1 70 On an ImprovemeTtl in ilia- 



It is plain that in this way, wit/hout some further pre- 

 caution, we must depend on the microscope not altering 

 its position in respect of the point during the oper-Ati(xa j 

 for which reason I should prefer placing the axis oF the 

 iTiicroscope at exactly the same di>tance from the centre of 

 ination d, as ihe point; but removed from it sideways, by 

 nearly the semi-dinmeter of the object glass ; so that hav- 

 ing made the division, wc may move the beam compass tiJI 

 tlK- division conties within the fiield of the microscope, and 

 |Iie,p sec whether it is bisected by the wire, and consequently 

 pee whethertlie microscope has altered its place. 



In the operaiic^n of bisection, as above described, it may 

 •be observed, that if the two scratches are placed so near to- 

 gether, that in making the second the point of the compasa 

 runs into the burr raised by the first, there seems to be 

 some danger that the point may be a little deflected from 

 its true course; though in Bird's account of his method^ 

 1 do not find that he apprehends any inconvenience from 

 it. One way of obviating this inconvenience, if it does 

 exist, would be to set the beam conipass not so <jxactly to 

 the true length, as that one scratch should run into the 

 burr oF the other ; but as this would make it more difficult 

 to judge oF the true point oF bisection, perhaps it might be 

 belter 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 divided 

 to df^grees, without trisection and quinquesection ; and 1 

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

 .ration, or whether they avoid it by some contrivance similar 

 to Rird's : namely, that of laving down an arch capable of 

 ^continued bisection; but iF thti method of quinquesection 

 is preierred, it may be perFormed by either of the three fol- 

 lowing methods : 



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 Hiicroscope to a, and with the point make tl>e 



,o^craich j', then bring the microscope to f, and drAw th^ 



^cratch € ; and in the same manner make the scratches d 



an<3 ^. 'I'hen turn the beam compass halF round, and hav- 



in«g brougVfi the microscope to a, make the scratch ^ ; and 



proceeding as beFore, make the scratches ^, s and <p. Then 



tiicirue position oF the first qninquesection will be between 



/; and ^, distant from /3 -by one fiFth of /; /3 , and the se- 



C4>nd will be distant Frojn o by two fii'ihs of rf 5, and so on. 



• Then, iii subdividing these arches, and striking the true 



divisions. 



