150 LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM.
if at equal azimuths on each side of the magnetic north,
i _ "1 + »aY — 2 ‘
“The formula fails if ^ + £' 2 = 180°, the denominator becoming zero; the truevalue of tan (\p — in that case is
_A_
sin 2 ^ cos 2 cot 8)2
Corrections for the Erebus .—We will seek in the first instance the values of theconstants a and b, because they are those which can be obtained with the greatestdegree of exactness, being derived from observations with the compass needle, w r hmhare made with greater precision than those with the inclination or intensity needl^S.Before the Expedition quitted England, a suitable position in the midship line waschosen for magnetic observations on board ship, and the effect of the ship’s attrac-tion on a standard compass placed in that spot, was ascertained by observations withthe ship’s head turned successively on each of the thirty-two principal points. Thiswas done in September 1839 at Gillingham near Chatham, where 6, or the Inclination,was at that epoch 69° 05'*.
The observations in the Erebus gave results as follows :—
Ship’s headby compass.
Attractiontowardsthe west.
Ship’s headby compass.
Attractiontowardsthe west.
N.
+ 5 06
w.
O !
+ 4 19
n. by w.
+ 1 12
w. by s.
+ 4 40
N.N.W.
+ 2 01
w.s.w.
+ 4 03
N.w. by n.
+ 2 10
s.w. by w.
+ 3 24
N.W.
+ 3 03
s.w.
+ 2 45
N.w. by w.
+ 3 28
s.w. by s.
+ 2 08
W.N.W.
+ 3 51
s.s.w.
+ 1 34
w. by n.
+ 4 09
s. by w.
+ 0 52
Ship’s headby compass.
Attractiontowardsthe west.
Ship’s headby compass.
Attractiontowardsthe west.
s.
+ 0 28
E.
O /
— 3 42
s. by e.
-0 19
e. by n.
— 4 53
S.S.E.
-0 48
E.N.E.
-3 46
s.e. by s.
-1 23
n.e. by e.
-3 18
S.E.
— 1 53
N.E.
-2 59
s.e. by e.
-2 21
n.e. by n.
-2 16
E.S.E.
-2 50
N.N.E.
-1 39
e. by s.
-3 17
N. by e.
-0 49
We perceive by this Table that, allowance being made for slight irregularities inthe observations, the masses of iron which acted on the compass needle of the Erebusin its standard position were distributed symmetrically, or very nearly so, on eitherside of the vertical plane, passing through the longitudinal midship section. Wemay therefore safely employ, in computing the corrections, the more simple formulaewhich are applicable under this condition.
To obtain the constants a and b of these formulae we may arrange equations on theseveral points, from the observations in the Table, of the form
cos £ sin — b sin £ cos = — a tan 6 sin
* Reports of the British Association, 1838.