48 ON DIVIDING ASTRONOMICAL INSTRUMENTS. 



pnss, having a point near S, and a microscope m made to 

 slide from one end to the other. This beam compass is sup- 

 ported at d, in such manner as to turn round on this point 

 as a centre, without shake or tottering; and at the tnd £ it 

 rests on another support, which can readily be lowered, so as 

 either to let the point rest on the circle, or to prevent its 

 touching it. It must be observed, however, that as the 

 distance of d from the centre of the circle must be varied, 

 according to the magnitude of the arch to be divided, the 

 piece on which d is-supported had best be made to slide 

 nearer to, or farther from, the centre ; but the frame must 

 be made to bear constantly against the edge of the circle to 

 be divided, so that the distance of tl from the centre of this 

 circle shall not alter by sliding the frame. 

 Method of This being premised, we will first consider the manner of 



using it for di- dividing by continued bisection. Let F and /"be two points 

 ▼ision by con- ... J ' 



tinued bisecti- on this limb, which are to be bisected in (p. Take the dis- 



• n * tanceof the microscope from the point nearly equal to the 



chord of/p, and place d so that the point and the axU of 

 the microscope shall both be in the circle, in which the divi- 

 sions are to be cut. Then slide the frame B B B, till the 

 wire of the microscope bisects the point F ; and having low- 

 ered the support at J, make a faint scratch with the point. 



Having done this, turn the beam compass round on the 

 centre d till the point comes to D, where it must rest on a 

 support similar to that at £; and having slid the frame till 

 the wire of the microscope bisects the point/*, make another 

 faint scratch with the point; which, if the distance of the 

 microscope from the point has been well taken, will be very 

 near the former scratch ; and the point midway between them 

 will be the accurate bisection of the arch F/; but it is un- 

 necessary, and better not to attempt, to place a point be- 

 tween these two scratches. 



Having by these means determined the bisection at <p, we 

 must bisect the arches F <p and/ p in just the same manner 

 as before, except that the wire of the microscope must be 

 made to bisect the interval between the two faint scratches, 

 instead of bisecting a point. 



It must be observed, that, when the arch to be bisected is 

 small, it will b« necessary to use a bent point, as otherwise 



