dividing astronomical Instruments. 223 
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 ftp 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 be necessary to use a bent point, as otherwise it 
could not be brought near enough to the axis of the micro- 
scope ; and then part of the rays, which form the image of 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 expedient 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 altered 
every time the magnitude of the arch is altered. 
It is scarcely necessary to say, that 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 must 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 continued till the divisions are all made. 
It is plain that in this way, without some further precaution, 
G g 2 
