Graduation of Jjlronomical Inftrumenn. 43 
the fcrews. I now confider the teeth of the dividing plate, fo 
formed, as having all the equality that the prefeat known ftate 
of human art has pointed out ; and the whole convertible upon 
the axis or mandrel upon which it has been originally formed, 
and the central hole of the plate concentric therewith : I there- 
fore confider the ground faces of the teeth of the plate as the 
a£tual divifions. It now remains to fhew how they are to be 
transferred, to form the divifions of an inftrument. 
Preparation of the dividing Plate for graduating Infir uments. 
If a fmall cylinder of hard fteel is duly poliftied, and made of 
a iize fo as juft to chock in betwixt the extremities of the teeth, 
then the center of that cylinder will be a fixed point, in refpedt 
to the circumference of the wheel : if another cylinder is applied 
in like manner, at the diftance of a number of divifions (fup- 
pofe it a prime number, fo as to crofs all former divifions, viz. 
17 or 19), then the middle of the line joining the centers of 
the two cylinders will remain in the diredlion of the fame radius , 
though one of them fhould force in a minute quantity further 
than the other ; and if a point is affumed in the diredlion of a 
tangent to a circle at this middle-point, then though both the 
cylinders fhould drop in a minute quantity further at one time 
than another, yet the middle-point would remain at the fame 
diftance from the point in the tangent; provided that point was 
removed to a competent diftance, that is, to five or fix inches. 
On this principle I would conftrud an index, the two cylinders 
being fixed in a frame, convertible about the middle-point, and 
to be centered in the end of the lever, reprefenting the tangent ; 
then this lever being again convertible about the point in the 
tangent line, the middle-point would always have a fixed diftance 
G 2 from 
