dividing astronomical Instruments. 229 
and j 3 then, without altering the frame, move the moveable 
wire of the microscope till it is four times nearer to $ than to 
e, and, having first rubbed out the former scratches, lay them 
down again with the compass thus altered ; but as this method 
possesses not much, if any, advantage over the second, in 
point of ease, and is certainly inferior to it in exactness, it is 
not worth while saying any thing further about it. 
It was before said,* 5 that the center of motion of the beam 
compass is to be placed, so that the point and axis of the mi- 
croscope shall both be in the circle in which the divisions are 
made ; but it is necessary to consider this more accurately. 
Let A (Fig. 4) be the circle in which the scratches are to be 
made, $ the point of the beam compass, which we will suppose 
to be exactly in this circle, d the center on which it turns, and 
M m the wire in the focus of the microscope, and let m be that 
point in which it is cut by the circle ; and let us suppose that 
this point is not exactly in the line d$, then, when the beam 
compass is turned round, the circle will cut the wire in a dif- 
ferent point p., placed as much on one side of d, as m is on 
the other, so that if the wire is not perpendicular to d d, the 
arch set off by the beam compass, after being turned round, 
will not be the same as before ; but if it is perpendicular, there 
will be no difference ; for which reason, care should be taken 
to make the wire exactly perpendicular to d which is easily 
examined by observing whether a point appears to run along 
it, while the beam compass is turned a little on its center. It 
is also necessary to take care that the point $ is in the arc of 
the circle, while the bisection is observed by the microscope, 
which may most conveniently be obtained, by placing a stop 
* Page 222. 
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MDCCCIX. 
