LIEUT.-COLONEL SABINE ON TERRESTRIAN MAGNETISM. 
147 
elements, for the use of nautical men, and of others who might be engaged in reducing 
magnetic observations made at sea. He has obligingly furnished me with the fol- 
lowing memorandum : — 
“ At a given geographical position let <p represent the total magnetic intensity of 
the earth ; 0 the dip, which is considered positive when the north end of the needle 
dips below the horizontal plane, negative when it inclines above it ; X, the azimuth of 
the ship’s head, or the angle between the principal section of the ship and the mag- 
netic meridian, which is considered positive when the ship’s head is to the west of 
the magnetic north, negative when to the east. Let p', 0', XX,, be the values of the same 
elements shown by a needle whose centre is at a given place in the ship, when affected 
by the magnetism induced in the soft iron of the ship by the magnetism of the earth. 
M. Poisson has shown that if the dimensions of the needle are very small compared 
to its distance from the iron by which it is affected, the following equations are true ; 
<p' cos 0’ cos XX, =<p [A' cos 6 cos £ + B cos 6 sin X, + C sin 0 ], 
<p' cos § sin = 9 [D cos 6 cos X, + E' cos 6 sin X, -f- F sin 6], 
<p' sin 0' = <p[ G cos 0 cos £ + H cos 0 sin X, + K' sin 0 ] . 
“ In these equations, A', B, C, D, E', F, G, H, K' are constants which depend only on 
the distribution of the iron in the ship relatively to the position of the needle and the 
plane of the horizon, and which continue the same for every geographical position 
of the ship, while the distribution of the iron within the ship, and the inclination of 
the ship to the horizon, remain the same. 
“ If the centre of the needle is placed in the principal section of the ship, and the 
iron is symmetrically distributed on each side of that section, it will easily be seen that 
for values of X, equal in magnitude and opposite in sign, the corresponding values of XX, 
are equal in magnitude and opposite in sign, and the corresponding values of <p' and 0' 
are respectively equal in magnitude and the same in sign. These results necessarily 
imply that B, D, F and H are equal to zero. The equations in this case become 
<p' cos § cos XX, — <p [A' cos 0 cos X, + C sin 0~\, 
<p' cos 0' sin X,' = <p . E' cos 0 sin £, 
<p' sin 0' — <p [G cos 0 cos X, -f K' sin 0 ~] . 
C jy G j£7 
“ If we divide each term by <p A' and put -^7 = a ’ A 7 = ^ A7 = c > — d, 
cos 0' cos X} = cos 0 cos £ + a sin 0 
^ 7 ^ cos 0' sin XX, — b cos 0 sin X,. . . , 
sin & — c cos 0 cos X, + d sin 0. 
OO 
( 2 .) 
MDCCCXLIII. 
X 
(3.) 
