MATHEMATICAL DIVIDING ENGINE. 7*?i 



nomical instruments divided by engines, or by any other 

 methods hitherto used by instruments of any size. It is, 

 tlierefore, my opinion, thjit the supposed necessity of making 

 very large circle?, for tlje sake of obtaining correct divisions, 

 will be done awav. 



JAMES ALLAN. 



Certificates. 

 After a close consideration of Mr. Allan's improvement Certificates of 

 in dividing engines, (I mean his mode of racking the teeth ^^ ^^^ - 

 only) when combined with the methods at this time known improvement. 

 and practised, I look upon it as an important discovery ; 

 it is a plan, that in my opinion will admit of a great degree 

 of accuracy, approaching nearly to perfection itself, parti- 

 cularly in circles of small radius, but not quite so applicable 

 in large machines for the purpose of dividing. 



JOHN STANCLIFFE. 

 Little Mury-le-Bone Street, Dec. ] 5, 1 8O9. 



sm. 



The method you have taken to produce a perfect equal 

 racking, for the constructing an accurate dividing engine, 

 is the greatest advance toward perfection that has been com- 

 municated to the public within my knowledge; and I 

 believe it to be a method never before practised in this 

 country. It is applicable to the construction of machines 

 of any dimensions, that mathematical or nautical instru- v • 

 nients can be graduated by. ■'' 



It is my belief, that the greater number of the machines Machines now 



now in use are far short of the perfection they are reputed to '" "/^ '^f^ 



^ . •' * j)crfect than 



have, I am, b>r, supposed. 



Your humble servant, 



M. BERGE, 

 Piccadilly, Jan. 8, 1810. 

 Mr. J. Allan. 



Reference to the Draioing of Mr. Allan's improvement on the 

 X)ividing Engine of Ramsden, PI. II. 



The dividing engine invented by Mr. Jesse Ramsden, Nature of the 

 and for which he received the reward of the Board of Lon- improvement, 

 gitude, in the year 1775, is minutely explained in a quarto 



pamphlet. 



