488 I'HILOSOPHICAL TRANSACTIONS. [aNNO 1731. 



of this object from that circle, nearly as double the sine of the angle of incli- 

 nation of the specula, is to the sine complement of the same. 



The instrument, fig. 2, consists of an octant abc, having on its limb bc an 

 arch of 45 degrees, divided into QO parts or half degrees; each of which an- 

 swers to a whole degree in the observation. It has an index ml moveable round 

 the centre, to mark the divisions: and on this, near the centre, is fixed a plane 

 speculum ef perpendicular to the plane of the instrument, and making such an 

 angle with a line drawn along the middle of the index, as will be most conve- 

 nient for the particular uses the instrument is designed for; for an instrument 

 made according to this figure the angle lmf may be of about 05 degrees, ikgh 

 is another smaller plane speculum, fixed on such part of the octant as will like- 

 wise be determined by its particular use, and having its surface in such direction, 

 that when the index is brought to mark the beginning of the divisions, i.e. 0°, 

 it may be exactly parallel to that of the other; this speculum being turned to- 

 wards the observer, and the other from him. pr is a telescope fixed on one 

 side of the octant, having its axis parallel to that side, and passing near the 

 middle of one of the edges ik or m of the speculum ikgh; so that half its 

 object-glass may receive the rays reflected from that speculum, and the other 

 half remain clear to receive them from a distant object. The two specula must 

 also be disposed in such manner, that a ray of light coming from a point near 

 the middle of the first speculum, may fall on the middle of the second in an 

 angle of 70°, and be thence reflected into a line parallel to the axis of the teles- 

 cope, and that a clear passage be left for the rays coming from the object to the 

 speculum ef by the side hg. st is a dark glass fixed in a frame, which turns 

 on the pin v, by which means it may be placed before the speculum ef, when 

 the light of one of the objects is too strong: of these there may be several. 



In the distinct base of the telescope, represented by the circle abcdef, fig. 3, 

 are placed three hairs, two of which, ac and bd, are at equal distances from, 

 and panillel to the line gli, which passes through the axis, and is parallel to the 

 plane of the octant; the third fc is perpendioular lo gh through the axis. 



The instrument, as thus described, will serve to lake any angle not greater 

 than 90°; but if it be designed for angles from 90° to 180°, the polished surface 

 of the speculum ef, fig. 2, must be turned towards the observer; the second 

 IKGH must be brought forward to the position no, so as to receive on its mid- 

 dle the rays of light from the middle of the first in an angle of about 25°, 

 their surfaces being perpendicular to each other when the index is brought to 

 the end of the divided arch next c; and this second must stand 5 or 6 inches 

 wide of the first, that the head of the observer may not intercept the rays in 



