LIEUT. CLERK’S REPORT: ELEMENTS OF REDUCTION. 
355 
in which H L H 2 represent the observed horizontal force in the two positions of the 
ship’s head. 
“ ‘ If the difference of the true azimuths of the ship’s head is 180°, the expression 
becomes v'B 2 +C 2 =± * 
which is the same expression as that for the value of a tan 0 in the Memorandum in 
No. V. of these Contributions. 
“ ‘The value of the horizontal force may be determined by vibrating a horizontal 
needle, or by deflecting the compass needle in the manner described by Lieut. Clerk 
in page 347- The difference of azimuths may be determined by the bearings of a 
distant object, or astronomically. 
“ ‘This method seems to be adapted to the case of a ship lying at moorings in a 
tideway. The observations may be made before and after the change of tide, and the 
rudder adjusted so that the difference of the compass bearings of the ship’s head may 
be exactly 180°. 
“ ‘ This formula is more accurate the more nearly the dip approaches to 90° ; and 
the method seems therefore particularly applicable in high magnetic latitudes. 
“ ‘ If the true magnetic azimuth of the ship’s head on the two positions is deter- 
mined, the values of B and C may be obtained by the formula 
Hgcos^ + H^os^ 
H 1 + H 2 
C= 
H 2 sin ^, + H, sin £ 2 
H, + H 2 
“ ‘ Lincolns Inn, March 3, 1846.’ 
“ ‘A. S.’ 
“The constants for correcting the declination observations were (in consequence of 
this Memorandum) calculated by the equations 21, 22, 23, 24 and 25, taking the 
mean of the two series at the Cape of Good Hope. 
“ The following are the deduced values of the constants 
Station. 
i. 
<?■ 
A. 
B. 
C. 
D. 
E. 
Cape of Good Hope 
-53 44 
—53 56 
-65 04 
1-013 
1-158 
1-703 
+ •00600 
+ •00479 
+ "01453 
— -01412 
— -01550 
-•03295 
+ •00742 
+ •00514 
+ •00658 
+ •00911 
+ •00448 
-•00156 
-•00333 
+ •00335 
+ •00082 
Mauritius 
King George’s Sound 
Means 
—57 35 
1-291 
+ •00844 
-•02086 
+ •00638 
+ •00401 
+ •00028 
“From the three values of B, and C, values of C' and P', F' and Q' were obtained 
by the equations 
B= — fc' tan^-f — t ) ; and C=F' tan 0-\- — Q-r ; 
\ 1 <p cos S / 1 <p cos 9 ’ 
