VOL. LXII.] PHILOSOPHICAL TRANSACTIONS. 303 



twcen this object, and any other object seen by reflection, will be the true angle 

 between them, as seen from the centre of the index glass. But if the quadrant 

 be already well adjusted by a distant object, and you do not chuse to alter it by 

 adjusting it by a near one, move the index, and bring the image of the near ' 

 direct object to coincide with the same seen directly, and the number of minutes 

 by which O of the index stands to the right hand of of the quadrant, on the 

 arch of the excess, is the correction, which added to the angle measured by the 

 arch of the quadrant, between this direct object and any other object seen by 

 reflection, will give the true angular distance between them, reduced to the 

 centre of the index glass. 



To find the angular Distance between 1 near Objects by the bach observation. 

 It is supposed that the horizon glass is truly adjusted ; if it is not, let it be so. - 

 Observe the distance of the objects by the back observation, and take the supple- 

 ment of the degrees and minutes standing on the arch of 180 degrees, which call 

 the instrumental angular distance of the objects ; this is to be corrected as fol- ' 

 lows. Keep the centre of the quadrant, or index glass, in the same place as it 

 had in the foregoing observation, and observe the distance between the near 

 object, which has been just taken as the direct object, and some distant object, 

 twice; by making both objects to be the direct and reflected ones alternately, 

 holding the divided arch upwards in one case and downwards in the other, still 

 preserving the place of the centre of the quadrant. The difference of these two 

 observations will be the correction, which added to the instrumental angular 

 distance, found as above in the first observation, between the first object and any 

 other object seen by reflection, will give the true angular distance between them, 

 reduced to the centre of the index glass. 



But if you should happen to be in a place where you cannot command a con- , 

 venient distant object, the following method may be used. The back horizon 

 glass being adjusted, find the instrumental angular distance between the objects ; 

 this is to be corrected by means of the following operations. Set up a mark at 

 any convenient distance opposite, or nearly so, to the object which has been 

 taken as the direct object, move the index of the quadrant, and bring the image 

 of the mark to coincide with the direct object, and read off the degrees and mi- 

 nutes standing on the arch of the quadrant, which subtract from J 80 degrees, if 

 Oof the index falls on the quadrantal arch; but add to 180 degrees, if it falls on 

 the arch of excess ; and you will have the instrumental angular distance of the 

 object and mark. Invert the plane of the quadrant, taking care at the same 

 time not to change the place of its centre, and looking at the same direct object 

 as before, move the index of the quadrant, and bring the image of the mark to 

 coincide again with the direct object, and read off" the degrees and minutes stand- 



