LIEUT. CLERK’S REPORT: ELEMENTS OF REDUCTION. 
349 
Z} is the deviation of the compass; B corresponds to the coefficient a tan 0 
of the former memorandum; D to the coefficient 1 — b. A, B, C, D, E are coeffi- 
cients, which are to be determined by observations of deviation made with the ship’s 
head on different azimuths. A, D and E, it will be seen, are independent of the dip, and, 
to the extent to which the hypothesis above mentioned is correct, will have the same 
values in different latitudes. B and C depend on the dip, and also on the proportion 
of the soft to the permanently magnetic iron. This ratio cannot be determined from 
observations made in one place. If P', Q', C, F' remain constant, they can severally 
be determined from values of B and C deduced in two different latitudes, and the va- 
lues of B and C in any other latitude may be deduced from the equations 
B = — f C' tan I . . ( 7 .) C=F tan 0-J-— — » .... (8.) 
) 1 <pcos0j ’ 1 pcosS v ’ 
the accurate values of B and C being 
„ <p! sin 6'C + P' 
<p cos 0' 5 
If the affected dip is zero, we have 
R= — 
P' 
c jp 1 sin 0 f F f + Q/ 
<p cos 0 
So that from observations on the line of no dip, or more accurately when the affected 
dip is zero, the effect of the permanent magnetism may be obtained. 
If we distinguish the points of the compass, reckoning from north to west, by 
the numbers from 1 to 32, north being 0 or 32, and north by west being 1 ; and if we 
designate by S 4 , &c. the westerly deviation when the ship’s head is north, or north 
by west, &c., so that & 8 represents the deviation at W. J ^16 at S. ? ^24 at E., it is evident 
from the equations that we have at once the following simple expressions for the 
values of the coefficients : — 
| sin & 0 + sin sin § 16 + sin S 24 
1 
/ 
(9.) 
B = 
C = 
D= 
E= 
~ |sinS 8 — sin § 24 j 
\ |sin^ 0 - sin ^ 16 | 
\ |sin \ - sin & 12 + sin ^ 20 - sin § 28 j . . . 
^ |sin ^ 0 — sin sin ^ 16 “ sin ^ 24 j . . . . 
. . ( 10 .) 
• • (11.) 
• • ( 12 .) 
. . (13.) 
“ ‘ More accurate values of the coefficients may be obtained by combining observa- 
tions of deviation, made with the ship’s head on the several points, in the following 
manner : — 
“ ‘ 1. Suppose the deviation to have been observed on all the thirty-two points. Let 
mdcccxlvi. 2 z 
