Improvements in a Mathematual Dividing Engine. 57 



evident, for thev are separated by the pellicle of water 

 around each. Lavoisier, in his Chemistry, says, that the 

 particles of the hardest bodies are not in actual contact. 

 If that were the case, it is probable that their cohesive af- 

 finity would be so powerful as not to be affected by ca- 

 loric. 



Xn. Description 'of Improvements in a Mathematical Di- 

 viding Engine. L'^ Jir. J. Allan*. 



,Sin, 1 BEG leave to send to you, here'.\ ith, for the inspec- 

 tion of the Society of Arts, &c. a model of my improvement 

 on the mathemaiical dividing engine which I have iarely 

 made, containing tliat part which d.ffers m principle from 

 those made by i!ie late Mr. Kamsden and others ; the draw- 

 ings or engraving!^ of svhich are, I suppose, in the Society's 

 possession. 1 therefore am of opinion the Society will 

 think that the wooden w'neel I have sent with the moveable 

 ring on its edge, will be ^ufFicient to demonstrate its good 

 effect in correcting the teeth or rack where the screw acts. 

 You will please to observe, that it is cut by a screw-calter 

 and it is required to go many times round the engine before 

 the teeth are full. To effect this, I reversed the moveable 

 ring not less than twenty times, so that I have not the least 

 doubt of the one ring having corrected the other to a decree 

 of perfection which had not hitherto been obtained in en- 

 gines. 



This simple, easy, and correct way of making engines, 

 may be applied with great advantage to circular instrumei;ts, 

 for the purposes of astronomy and land-survevins;. If the 

 Society will do me the honour to appoint a conimittee to 

 view the engine itself, I will demonstrate its effects. 

 I am, sir. 



Your very humble servant. 

 No. 1?, Blewa's Buildings, JamES AllAN 



Fc-cter.Lane, Nov. ^0, 1809. j^-,-^^^ ^f Mathematical Instruments. 



To C. Taylor, M.D. Sec. 



Mr. Allan's Description of Im Mathematical Dividing En- 

 gine, and his Method cj forming it. 

 My engine is of bell- metal, thirty incites in di.imaer. I 

 turned a brass ring about ihree-si.xteeiilh.s of an inch thick, 



• From Tr.i'i^aclio'is of the Sncieiyfor Ihe l^ntunraficmnil of .■tr'<. Mnmi. 



f.i'liiTfs, ami Commtrrt, vol. xxviii. 'I he Sccictv voted the gold medal 



to Mr. Allan for tht-j coir.miiuica'.ijii. 



and 



