dividing astronomical Instruments. 
2 25 
First Method. 
Let a a (Fig. 2 ) be the arch to be quinquesected. Open the 
beam compass to the chord of one fifth of this arch ; bring 
the microscope to a, and with the point make the scratch f ; 
then bring the microscope to/, and draw the scratch e ; and 
in the same manner make the scratches d and b. Then turn 
the beam compass half round, and having brought the micro- 
scope to a, make the scratch (3 ; and proceeding as before, 
make the scratches 3, s and <p. Then the true position of the 
first quinquesection will be between b and (3, distant from (3 
by one fifth of b (3 ; and the second will be distant from * by 
two fifths of d$, and so on. 
Then, in subdividing these arches, and striking the true 
divisions, the wire of the microscope, instead of bisecting the 
interval between the two scratches, must be brought four 
times nearer to (3 than to b. But in order to avoid the con- 
fusion which would otherwise proceed from this, it will be 
necessary to place marks on the limb opposite to all those 
divisions, in which the interval of the scratches is not to be 
bisected, shewing in what proportion they are to be divided ; 
and these marks should be placed so as to be visible through 
the microscope, at the same time as the scratches. Perhaps, 
the best way of forming these marks, would be to make dots 
with the point of the beam compass contiguous to that scratch 
which the wire is to be nearest to, which may be done at the 
time the scratch is drawn. 
Perhaps an experienced eye might be able to place the wire 
in the proper manner, between the two scratches, without 
further assistance ; but the most accurate way would be to 
