148 
LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
“ From these equations are derived the following 1 : — 
(V 
cos & = (cos Z, cos XI + b sin £ sin XI) cos 0 -j- a cos Xj sin 6, . . . (4.) 
cos £ sin XX, + a tan 0 sin XX, = b sin £ cos XX ; . . . (5.) 
and representing X, — XX, or the deviation by c>, 
sin S = a tan 6 sin XX + ( 1 — b) cos XX sin £ (6.) 
= nr3 tan ^sin^ + ~|sin (£ + %) (7.) 
Y' = bsin *> 
^ cos £ -f «tan O’ 
( 8 .) 
c cos X, + c? tan 0 = 6 sin £ cosec tan 0' ........... (9.) 
= (cos £ -f- a tan 0) sec XI tan & . (10.) 
= ^/(cos £ + a tan Q) 2 + b°- sin 2 X, tan & . . . . . (11.) 
..... (12.) 
tan $' = -£-• (cos -f- ~ tan sin XX cosec £ 
<, d , 
cos c 4 tan 9 
c y, 
= c — ; — i — r . cos g 
cos £ + a tan 9 
(13.) 
d 
cos £ tan ( 
c 
v^cos^ + a tanfl) 2 -f 6 2 sin 2 £’ **""*’*’ 
“From these equations, and observations made at one geographical position with 
the ship’s head on different azimuths, the constants a, b, c, d, A 1 may be determined, 
and the corrections of the affected elements at any other geographical position may 
be calculated. 
“ a and b may be determined from observed deviations of the compass needle by 
means of equation (5.). A table of the deviations on each affected or compass course, 
and of the true magnetic course for each affected or compass course, may then be 
calculated by equations (6.) or (7.). In these equations X,, which is an unknown 
quantity, occurs in the second term on the right-hand side ; but the term is so small 
that an approximate value of £ may be used, and the error caused thereby neglected. 
This error is least in equation (7.), which is also the most convenient for calculation 
except on east and west courses. 
“ To find the compass course for each true magnetic course, it will generally be 
sufficient to apply the deviations corresponding to the nearest true magnetic courses 
contained in the Table last described ; but if the deviations are large, it will be better 
to construct a separate table by means of equation (8.). 
“ c and d may be determined from the true dip and the affected dips observed on 
different courses by means of equation (11.), or more easily by means of (9.) and (10.); 
observing that the values of £ employed should be not observed values, but tabular 
