ON DIVIDING ASTRONOMICAL INSTRUMENTS. 103 



sectingthe first of the 256 dots. And it should be observed, 

 that the cutting frame and this must not vary respecting 

 €ach other, during the time that the divisions are cut; for 

 any motion that took place in either wouhl ^o undiminished 

 to the account of errour. The microscope I is also fastened 

 to the main frame; but it is only required to keep its posi- 

 tion unvaried, while the divisions of the sector pass once 

 under its notice; for it must have its wires adjusttd afresh 

 to these divisions at every distinct course. The microscope 

 I has two wires, crossing ea(.'h other at an angle of about 

 40° ; and these are to be placed so as to make equal angles 

 with the divisions of the sector, which are not dots, but 

 lines. The sectorial arc must also be adjusted to its proper 

 radius by the screw E, Fig. 5 ; i.e. while the main frame 

 has been carried along the circle through a mean interval 

 fliown by H, the sector must have moved through exactly 

 l6| of its divisions, as indicated by I*. 



Things being in this position ; after having given tlie Cutting th© 

 parts time to settle, and having also sufficiently proved the divisions. 

 permanence of the micrometer H and the cutting frame 

 with respect to each other, the first division may be made; 

 then, by means of the screw for slow motion, carry the ap- 

 paratus forward, until the next line upon the sector comes 

 to the cross wires of I ; you then cut another division, and 

 thus proceed until the l6th division is cut, — l'' 20'. Now 

 the apparatus wants to be carried farther, to the amount 

 of |- of a division, before an interval is complete; but at 

 this last point no division is to be made ; we are here only 

 to compare the division on the sector with the corresponding 

 dot upon the instrument. This interval, however, upon the 



. , , * For the sake of simplicity, the account of the process is carried on as 



if the roller measured the mean interval without errour : But it was <?aici 



(Page 3) that the roller, in a coiKinued motion quite round the circle, 



would in some part of its course err hy 30 ' or more; therefore, when 



this is the case, an extreme run of the roller cannot agree with a mean 



30" 



interval of the circle nearer than — ^ = 023' ; and most probably this 



128 



kind of errour will on some intervals amount to double that quantity. 

 It therefore becomes matter of prudent precaution, to examine every in- 

 terval previous to making the divisions ; and where necessary, to adjust 



the sector, so that its arc may exactly measure the corresponding inter- 



ral as corrected by th« tabulated errours. 



circle 



