184 REPORT ON 



COEFFICIENTS OF THE DEVIATIONS OF THE FORWARD RITCHIE COMPASS. 



In the case of the Admiralty Standard Compass, for some not very evident 

 reason, the variations in the value of the coefficient. J., are greater than might 

 have been expected. The After Binnacle, Forward Alidade, and Forward Binnacle 

 Compasses were frequently removed from their places, and the fittings were not 

 sufficiently exact to give any certainty of replacing them with their lubber lines 

 always precisely in the same position. This source of error sufficiently accounts for 

 the variations in the values of the .^s belonging to them. The Forward and After 

 Ritchie Compasses were firmly fixed in their places, and were not removed during 

 the cruise, except at Valparaiso; but the arrangements for reading off their cards 

 were such that an improper position of the eye of the observer might easily intro- 

 duce a large parallax, which accounts for the changes in the values of the Afi 

 belonging to them. The After Azimuth Compass was always taken down after 

 each swing, and as there was no fixed mark by which to adjust its lubber line, the 

 changes in the value of its A l are not surprising. 



It now becomes necessary to determine the probable errors of the values of the 

 coefficients which have just been given. To do this for any compass, at any parti- 

 cular station, the value of 5 at each of the thirty-two points must be computed from 

 the coefficients for that station. Comparing the values thus found with the corrected 

 observed values, a scries of thirty-two residuals are obtained, from which the pro- 

 bable error of b for that station is deduced by means of the formula 



r = 0.6745 



I [w] 



\OT H 



where r is the probable error of a single observed value of 8; [vv] the sum of the 

 squares of the thirty-two residuals; m the number of the residuals, in this case 

 thirty-two; and ft the number of the coefficients, in the present instance five. Then, 

 letting p A , p B , p n PD-, Pr., represent respectively the weights, and r A , r n , r n r D , r E , 

 the probable errors, of the values of A t , 7?,, C^ D E when determined from a 

 set of deviations observed on each of the thirty-two true magnetic points; we have 



r A = r=z 



&c. 



