Manner ofdlvid'mg astronomical Instruments, 171 



tJlvisions. the wirc^ of the microscope, instead of bisecting 

 the interval between the two scratches, must be brought 

 four times nearer to j8 than to h. But in order to avoid 

 the contusion which would otherwise proceed from this, 

 it will be necessary to place ujarks on the limb opposite to 

 all those divi^i()ns, in which the interval of the scratches i» 

 nut to be bisected, shown}g in what proportion they are to 

 be divided; and these marks should be placed so as to be vi- 

 sible 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 com- 

 pass contiguous to that scratch which the wire is to be 

 nearest to, which may be done at the time the scratch is 

 drawn. 



Perhaps an experienced eye might be able to place the 

 wire in the proper manner, between the two scratches,^ 

 without further assistance; but the most accurate way 

 would be to have a moveable wire with a micrometer, in 

 the focus of the microscope, as well as a fixed one; and 

 then having brought the fixed wire to h, bring the move- 

 able one to /3, and observe the distance of the two wires 

 by the micrometer; then reduce the distance of the two 

 wires to one fifth part of this, and move the frame till the 

 moveable wire comes to j6, and then the fixed wire will be 

 in the proper position, that is four times nearer to ^ than 

 lo h. 



It will be a great convenience, that the moveable wire 

 'should be made in sucti manner, as to be readily distin- 

 guisned from the fixed, without the trouble of moving it. 



In this manner of proceeding, 1 think a careful operatOFf 

 can hardly make any mistake : for if he makes any con- 

 siderable error in the distance of the moveable wire from 

 the fixed, it will be detected by the fixed wire not appearing 

 in the right position, in respect of the two scratches; and 

 as the mark is seen through tlie microscope, at the same 

 time as the scratches, there is no danger of his mistaking 

 which scratch it is to be nearest to, or at what distance it 

 is to be placed from it. 



To judge of the comparative accuracy of this method 

 with that of bisection, it must he considered that the arches 

 «|S, /3 ^, &c. though made with the same opening of the 

 Compass, will noi be exactly alike, owing partly to irregulari- 

 ties in the brass, and partly to other causes. Let us suppose, 

 therefore, that in dividing the arch a a, into five parts, the 

 beam compass is opened lo the exact length, but that from 

 the abovementioned irregularities the arches, a /3, /S (^, ^s, 



and 



