MADE BY CAPTAIN BACK DURING HIS LATE ARCTIC EXPEDITION. 385 
to judge how far this is likely to be the case in any dipping instrument ; I can only 
say that in the observations which I have myself made, and in those of others which 
I have examined, I have rarely considered that the observed angles could be relied 
upon, as being absolutely those which the axis of the needle would make with the 
horizon, if perfectly free, in any assumed position ; and even when a mean of several 
observations has been taken, I have in general felt that it might differ from the truth 
by several minutes. I do not therefore consider that all the discrepancies in the 
relative terrestrial intensities can properly be attributed to the want of permanence 
in the axis of the needle, though no doubt some, those which are the greatest, are 
principally attributable to this cause. It may, however, be proper to inquire what 
errors in the observed values of '6 and fi will account for these discrepancies, as we 
shall thus be enabled to judge whether they may not in some cases be ascribed to 
this cause. It however unfortunately happens that in this inquiry a knowledge of 
the dip itself is absolutely necessary ; and it is only by assuming that which has been 
determined by means of the values '8 and 8, now supposed to be erroneous, that we 
can determine the changes requisite in the values to account for the discrepancies in 
the relative intensities. 
The equations (1.) and (2.) give immediately, 
cot '8 — 
cot = 
M cos 8 — sin y 
M sin 8 -j- cos y 
M cos 8 + sin y 
M sin 8 + cos y 
( 12 .) 
(13.) 
Assuming then the values of M already given as deduced from the times of vibration 
of the needle, the dips as first deduced from the observations, and the constant value 
y = 16° 29' 19", the values of '8 and fi in the following Table are deduced from these 
equations. 
Place of observation. 
Value of M 
deduced from 
the time of 
vibration of 
the needle 
No. II. 
Dip first 
deduced or 
value of 
Value of '6 
computed 
from the 
equation (12.). 
Observed 
value of '0. 
Resulting 
error in the 
observed value 
of 'd. 
Value of ,0 
computed 
from the 
equation (13.). 
Observed 
value of j9. 
Resulting 
error in the 
observed value 
of j6. 
New York 
8-140936 
o / // 
72 49 18 
0/77 
76 21 23 
O/// 
73 37 51 
o ✓ ✓✓ 
+2 43 32 
72 53 48 
0 7/7 
72 50 21 
0 7/7 
+0 3 27 
Montreal 
8-3 1 
77 6 27 
80 10 10 
78 43 00 
+ 1 27 10 
76 43 16 
76 54 12 
-0 10 56 
Fort Alexander 
8-569610 
78 53 37 
81 41 53 
79 59 35 
+ 1 42 18 
78 19 54 
78 40 19 
-0 20 25 
Cumberland House... 
8-409142 
79 29 59 
82 17 38 
82 53 37 
-0 35 59 
78 51 53 
78 43 45 
+0 8 8 
Isle a la Crosse 
8-278406 
79 28 24 
82 18 34 
82 21 28 
-0 2 54 
78 49 54 
78 49 15 
+0 0 39 
Fort Chipewyan 
8-324042 
81 00 39 
83 40 48 
83 26 30 
+0 14 18 
80 12 29 
80 16 45 
-0 4 16 
Fort Resolution 
8-612853 
82 3 9 
84 32 23 
85 20 30 
-0 48 7 
81 9 59 
80 53 00 
+0 16 59 
Musk-Ox Rapid 
8-169870 
85 53 32 
88 6 16 
87 35 56 
+0 30 20 
84 32 58 
84 49 23 
-0 16 25 
Rock Rapid 
8-327742 
87 39 34 
89 39 9 
89 40 45 
-0 1 36 
86 9 13 
86 8 00 
+0 1 13 
Point Beaufort 
8041422 
88 3 15 
90 4 7 
89 35 00 
+0 29 7 
86 27 28 
86 50 30 
-0 23 2 
Montreal Island 
8-154152 
87 35 49 
89 38 5 
88 46 30 
+0 51 35 
86 4 9 
86 42 45 
-0 38 36 
Point Ogle 
8-277498 
89 24 12 
91 13 34 
90 21 00 
+0 52 34 
87 42 22 
88 31 15 
-0 48 53 
The differences here shown between the observed and computed values of the 
angle fi are, with a few exceptions, within the limits of the errors of dip observations; 
but those of the angle '8 are by no means so, excepting in a few instances. Upon the 
whole we must therefore conclude, that the discrepancies which appear between the 
mdcccxxxvi. 3 D 
