58 Improvements in a Mathematical Dividing t,ngine. 



and fitted in on the underride of the above bell-metal w heel, 

 which I n)ade fast by twenty-four rivets; I then fixed in 

 the axis, and turned tlie wheel and ring together on the 

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

 axis. This being done, and having mounted it on its own 

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

 to turn the edge of the btll-metal wheel where the upper- 

 most or moveable ring of the same thickness as the other 

 is fitted on; for if the circle, where the moveable ring fits 

 the bell-metal, is not turned as true as possible, (which can- 

 not be Aor.G properlv by any other means than by a fixed 

 tool,) the moveable rinii; will nut reverse correctly. When 

 this M'as done, I fitted on the moveable ring. I then divided 

 the lower under ring into twenty-four parts, for the screws 

 which keep the rings tocether. I also 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 uppermost 

 ring correctlv, which were my guide in broaching for my 

 steady pins, and which I did with a broach to a stop fixed 

 on it. In broaching I reversed the moveable ring many 

 times, taking care at the same time that my opposite divi- 

 sions vi-ere 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 me an op|X)rtunity 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 

 methods comes to the same point, and I preferred the way 

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

 ^elf-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 I consider it to be the greatest improvement ever 

 made in the art of dividing. I call it self-correcting, be- 

 cause every lime it is reversed in cutting the teeth, the 

 screw has a fresh opportunity to correct errors insensible to 

 the eye. 



I have well considered the subject, and think that a circle 

 of twelve inches diameter, made on this principle, would 

 measure angles equally if not more accurately than astro- 

 nomical instruments divided by engines, or by any other 

 methods hitherto used by instruments of any size. It is 

 therefi)re my opinion, that the supposed necessity of making 

 very large jircks, for the sake of obtaining correct divisions, 

 will be done away. James Allan. 



SiK, — 



