354 
MAGNETIC SURVEY OF A PART OF THE SOUTHERN HEMISPHERE. 
“ 4 If the deviations are so small that the angles may be used instead of their sines, 
then the differences between the observed deviations and the deviations calculated 
with the first five terms may be used instead of s 2 , s 4 , &c. in finding F and G or 
H and K. There is however no advantage gained thereby, as the quantities within 
the brackets in F and G have already been found in calculating B and C. 
“ 4 As an example of the use of these formulae, we may take the deviations observed 
on board Her Majesty’s ship Erebus at Gillingham, in Sept. 1839*. 
“ ‘ From the deviations observed on the sixteen principal points, I find 
&= 17'+235'- sin £—13' cos £+21'* sin 2£- l'*23 cos 2£. 
“ e From the deviations on the eight principal points, I find 
1 = 16'+233'-5 sin £-14'* cos £+21 sin 2£-0'75 cos 2£. 
“ 4 Applying the correction derived from the first formula, the residuary differences 
on the sixteen principal points, beginning with north, are respectively — 
-3', 0, + 6', +14', -6', -18', +12', +7', +1', —11', - 12', -9', +5', +7', +6', 0. 
“ 4 These differences evidently nearly follow the law of sin 3£ ; they give 
F=5'-5; G=— 7'. 
44 4 After applying the correction 5'*5 sin3£— 7'cos3£, the residuary difference is 
+4' -2', -3', +9', O', -9', +13', -1', -6', -9', -3', -4', -1', -2', +5', +8'. 
44 4 The differences, it will be seen, are smaller, and do not distinctly follow any 
regular law. If we calculate H and K we shall find 
H = 2'; K=l'. 
But these corrections are so much within the errors of observation, that there could 
be no advantage in using them. 
44 4 The expression for sin & may be put under the following form, viz. — 
sin &=A+ v / B 2 +C <J sin (£+a)+D sin 2£+E cos 2<£', . . . . (35.) 
in which a is the angle whose tangent is g, and is nearly the easterly azimuth of the 
line of no deviation. 
44 4 It seems probable that in ordinary cases A, a, D and E will not change materi- 
ally with a change of latitude, while ^B 2 +C 2 will vary nearly as the tangent of the 
dip. The last-mentioned term is also the most important, from its magnitude and 
its dependence on the changes which the permanent magnetism undergoes. It may 
therefore be useful to have the means of obtaining this quantity separately. This 
may be done from observations of the horizontal force, made in the position of the 
standard compass, with the ship’s head on any two opposite (affected) courses, from 
the formula 
vT^+C^ 
-/H, 2 + H 2 2 + 2H!H 2 cos (diflf. of true azimuth) 
IB + H, ’ 
. . (36.) 
* Contributions, No. V., p. 150. 
