118 * 
LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
“ By the introduction of the same quantities, the equations numbered from (4.) to 
(14.) in the former memorandum become 
= cos £ cos -\-b sin £ sin + L cos g + M sin . . . (4.) 
(cos ^*+L) sin £ = (b sin <^+ M) cos ; (5.) 
and representing or the deviation, by S, 
sin c5 = L sin — M cos £' + (1 — b) sin £ cos (6.) 
= L sin cos + 1 r =|-sin (? + ?') .... (7.) 
tan? . = £=|+M (8.) 
c cos <^-j-N=(Z> sin <^-j-M) cosec tan & (9.) 
= (cos <^+ L) sec tan & (10.) 
= v /(cos^'+L) 2 +(6sin^ + M) 2 . tan0' (11.) 
cos N 
tan O' — 4 \ — sin % (12.) 
sin?+-^-M 
cos f + — N 
— c - J - f - ■ cos V (13.) 
cos £ + L ^ v J 
c cos | + N (J 4 \ 
V (cos £ + L ) 2 + ( b sin \ + M ) 2 
“ Equation (7-) may also be put under the form 
sin & = Y + M ' 2 sin (S' -P 1 ) + irl sin + O’ 
where = L sec (* sin (% ~ l Jj ) + TTb sin (S + %)> 
M 
in which tan y., = jj, and p represents the displacement of the line of no deviation 
towards the starboard side. 
“ By means of these equations we can determine A', L, b, M, c, N, from observa- 
tions made at sea alone. The first four of these quantities furnish the corrections for 
the horizontal force and the declination. There is greater difficulty in obtaining the 
correction for the inclination. It will be observed that 0 only occurs in these equa- 
tions involved in the quantities L and N. If there were no permanent magnetism in 
the vessel, it would be necessary, in order to determine the correcting factors a and d , 
that observations of the inclination on shore, and corresponding observations on 
board, should be made in at least one magnetic latitude. If there is any appreciable 
permanent magnetism, observations of the inclination on shore and on board, and of 
the horizontal force, should be made in at least two magnetic latitudes. This would 
be sufficient if a, P, d, R remained absolutely constant. As that appears not to be 
