150 LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
if at equal azimuths on each side of the magnetic north, 
__ w l + « a 
T ~ 2 
“The formula fails if + ^' 2 = 180°, the denominator becoming zero; the true 
value of tan (ip — Wl + ^ in that case is 
b 
sin 2 JJ'j + b cos 2 £'j cot Wl — 
Corrections for the Erebus . — We will seek in the first instance the values of the 
constants a and b, because they are those which can be obtained with the greatest 
degree of exactness, being derived from observations with the compass needle, which 
are made with greater precision than those with the inclination or intensity needles. 
Before the Expedition quitted England, a suitable position in the midship line was 
chosen 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 with 
the ship’s head turned successively on each of the thirty-two principal points. This 
was done in September 1839 at Gillingham near Chatham, where 0, or the Inclination, 
was at that epoch 69° 05'*. 
The observations in the Erebus gave results as follows : — 
Ship’s head 
hy compass. 
Attraction 
towards 
the west. 
Ship’s head 
by compass. 
Attraction 
towards 
the west. 
Ship’s head 
by compass. 
Attraction 
towards 
the west. 
Ship’s head 
by compass. 
Attraction 
towards 
the west. 
N. 
N. by w. 
N.N.W. 
n.w. by n. 
N.W. 
n.w. by w. 
W.N.W. 
w. by n. 
+ 6 06 
+ 1 12 
+ 2 01 
+ 2 10 
+ 3 03 
+ 3 28 
+ 3 51 
+ 4 09 
w. 
w. by S. 
w.s.w. 
s.w. by w. 
s.w. 
s.w. by s. 
s.s.w. 
s. by w. 
+ 4 19 
+ 4 40 
+ 4 03 
+ 3 24 
+ 2 45 
+ 2 08 
+ 1 34 
+ 0 52 
s. 
s. by e. 
S.S.E. 
s.E. by s. 
S.E. 
s.e. by e. 
E.S.E. 
e. by s. 
+ 0 28 
-0 19 
-0 48 
— 1 23 
-1 53 
— 2 21 
-2 50 
— 3 17 
E. 
E. by N. 
E.N.E. 
n.e. by e. 
N.E. 
n.e. by N. 
N.N.E. 
n. by e. 
O / 
-3 42 
— 4 53 
-3 46 
-3 18 
-2 59 
-2 16 
-1 39 
-0 49 
We perceive by this Table that, allowance being made for slight irregularities in 
the observations, the masses of iron which acted on the compass needle of the Erebus 
in its standard position were distributed symmetrically, or very nearly so, on either 
side of the vertical plane, passing through the longitudinal midship section. We 
may therefore safely employ, in computing the corrections, the more simple formulae 
which are applicable under this condition. 
To obtain the constants a and b of these formulae we may arrange equations on the 
several 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. 
