VOL. XXXVII.] PHrLOSOPHICAL TRANSACTIONS. 489 



their passage towards it, when the angle to be observed is near 180°. The 

 smaller speculum is fixed perpendicularly on a round brass plate, toothed on 

 the edge; and may be adjusted by an endless screw. 



In order to make an observation, the axis of the telescope is to be directed 

 towards one of the objects, the plane of the instrument passing as near as may 

 be through the other, which must lie to such hand of the observer, as the par- 

 ticular form of the instrument may require; viz. the same way that the specu- 

 lum EP does from ikgh, if it be composed according to this figure and de- 

 scription. The observer's eye being applied to the telescope, so as to keep 

 sight of the first object; the index must be moved backward and forward till 

 the second object is likewise brought to appear through the telescope, about 

 the same distance from the hair cf, fig. 3, as the first: if then the objects 

 appear wide of one another, as at i and k, the instrument must be turned a 

 little on the axis of the telescope, till they come even, or very nearly so, and 

 the index must be removed till they unite in one, or appear close to one another 

 in a line parallel to cf, both of them being kept as near the line gh as they can. 

 If the instrument be then turned a little on any axis perpendicular to its plane, 

 the two images will move along a line parallel to gh, but keep the same position 

 in respect of one another; so that in whatever part of that line they be ob- 

 served, the accuracy of the observation will be no otherwise afi^ected than by 

 the indistinctness of the objects. If the two objects be not in the plane of the 

 instrument, but equally elevated on, or depressed below it, they will appear to- 

 gether at a distance from the line gh, when the index marks an angle some- 

 thing greater than their nearest distance in a great circle : and the error of the 

 observation will increase nearly in proportion to the square of their distance 

 from that line; but may be corrected by help of the 5th corollary. Suppose 

 the hairs ae and bd, each at a distance from the line, gh, equal to V-nre- of 

 the focal length of the object-glass, so as to comprehend between them the 

 image of an object, whose breadth to the naked eye, is a little more than 24°: 

 and let the images of the objects appear united at either of those hairs: then 

 as the sine complement of half the degrees and minutes marked by the index, 

 is to the doubled sine of the same; so is one minute to the error, which is 

 always to be subtracted from the observation. Other hairs may also be placed 

 in the area abcdef, parallel to gh, and at distances from it proportional to the 

 square roots of the numbers 1, 2, 3, 4, &c. and then the errors to be sub- 

 tracted from the same observation, made at each of those hairs respectively, 

 will be in proportion to the numbers J, 2, 3, 4, &c. This correction will 

 always be exact enough if the observer take care (especially when the angle 



VOL. VII. 3 R 



