Impi'ovemenls in a MatkemVticai Dividing Engine. 59 



Sir, — The method you have taken to produce a perfect 

 equal racking, for ihe constructing^n accurate divriding en- 

 gine, is the greatesi advance towards pertect.on that ti;j« 

 been comniunicatcd to the public whhin my knowledgej 

 an J I beheve it to be a method never before practised in ihi* 

 country. It is apphc-ible to the construction of machines 

 of any dimensions, that mathematical or nautical instru- 

 ments can be mad lated bv. 



It is my bvliei, that the greater number of the machines 

 now in use, are far short of the perfection they are reputeU 

 to liave. 



I am, sir, your humble servant, 



Piccadilly, Jan. 8, 1810. Jsl, BerGP:. 



Reference to ihe Drawing of Mr. Allan's Imf)ror'ement oil 

 the Dividing Engine of Rcunsden . PI. II. 



The dividing engine invented bv Mr. Jesse Ramsden,and 

 for which i.t received the reward uf the Board of Lontiitude 

 in the year 1775, is minutely explained in a quarto pam- 

 phlet, publishetl byiinicrof the Commissioners of Longitude; 

 also, in the article Engine, in Dr. Rees's New Cyc!op£Edia, 

 as well as some other works of a similar nature; it thcre- 

 foie becomes unnecessarv for the Society to give any nior"? 

 of Mr. Allan's tngine m their drawmgs than is explanatory 

 of the iinprovtment, the engine bi'ing used in ihe same 

 mannt! ;iS Ramsden's : this part is the great circle upon 

 which the arch to be divided is placed, and the circle turned 

 about a determinate quantitv at each division, by means of 

 a screw v>h(jbe threads engage fine teeth, cut around the 

 periphery of the circle. 'J'he improvement by Mr. Allan 

 consists in the method of cuttintr or racking these teelh, to 

 ensure their beiuir perfectly ot equal size in all parts of the 

 circle. 



'Ihe plan, fls;. ], in Plate II, represents ihc upper surface 

 of a b(ll-mttal circle mounted upon an axis, A, lig. '2, and 

 its surface made trulv^plane, and perpendicular lo the axis: 

 the section shows the tigure of the axis, and the central ring 

 1j, to give the greatest strength to the circle; C is a section 

 (jI a portion of the frame cf the engine; and D a socket 

 into which the axis A is litied; liie circumtereiice of the 

 large circle is turned lo such a ligme as to receive a ring of 

 brass, n, fig. 3, wbicli is united lirinly to it by a number 

 of pins, one of which is shown in the figure. Upon this 

 ring, a second b is ])laccd, the two making the s;ime thick- 

 ness as the circle, 'i'hi' lu-lde of the ring b, and the out- 

 side 



