4gO PHILOSOPHICAL TRANSACTIONS. [aNN0 1731. 



comes near 180°) to keep the plane of the instrument from varying too much 

 from the great circle passing through the objects. 



Ill regard to the workmanship, if an exactness be required in the observa- 

 tions, the arch ought to be divided with the greatest care; because all errors 

 committed in the division are doubled by the reflections. The index must have 

 a steady motion on the centre, so that its axis remain always perpendicular to 

 the plane of the octant; for if that alter, it will be liable to vary the inclination 

 of the speculum it carries to the other : the motion must likewise be easy, lest 

 the index be subject to bend edgeways: for the same reason it should be as 

 broad at that end next the centre, as conveniently can be. The specula should 

 have their surfaces of a true fiat; because a curvature in either of them, besides 

 rendering the object indistinct, will vary its position, when seen by reflection 

 from different parts of them: they must also be of a sufficient length and 

 breadth for the telescope to take in a convenient angle, without losing the use 

 of any part of the aperture of its object-glass, and that in all the different po- 

 sitions of the index. They may be either of metal, or glass plates foiled, 

 having their two surfaces as nearly parallel as they can; yet a small deviation 

 may be allowed; provided either their thickest or thinnest edges, and conse- 

 quently the common section of their surfaces, be parallel to the plane of the 

 octant : for in that case, though there are several representations of the object, 

 they will be always very near one another, in a line parallel to cf; and any of 

 them may be used, except when the angle to be observed is very small. The 

 chief inconvenience will be, that a small star will be more difficultly discerned, 

 the light being divided among the several images. The telescope may be con- 

 trived to alter its situation, so as to receive the reflected rays on a greater or 

 less part of its object-glass, if the objects differ in brightness. The second 

 speculum may have a part unfoiled, that if either of them be sufficiently lu- 

 minous, the less bright may be seen through it by the whole aperture. If the 

 sun be one of the objects, or the moon be compared with a smaller fixed star ; 

 their reflected images must be still more weakened by the interposition of 

 one or more of the dark glasses st. An exact position of the telescope is 

 not necessary ; and the instrument may be used without one, the disposition 

 of the specula, with regard to the sector and index, being such, as may allow 

 the eye to be brought as near tiie second speculum as may be, and make the 

 instrument the most commodious for the observer. 



It will be easy to judge, that scarcely any greater degree of steadiness is 

 requisite in the pedestal, or machine which carries this instrument, than what 

 is sufficient for the telescope used with it: for though the vibrating motion of 



