130 REPORT ON 



that in some cases the adopted value was in error by more than three degrees. But 

 an error in the adopted value of the variation produced an error of the same amount 

 in the magnetic azimuth of the distant object used as an azimuth mark, and, there- 

 fore, in the pointing of the ship's head to each of the true magnetic points. Bear- 

 ing in mind that the observed deviations were obtained by simply taking the 

 difference between the heading of the ship and the reading of the compass, it will 

 be apparent that if we apply to each observed deviation the difference between the 

 true and adopted variation of the compass, with its proper sign, we shall obtain the 

 true deviations for the directions in which the ship's head actually pointed at the 

 time the readings of the compasses were made. From these corrected deviations 

 the deviations on the true magnetic points can be found by simple interpolation. 



Therefore, if we let 



?n = the true, minus the adopted, magnetic azimuth of the distant object 



used as an azimuth mark : the azimuths being taken as increasing from 



the south around by the west. 

 ' = the observed deviation of the compass when the ship headed in the direc- 



tion A. 

 5" = the observed deviation of the compass when the ship headed in the direc- 



tion A^\\ 15'; the upper sign being taken when m is positive, 



the lower when in is negative. 

 i = the deviation of the compass when the ship heads to the true magnetic 



point which lies between A and A^ll 15'; that point being of the 



same name as A was intended to be when the ship was swung. 

 Then we shall have with sufficient accuracy 



the upper sign being taken when m is positive, the lower when m is negative. By 

 this formula the deviations of the Forward Alidade, Forward Binnacle, Forward 

 Ritchie, Admiralty Standard, and After Azimuth Compasses, on the true magnetic 

 points, have been computed from the observed deviations. 



2. In addition to the correction which has just been explained, the observed 

 deviations of the After Binnacle and After Ritchie Compasses require a further 

 correction on account of the lubber lines of these instruments revolving with the 

 after turret, and thus being frequently out of their true position. This correction, 

 which we will represent by L, is constant, and is equal in amount to the displace- 

 ment of the lubber line. Its sign is -|- if the lubber line is to starboard, -- if it 

 is to port, of its true position. The deviations of the After Binnacle and After 

 Ritchie Compasses, on the true magnetic points, were therefore computed from the 

 observed deviations by the formula 



t __ t'_l / I rN-i-" 1 ^' &") 



~ 5 ~ 





 the upper sign being taken when m is positive, the lower when m is negative. 



To hiivc computed numerically all the values of f> for each compass by means of 

 the expressions just given, would have involved a great amount of labor; it was 

 therefore done graphically as follows: 



