its Olfifvathns and ExpirimtMts reLuiig To tit Error j of ^afiphig &:rttvt, 



5. The oppofite extremes of <Hc thread in »he dies incline towards different regions, and 

 therefore in effect crofs eacii otiicr. For this rcafon, it is impoflible for two dies to be made 

 to apprcxich each other in the direction of the thread. In faifl, they approach in a plane at 

 right angles to the axis. This is the circumftance which limits the diameter and tiie 

 depth and inclination of the cut, beyond which dies cannot operate. Hence alio it is, that 

 a true flat-thread fcrew cannot be cut in dies, and a many-threaded fcrew, or fcrew of great 

 obliquity, can only be cut in the common ftock by two or three pair of dies in fucceffion. 



6. As it is certain that a pair of well fitted dies can never run both along tlie fame llrokc 

 till perfc£lly home to their natural place of coincidence, the cut made by one die will tend 

 to draw the other along the cylinda". So that while one die cuts ilie upper fide of tlie 

 thread, the other die will cut the oppofite or under fide. In this crofs s£lion, the frame and 

 the dies themfelves will yield from elafticity, and that the more where the material is tJie 

 hardell, or the work forced. Hence with a like prefl'ure the foft frde will have the 

 widell cut, and be fooneft cut down, and the fides of the thread will be waving. This 

 feems to be the chief reafon why tapping a fcrew renders it lefs itraight and round than 

 before. 



7. The dies operate, rather in confequence of the force of prefl'ure by means of the fcrews 

 ef the ftock than by the efFcfl of their edge. This force mull not only be produclive of 

 an oval figure and other irregularities, from the uncertain fpring and yielding of tlie in- 

 ftrument and material, but muft probably occafion a change, of the nature of lamination or 

 hammering. Whenever this latt event happens the thread will be thinner, the cut wider, 

 and the fcrew itfelf coarfer than it would otherwife have been. I have three flat-thread 

 ftecl fcrews, each 11 inches long, 0.6 in. outfide diameter, and depth of thread near o.i 

 inch. They were tapped in dies 0.9 inch deep produced by an original tap containing 13 

 threads in i .4 inch. The motion was flow and uniform between the centres of a kind of lathe 

 conrtrufted for the purpofe. None of the fcrews are of the fame uniform finenefs from 

 end to end. One fcrew is fcavcely coarfer than the original tap ; another is half a thread 

 coarfer in 102 threads, or j 1 inches ; and the third is a whole thread coarfer in the fame 

 quantity. Thefe dilTerences feemed to arife from the different degrees of foftnefs in the 

 fteei ; the laft having been more annealed than the fecond, and the firft not at all. 



Hence is deduced the important conclufiou, that however we may by mechanical expe- 

 dients diminiih the irregularities, of obhquity and diftance of contiguous threads, in a tapped 

 fcTCw, yet in fcrews of feverat inches long there is an irregularity growing out of the na- 

 ture of the materials, which does not appear to admit of any otiier remedy in this method 

 than extreme care and flownefs of working. 



The regular inclination of a fliort tapped fcrew of about forty threads in the inch, was 

 found, by experiments at the end of a very fliort lever or radius fet by a fpirit-Ievel, to be 

 difccrniblc in much lefs quantities than the hundred thoufandth part of an inch. 



Since all thefe fources of irregularity in tapping would be much diminiflied by in- 

 CTcafing the number of dies, I have noted among my Agenda a Rock with four pair of 

 dies aQing at once with eight edges. In thefe the error of obliquity incoming up, as re- 

 marked in the numbered paragraph 5, and of the firft run (paragraph 3.) are incomparably 

 kfs than in a fingle pair of dies. As I have not yet made it up, and every new inflrument 

 it likely to be altered and Cmplified during the adlual conftrudion, I fiiall not particularly 



ftatc 



