42 PHILOSOPHICAL TRANSACTIONS. . [anNO 1786. 



from what workmen term drunkenness ; and also showed me how, by the single 

 screw of his lathe, he could cut, by means of wheel-work, screws of every ne- 

 cessary degree of fineness,* and by taking out a wheel, could cut a left-handed 

 screw of the very same degree of fineness ; by which means he was enabled not 

 only to adapt his plain screw to the size of the teeth of his wheel, but also to 

 prevent any drunkenness that otherwise the curved screw would be subject to in 

 consequence of being produced from the plain one ; also, that the screw and 

 wheel, being ground together as an optic glass to its tool, produced that degree 

 of smoothness in its motion that I observed ; and lastly, that the wheel was cut 

 from the dividing plate : yet, how the dividing plate was produced, he for par- 

 ticular reasons reserved to himself. 



Nor can he be blamed for the reservation of this one secret ; as he had, even 

 at the time of my early acquaintance with him, a kind of foresight that from the 

 superior merit of Hadley's quadrant, a demand for that, and other instruments 

 for the purpose of navigation, was likely to increase ; and that he might live to 

 see a public reward offered for a method of dividing them with greater accuracy 

 and dispatch than had at that time appeared. Indeed he had himself an idea, 

 from the satisfactory success that had attended his operations in dividing, that a 

 screw and wheel, produced from his engines of 1 foot diameter, would have as 

 much truth as the 8-feet quadrant at Greenwich : and though he doubtless 

 greatly over-rated the accuracy of these miniature performances, yet it does not 

 follow, as his methods were not confined to so narrow a compass, but that, his, 

 scale of operation being proportionably enlarged, a degree of accuracy in the 

 graduation of astronomical instruments may be attained in proportion. 



I must here beg leave to observe, that there appears to me to be a natural 

 limitation to the accuracy of instruments, consisting of considerable portions of 

 a circle, such as quadrants, Scc.-f- I do not find that the finest stroke on the 

 limb of a quadrant, made by Bird's own hand, if removed from its coincidence 

 with its index, can be replaced with any degree of certainty nearer than the 

 4000th part of an inch, though aided by a magnifying glass. J A 4000th part 

 of an inch being then determined to be the minimum visibile by the strokes of 

 an instrument, this will be less than 1''' of a degree on a radius of 4 feet; and 



* A machine for cutting the endless screw of Mr. Ramsden's engine, on principles exactly similar, 

 is fully and accurately set forth in his description of his dividing engine above-mentioned. — Grig. 



"t The zenith sector consists but of few degrees, with little variation of its position in using it.— 

 Orig. 



+ It will be to little purpose to attempt it with a greater power. Double microscopes can doubt- 

 less be formed to magnify objects, far less than a 4(;00th part of an inch, to distinct surfaces ; but 

 then the advantage of such degrees of magnifying power is chiefly on the organized bodies of nature. 

 Let a dot, or the finest point that can be made by human art, be so viewed, and it will appear not 

 round, but a very ragged irregulai" figure. — Orig. 



