ON DIVIDING ASTRONOMICAL INSTRUMENTS. 53 



less trouble ; but it is not quite so exact, as we are liable to 

 the double errour of placing the intermediate point, and of 

 subdividing it. 



As in this method the intermediate points are placed by 

 means of the micrometer, there is no inconvenience in plac- 

 ing the extreme scratches b and & &c, at such a dis- 

 tance from each other, that the intermediate one shali 

 be in no danger of running into the bur raised by the ex- 

 tremes. 



Third method. Let a a. (Fig. 3) be the arch to be quin- 3d method of 

 quesected ; lay down the arches a 6, h d, and d e, as in the div - ld,n f e ^ e y ti . 

 first method; then turn the beam compass half round, and on. 

 lay down the arches * /3 and /3 £ ; then, without altering the 

 frame, move the movable wire of the microscope till it is 

 four times nearer to S than to e, and, having first rubbed out 

 the former scratches, lay them down again with the compass 

 thus altered ; but as this method possesses not much, if any 

 advautage over the second, in point of ease, and is certainly 

 inferior to it in exactness, it is not worth while saying any 

 thing farther about it. 



It was before said, p. 48, that the centre of motion of the Farther gene- 

 beam compass is to be placed, so that the point and axis of JJj^ sewau- 

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

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

 curately. Let A S (Fig. 4) be the circle in which the 

 scratches are to be made, 5 the point of the beam compass, 

 which we will suppose to be exactly in this circle, d the cen- 

 tre on which it turns, and M m the wire in the focus of the 

 microscope, and let m be that point in which it is cut by the 

 circle ; and let us suppose, that this point is not exactly in the 

 Jine d S, then, when the beam compass is turned round, the 

 circle will cut the wire in a different point/*, placed as much 

 one side of d l 9 as m is on the other, so that if the wire is 

 not perpendicular to d S, the arch set off by the beam com- 

 pass, after being turned round, will not be the same as be- 

 fore ; but if it is perpendicular, there will be no difference; 

 for which reason care should be taken to make the wire ex- 

 actly perpendicular to d £, which is easily examined by ob- 

 serving whether a point appears to run along it, while the 

 beam compass is turned a little on its centre% It is ateo ne- 

 cessary 



