t 168 ] 



JCXVIIT. On an hnprovement hi the Manner of divulrng 

 astronomical Instrmnents* By Henrv CAViiNDisH, 

 Esq.^FJlS.* 



J- HE great inconvenience and difficulty in the common 

 method oF dividing, arises from the danger of bruising the 

 divisions by putting the point of the compass into them, 

 land from the difficulty of placing that point mid-way, be- 

 tween two scratches very near together, without its slipping 

 towards one of them ; and it is this imperfection in the 

 common process, which appears to have deterred Mr^ 

 Troughton from using it, and thereby gave rise to the in- 

 genious method of dividing described in the preceding part 

 of this voUnnef 1 Thi* induced me to consider, whether 

 the above-mentioned inconvenience might not be removed, 

 ^y using a beam compass with only one point, and a mi- 

 croscope instead of the other ; and I find, that in the fol- 

 lowing manner of proceeding, we have no need of ever 

 setting the point of the compass into a division, and con- 

 sequently that the great objection to the old method of di- 

 viding is entirely removed. 



In this method, it is necessary to have a convenient sup- 

 port for the beam compass : and the following seems to me 

 to be as convenient as any. Let C C C (Plate V. Fig. 1.) be 

 the circle to be divided, B B B a frame resting steadily on its 

 face, and made to slide round on it with an adjusting mo- 

 tion to bring it to any required point ; d^ is the beam com- 

 pass, having a point near ^, and a microscope m made to 

 slide from one end to the other. This beam compass is 

 supported at d, in such manner as to turn round on this 

 point as a centre, without shake or tottering , and at the 

 end $ it rests on another support, which can readily be 

 lowered, so as either to let the point rest on the circle, or 

 to prevent its touching it. ft must be observed, however, 

 that as the distance of of from the centre of the circle must 

 be varied, according to the magnitude of the arch to be 

 divided, the piece on which d is supported had best be 

 made to slide nearer to, or further from, the centre; but 

 the frame nmst be made to bear constantly against the 

 edge of the circle to be divided, so that the distance of d 

 from the centre of this circle, shall not alter by sliding the 

 frame. 



This being premised, we will first consider the manner 

 of dividing by continued bisection. Let Fandy be two 



• From Phllosopliical Transactions for 1 809, Part II. 

 I jSee Phil. Mag. vol, >xxiv. pages 8 ( and 163. 



points 



