t) MATHEMATICAL DIVIDING ENGJNE. 



and fitted in on the under&ide of the above belmelal wheel, 

 which I made fast by twenty four rivets ; I then fixed in 

 t'ue axis, and turned the wheel and riui; together on th« 

 lathe, as near as possible to the required shape on its own 

 axis. This bein;^ done, and havin^^ mounted it on its own 

 stand, where it "now acts, I fixed a tool, with an adjustment 

 to turn the e(l;4e of the belraetal wheel where the uppermost 

 or ii^oi'able ring of the same thickness as the other is fitted 

 on ; for'if the circle, where the movable ring fits the belmetal, 

 is not turned as true as possible, (which cannot be done 

 properly by any oilier means than by a fixed tool) the mova- 

 ble ring will not reverse correctly. When this was done, I 

 fitted on the movable ring. I then divided the lower under 

 ring into twenty four parts, for the screws which keep the 

 rings together. I alid divided it into four parts for the 

 steady pins ; the holes of which I made by an upright drill 

 fixed and adjusted for the purpose. I then cut two opposite 

 divisions, in order to reverse the uj)perrriost ring correctly, 

 which were my guide in broaching for my steady pins, and 

 which I did with a broach to a stop fixed on it. In broach- 

 ing I reversed the movable ring many times, taking 

 care at the same time that my opposite divisions were 

 correct, 



My first idea -was to have two wheels or circles, acting on 

 the same centre, so as to constitute a double edge, to afford 

 mean opport;inity to reverse in the act of cutting the rack 

 or teeth ; but I thought the method in which I have done 

 it would with care be equally correct. Either of the me- 

 thods come to the same point, and 1 preferred the way 

 I have employed, thinking it the least expensive. By this 

 self-correcting method, instruments may be made for astro- 

 nomical purposes, racked and divided on their own centre; 

 and if carefully done would border on perfection itself, con- 

 sequently 1 consider it to be the greatest improvement ever 

 made in the art of dividing. 1 call it self-rcorrecting, because 

 every time it is r-eversed in cutting the teeth, the screw has a 

 fiesh opportunity to correct errours insensible to the eye. 

 Small circles I have well considered the subject, and think, that a circl^ 

 of great of twelve inches diameter, made on this principle, would 



measure angles equally, if not more accurately, than astro- 

 nomical 



accuracy, 



