Manner of dividing astronomical Instruments, \ 73 



ration of placing it in the proper proportion of distance 

 between the two extremes. 



This method certainly requires less attention than the 

 former, and on the whole seems to be -attended with con- 

 siderably less trouble ; but it is not quite so exact, as we 

 are liable to the double ^iror of placing the intermediate 

 point and of subdividing from it. 



As in this method tlie iniermediate points are placed by 

 means of the micrometer, there is no inconvenience in 

 placing the extreme scratches b autl jS, &c. ^lt such a di- 

 stance from each other, that the intermediate one shall bfe 

 in no danger of running into th^ burr raised by the ex- 

 tremes. 



Third Method, 



Let a a (Fig. 3.) be the arch to be quinquesected ; \vf 

 down the arches uh, d b^ and de, as in the first method; 

 then turn the beam compass half round, and lay down the 

 arches a jS and /3 ^ ; then, without altering the trame, move 

 the moveable wire of the microscope till it is four tunes 

 nearer to iJ than to i?, and, havinfi^ first rubbed out the for- 

 mer scratches, lay Ihem down again with the com^H^si*. 

 thus altered: but as this meihod 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*, that the centre of motion of the 

 beam compass is to be placed, so that the point and axis of 

 the microscope shall both be in the circle in which the di- 

 visions are made ; but it is necessary to consider this more ac- 

 curately. 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 he exactlv in this circle, d the centre on 

 which it turns, and Mm the wire in the focus of the mi- 

 croscope, and kt m be that point in which it is cut bv the 

 circle; and let us suppose that this point is not exactlv in 

 the line o?^, then, when the beam compass is turned round, 

 the circle will cut the wire in a different point ja, placed as 

 nuich on one side of t/ J, as m is on the other, so that if 

 the wire is not per[)endicular to d^, the arch set off by the 

 beam compass, alter beini: turned round, will not be the 

 same as before; but if it is perpendicular, there will be no 

 differenct ; for which reason, care should be taken to make 

 the wire exactly perpendicular to c?^, which is easily ex- 

 anjined by observing whether a point appears to run alon^*- 



• Page 168. 



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