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IX. On the Effect produced on the Deviations of the Compass hy the Length and Arrange- 
ment of the Compass-Needles ; and on a New Mode of correcting the Quadrantal 
Deviation. By Aechibald Smith, Esg., M.A., F.B.S., late Fellow of Trinity College, 
Cambridge ; and Fkedeeick; Johh Evans, Esg., R.N., Superintendent of the Compass 
Department of Her Majesty s Navy. 
Eeceived April 13, — Bead April 18, 1861. 
Introductory observations. 
In the mathematical investigations of the deviation of the compass which have been 
hitherto published, and in the practical methods for correcting the deviation which have 
been proposed by Captain Flindees, Mr. Baelow, and Mr. Aiet, the assumption is 
tacitly or expressly made that the length of the compass-needle may be considered as 
infinitesimal compared with the distance of the nearest disturbing iron. Expressed 
mathematically, as only even powers of the ratio of the projection of the needle on the 
direction of the disturbing mon to the distance of the disturbing iron enter into the 
expressions, the assumption is that the square and higher powers of that ratio may be 
neglected. By this assumption the formulae which express the deviation are materially 
simplified ; and on the supposition that the iron of a ship consists entirely of iron of 
one or other of the two extreme qualities described magnetically as “ hard ” iron and 
“ soft” iron, the following expression is accurately true: — 
sin cos ^+B sin cos ^'+1) sin (^+^0 > 
in which ^ is the azimuth of the ship’s head measured eastivard from the correct 
magnetic north ; 
is the same azimuth, but measured from the direction of the disturbed needle ; 
is the easterly de\iation of the needle; 
A, D, E are coefficients depending only on the distribution of the soft iron of the 
ship, and being independent of the magnetic dip and force, and therefore not changing 
with a change in the geographical position of the ship, 
B and C are coefficients depending partly on the distribution of the hard and soft iron 
of the ship, and partly on the dip and horizontal force, and therefore changing with 
a change of geographical position of the ship, as well as with a change in the magnetism 
of the hard iron in the ship. 
If the soft iron of the ship be symmetrically arranged on each side of the fore-and-aft 
vertical plane which passes through the compass, the coefficients A and E are zero, and 
in all ships the deviations of which have been examined, these coefficients are so small 
MDCCCLXI. 2 A 
