376 
LIEUT. -GENEEAL SABINE ON TEEEESTBIAL MAGNETISM. 
Formulae for the correction of observations of Dip and Total Intensity made in 
Wood-built Ships. 
In the Memorandum printed in the Contributions to Terrestrial Magnetism, No. V., 
Philosophical Transactions, 1843, p. 147, the following expressions will be found which 
are immediately derived from the formulae given by Poisson in the Memoirs of the 
Institute, vol. v. p. 533. 
±_ 
A'<p 
cos 6' cos %'= 
cos 0 cos £ + a sin 0, 
cos 0' sin %—b cos 0 sin £, 
JL 
A'<p 
sin &=c cos 0 cos %-\-d sin 0 
( 1 ) 
( 2 ) 
( 3 ) 
In these expressions 
<p is the total Magnetic Intensity expressed in any unit. 
0 is the Dip. 
£ is the magnetic azimuth of the ship’s head. 
<p', O', %' are the same quantities affected by the induced magnetism of the soft iron in 
the ship. 
A', a, b, c, d are coefficients depending on the amount and distribution of the soft 
iron. 
These expressions are based on the assumptions that all the iron of the ship is (mag- 
netically) soft, and that it is symmetrically arranged on each side of the fore-and- 
aft section. These assumptions are nearly true in ships such as the ‘Erebus’ and 
4 Terror.’ 
In the same memorandum, p. 148, expressions are given for O' and <p' in terms of 
0, <p, £, from which the coefficients may be determined if we have a sufficient 
number of corresponding observations ; and from them Tables of double entry may then 
be constructed, giving the corrections to be applied to the observed values 0' and <p' in 
any required dip. These formulae are exact, and may be used whatever be the amount 
of disturbing force, but are not very conveniently adapted for calculation. 
When, as in the ‘Erebus’ and ‘Terror,’ the disturbing force is small, we may treat 
the errors of Dip and Force as small quantities of which the squares and products may 
be neglected, and we may then obtain the errors of dip and force by simple expressions 
of the form 
c$0=L-J-M cos£+N cos 2£, 
^=P-}-Qcos£4-Ksin 2?. 
If the observations of $0 and 
are made on any number of equidistant magnetic points 
exceeding two, the coefficients L, M, N, P, Q, R may be obtained with great facility 
