Improvement in dividing astronomical Instruments, 169 



points on this limb which are to be bisected in <p. Take 

 the distance of the microscope from the point nearly equal 

 to the chord of ftp, and place d so that the point and the 

 axis of the microscope ^hall both be in the circle in which 

 the divisions are to be cut. Then slide the frame B B B 

 till the wire of the microscope bisects the point F ;> and 

 having lowered the support at $, 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 f, make an- 

 other 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 mid-way be- 

 tween them will be the accurate bisection of the arch Ff; 

 but it is unnecessary, and better not to attempt to place a 

 point between these two scratches. 



Having by these means determined the bisection at (p, 

 we must bisect the arches F <p and f<p in just the same 

 rtianner 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 points 



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

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

 it, could not be brought near enough to the axis of the mi- 

 fci^dScope ; and then part of the rays, which form the image 

 \jf the object seen by the microscope, will be intercepted 

 by the point ; but I believe, that by proper management 

 this may be done without either making the point too 

 weak, or making the image indistinct; but if this cannot 

 be done, we may have recourse to Mr. Troughton's expe- 

 dient of bisecting an odd number of contiguous divisions. 



It must be observed too, that in the bisections of all the 

 arches of the same magnitude, the position of the point d 

 on the frame remains unaltered ; but its position must be 

 •Itered every time the magnitude nf the arch is altered. 

 * It is scarcely necessary to say, tliat the bisections thus 

 made are not intended as the real divisions, but only as 

 marks from which they are to be cut. In order to make 

 the real divisions, the microscope nmst be placed near the 

 point, and the support d must be placed so that d $ shall be 

 a tangent to the circle at $. The wire of the microscope 

 must then be made to bisect one of these marks, and a 

 point or division cut with the point, and the process con- 

 tinued till the divisions are all made. 



It 



