348 
MAGNETIC SURVEY OF A PART OF THE SOUTHERN HEMISPHERE. 
“‘The coefficients A'B' . . . R/ might, if required, be expressed in terms of the cor- 
responding coefficients of Contribution No. VI. It is here however only important to 
observe that A' B' C' D' E' F' G' H' K' depend only on the amount and distribution 
of the soft iron. P' Q' R' depend partly on the amount and distribution of the soft 
iron, and partly on the amount and distribution of the permanently magnetic iron, 
and become zero when there is no permanently magnetic iron. If the soft iron is 
symmetrically distributed on each side of the fore and aft vertical section passing 
through the compass, B' D' F' H' are equal to zero. 
“ c The above equations are deduced, it must be remembered, on the hypothesis that 
the soft iron of the vessel receives its full charge of induced magnetism instantly on 
the vessel assuming a new position, and that the rest of the iron in the vessel is in a 
permanently magnetic state. On this hypothesis, and supposing that no iron is very 
near the compass, the equations are accurate, and the coefficients A' B', &c. are con- 
stant, and independent of the latitudes. The hypothesis is however evidently not 
strictly true. The magnetic state of the hard, if not of the soft iron of the vessel, 
changes with a change of position and with time. In consequence of this, different 
values of the coefficients are derived from observations made at different places, and 
at the same place at different times. 
“ ‘Careful observations, made in a variety of circumstances and localities, and par- 
ticularly, (for a reason which will appear in a subsequent part of this Memorandum,) 
observations made near the line of no dip, when the affected dip is zero, may 
hereafter throw light on the nature of the change which takes place in the magnetic 
state of a vessel, and furnish the means of determining the change which the coeffi- 
cients undergo. In the present Memorandum they are supposed to be constant. 
“‘From equations (1.) and (2.) the following may be deduced: 
<p' sin S'F'-f Q/ 
i p' sin Q' C' + P* 
sin£- 
COS Zj 
(4.) 
fcosfi S I ipcosfl 
“ ‘ This equation is rigorously accurate, on the assumptions which have been made. 
If <p' cos 0' and <p' sin § were known in terms of <p, 0 and and the coefficients deter- 
mined by observation, this equation would furnish accurate corrections for observa- 
tions of Declination. The expression is very much simplified if we may assume §—0, 
and <p' = <p. This assumption may I believe in general be safely made, except in high 
magnetic latitudes. Making this assumption, we have the following approximate 
formula, 
sin (£-0 = 5-=A- jc tan C +^- 4 } sin £+{p tan 0+^j cos £ 
A'-E' . „„ , JS' + I)' 
~ sin 2 £ 4 cos 2 £ 
c This equation may conveniently be put under the form 
sin^=A+B sin^'+C cos £'-j-D sin 2^' +E cos 2'Q , 
> • • ( 5 -) 
( 6 .) 
