LIEUT. -GENERAL SABINE ON TERRESTRIAL MAGNETISM. 
377 
by applying the method of least squares, as in the Memorandum in Contribution 
No. VIII., Philosophical Transactions, 1846, p. 346, and as in the ‘Admiralty Manual 
for the Deviation of the Compass.’ 
In this way, from observations made on sixteen points in the ‘ Erebus ’ at Hobarton in 
1840-1841, we obtain 
<50= — 2'— 66' cos £+6' cos 2£, 
^= + -0053 - -0146 cos £+ -0009 cos 2£. 
These formulae give the error, and therefore, changing the sign, the correction of the 
Dip and Total Intensity on any magnetic azimuth at the place of observation. 
If we wish to know how the coefficients L, M, N, P, Q, R are affected by a change of 
dip, we may proceed as follows. 
From equations (1), (2), (3) we obtain 
<p' cos 0' cos — <p cos 0 cos £ 
cp cos 0 
<p cos I 
—A! a tan 4+ (A'— 1) cos £, 
(A!b — 1) sin . . . 
( 4 ) 
( 5 ) 
sin o — <s sin \ 
i p sin i 
= Aid — 1 -f- A!c cot 0 cos 
re) 
Let x, y , z be the components of in the three rectangular directions, to head, to star- 
board, and to nadir, so that x=<p cos 0 cos £, y= <p cos 0 sin £, z=cp sin 0, and let x J , y', z 1 
be the same quantities affected by the magnetism of the ship, and let h be the horizontal 
force =\/x 2 -\-y 2 =(pcosQ, and let x'—x^x, y'—y=ty, z' — z=lz, then equations (4), 
(5), (6) become 
j=A!a tan 4 + (A'— 1 ) cos £, 
(Alb — 1) sin £, 
and as tan &=?-> 
h 
=A!d— 1 + A'c cot 0 cos £ ; 
10 = 
khz — zVi 
hz (iz U 
h 
= sin $ cos cos^ — j sin ^j 
=L+M cos ^ -f- N cos 2£, 
-h^A'^— ^ sin 20, 
where 
