14 THE VOYAGE OF H.M.S. CHALLENGER. 



in a tranquil sea, towards sunset or sunrise, or when in sight of distant land, a complete set of devia- 

 tions can be obtained in half an hour. Again, if we assume A and E to be zero, B and C can be 

 determined at any time (D being known) by observing on any two cardinal points. Formulae for 

 several methods of determining B, C, D, without completely swinging the ship, will be found in the 

 " Admiralty Compass Manual," pp. 47-61. No difficulty would appear, therefore, to prevent B and C 

 being determined for every 10 or 15 change of Dip in the ordinary prosecution of the ship's duties. 



To recapitulate For the Standard compass, in order to correct the observations for Declination 

 made at that position, we require to know the coefficients A, B, C, D, E. 



For Fox's circle position, in order to correct the observations for Inclination and Force we require 

 to know the coefficients B, D, c, d, A'. 



For the corrections of the Inclinations observed at sea, the variable coefficients c and d may be 

 computed from the disturbances on the several compass points shown by the observations of the 

 Inclination with Fox's circle, when the ship was swung in harbour, by the formula 



c cos f + d tan 6 = (1 2 sin D) sin f cosec f tan 0' 



for all other points than north or south ; and with the ship's head north or south by 



c cos f + d tan 9 = (cos f + sin B) sec " tan &'. 



In these formulae it must be observed that f is the correct magnetic azimuth of the ship's head 

 counted from the magnetic north, 6 the inclination observed on shore by Fox's circle ; & and f are 

 the same elements observed by the needles of the Fox circle and Fox position compass on board. 



[Note. It may here be observed that the points of no deviation with the compass, become the 

 points of extreme deviation of the Inclination and Intensity.] 



With the values of c and d thus obtained, tables for the correction of the Inclinations observed 

 on different courses at sea in all values of 6 may be computed by the formula 



C % + tan Q siu ' cosec f 



(1 - 2sin D) 



on all points of the ship's course between N.E. and S.E., or N.W. and S.W., that is, when near the 

 east or west points, and by the formula 



cos f+ -tan6 



when the ship's course is nearer the north and south points ; observing in either case that the values 

 of f should be calculated by means of the Declination coefficients. 



The coefficient A' required for the correction of the intensities of the Force observed at sea, may 

 be computed by the subjoined formulae from the observations of the Intensity made with Fox's circle 

 on board compared with those made by the same instrument on shore, and with the known absolute 

 value of the Total Force on shore (<p) ; <p' being the Total Foice on board. 



