ON DIVIDING ASTRONOMICAL INSTRUMENTS. 51 



in the proper manner, between the two scratches, without 

 farther assistance ; but the most accurate way would be to 

 have a movable wire with a micrometer, in the focus of the 

 microscope, as well as a fixed one; and then having brought 

 the fixed wire to b, bring the movable 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 movable wire comes to /3, and then 

 the fixed wire will be in the proper position, that is four times 

 nearer to /3 than to b. 



It will be a great convenience, that the movable wire 

 should be made in such manner, as to be readily distin- 

 guished from the fixed, without the trouble of moving it. * 



In this manner of proceeding, I think a careful operator 

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

 derable errour in the distance of the movable 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 the 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 This method 



that of bisection, it must be considered, that the arches com P ared wilh 

 ^/,^n i i i-ii . «, that by biseo 



a/3, /S 5, &c, though made with the same opening of the tion. 



compass, will not be exactly alike, owing partly to irregula- 

 rities in the brass, and partly to other causes. Let us sup- 

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

 the beam compass is opened to the exact length, but that 

 from the abovementioned irregularities the arches «/3, /3£, h, 

 and t <p are all too long by the small quantity e, and that the 

 arches af,f e, e d, and d b are all too short by the same quan- 

 tity, which is the supposition the most unfavourable of any 

 to the exactness of the operation ; then the errour in the 

 position of /3 ~ e, and the point b errs 4 i in the same 

 direction, and therefore the point assumed as the true 



point of quinquesection will be at the distance of ?_ffrom 



5 

 0, and the errour in the position of this point 22 • x 1J-. 



E2 By 



