50 ON DIVIDING ASTRONOMICAL INSTRUMENTS. 



Method of us- would be to set the beam compass not so exactly to the 



siiVby conti-' true l fcn g tn » as that one scratch would run into the bur of 



nued bisection, the other ; but as this would make it more difficult to 



judge of the true point of bisection, perhaps it might be 



better to make one scratch extend from the circle towards 



the centre, and the other from it. 



It is clear, that the entire arc of a circle cannot be di- 

 vided to degrees, without trisection and quinquesection ; and 

 I do not know whether our artists have recourse to this ope- 

 ration, or whether they avoid it by some contrivance similar 

 to Bird's, namely, that of laying down an arch capable of 

 continued bisection ; but if the method of quinquesection is 

 preferred, it may be performed by either of the three fol- 

 lowing methods : 

 Me* hod of di- First method. Let a x (Fig. 2) be the arch to be quin- 



ng J ' qum " quesected. Open the beam compass to the chord of one 

 quesection. n r r . 



fifth of this arch; bring the microscope to a, and with the 

 point make the scratch/; 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 microscope to a, make the scratch 

 /S; and, proceeding as before, make the scratches S, e, and p. 

 Then the true position of the first quinquesection will be be- 

 tween b and /3, distant from jS by one fifth of b (3 ; and the 

 second will be distant from S 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 bistcting the 

 interval between the two scratches, must be brought four 

 times nearer to /3 than to b* But in order to avoid the 

 confusion, 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, showing 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 bedone 

 at the time the scratch is drawn. 



Perhaps an experienced eye may be able to place the wire 



in 



