-29 
8-612853 
Fort Reliance 
8-26702 
8-26702 
Musk-Ox Rapid 
10-73 
8-169870 
Rock Rapid 
8-20 
8-327742 
Point Beaufort 
10-90 
8-041422 
Montreal Island 
14-80 
8-154152 
Point Ogle 
16-82 
8-277498 
Fort Reliance, Oct. 9, 1834. 
10-03 
8-269714 
Making every allowance for the want of adaptation of the needle to this method 
of determining the relative intensities, for errors of observation in determining the 
times of vibration of the needle, and for any disturbing causes affecting these obser- 
vations, such differences are here exhibited in the results obtained by the two methods, 
at New York, Montreal, Fort Alexander, Montreal Island, and Point Ogle, as can 
only be accounted for by errors in the assumed value of the angle y, and clearly in- 
dicate a want of permanence in that angle. It therefore becomes necessary to inquire 
what changes in the angle y will account for these discrepancies, and how far the dip 
may be affected. For this purpose either y or S must be eliminated from the equa- 
tions (3.) and (4.), and the value of the other determined in terms of M. 
Putting these equations in the form 
M 2 cos 2 D . sin 2 (S — &) = cos 2 S . cos 2 (y — D) j 
M 2 sin 2 D . cos 2 (S — &) = sin 2 S . sin 2 (y — D) j 
we obtain immediately 
M 2 (sin 2 S . cos 2 D — cos 2 S . sin 2 D} . sin 2 (S — S) = sin 2 S . cos 2 S — M 2 cos 2 S . sin 2 D, 
M 2 {sin 2 S . cos 2 D — cos 2 S . sin 2 D} . cos 2 (S — &) = M 2 sin 2 S . cos 2 D — sin 2 S . cos 2 S. 
Putting P = M . and Q = M . these equations become 
M 2 sin '6 sin fi sin 2 (S — ci) = — sin 2 2 S (1 — P 2 ) (8.), 
M 2 sin ’0 sin fi cos 2 (S — ci) = sin 2 2 S (Q 2 — 1 ) (9.) ; 
whence, 
