LIEUT. CLERK’S REPORT: ELEMENTS OF REDUCTION. 
347 
Cape of Good Hope . . . « = -0148 . . . Z>= ’9848 
King George’s Sound . . . a = -Q199 . . . &=r0040 
Mauritius «=•()] 58 . . . b= '9907 
Mean . . a =’01 68 . . . b— ‘9932 
“The values of a and b can also be obtained by observations of the horizontal in- 
tensity on the N., S., E. and W. points alone. 
“ If the card of the azimuth compass be deflected by another magnet (the small 
deflectors belonging to the dipping-needle for instance), and if v n , v s , v w , and v e be the 
angles of deflection observed on the N., S., W. and E. points respectively, then 
. cosec v n — cosec v s , cosec v w + cosec v e 
a tan 0 = ; ; b= n ■= . 
cosec v n + cosec v s 2 V cosec v w . cosec v e 
“The deflections were obtained in this manner at the Cape of Good Hope, and at 
King George’s Sound on the N. and S. points, viz. — 
Cape of Good Hope. King George’s Sound. 
At N. the deflection . . =16 20 At N. the deflection . =15 23 
At S =15 35 At S =14 06 
Hence a= *0168 And a~ -0198 
Agreeing very closely with the values determined above. 
“After an inspection of the observations at the several stations, Mr. Archibald 
Smith has kindly furnished the following Memorandum. 
“ ‘ The formulae for the correction of observations of magnetic declination, made on 
board ship, given in the Vth and Vlth numbers of the Contributions, are deduced 
on the supposition that the soft iron of the ship is symmetrically distributed on each 
side of the fore and aft vertical section passing through the compass. The deviations 
observed in the Pagoda by Lieut. Clerk, seem to show that the soft iron was not so 
distributed in that vessel, and to require for their correction formulae in which no 
supposition is made as to the distribution of the iron of the vessel, except that there 
is no iron very near the compass. 
“‘Using the notation of the memorandums in Nos. V. and VI. of the Contribu- 
tions, let <p represent the total magnetic force of the earth at the place of observation, 
dthe inclination, £ the azimuth of the ship’s head, reckoning from (magnetic) north to 
west, and let <p', represent the values of the same quantities, shown by an in- 
strument placed at a fixed position in the vessel, and affected by the attraction of the 
iron in the vessel. 
“‘The first three equations in the memorandum in Contribution No. VI. may be 
transformed into the following, viz. — 
< p cos 6 cos £=<p' cos 6'{ A' cos sin sin & C'+P'. 
<p cos 6 sin £=<p' cos 0 '{D' cos £'-|-E' sin sin & F'+Q'. 
<p sin 6 =<p' cos 0 '{G'cos IT sin £'} + 9 ' sin $'K'-f-R/ 
( 1 .) 
( 2 .) 
(3.) 
