332 POPULAR LECTURES AND ADDRESSES. 



round its vertical axis through one degree will only 

 alter the apparent bearing of an object on the 

 horizon by "12. Thus it is not necessary to 

 adjust it exactly to the direct position for the 

 bearing of any particular object. If it be de- 

 signedly put even as much as 4 awry on either side 

 of the direct position, the error on the bearing 

 would hardly amount to half a degree. If the 

 instrument were to be used solely for taking 

 bearings of the objects on the horizon, the focal 

 length of the lens should be made exactly equal 

 to the radius of the circle, and thus even the small 

 error of '12 in the bearing for one degree of error 

 in the setting would be avoided. But one of the 

 most important uses of the azimuth instrument at 

 sea is to correct the compass by bearings of sun or 

 stars at altitudes of from o to 50 or 60 above the 

 horizon. The actual focal length is chosen to suit 

 an altitude of 27, or thereabouts, (this being the 

 angle whose natural secant is ri2). Thus if two 

 objects whose altitudes are 27, or thereabouts, and 

 difference of azimuths i, are taken simultaneously 

 in the azimuth mirror, their difference of bearings 

 will be shown as one degree by the divided circle 

 of the compass-card seen through the lens. Hence 

 for taking the azimuth of star or sun at an altitude 

 of 27, or thereabouts, no setting of the azimuth 

 mirror by turning round the vertical axis is 

 necessary, except just to bring the object into the 

 field of view, when its bearing will immediately be 



