VOL. LXXVI.J PHILOSOPHICAL TRANSACTIONS. ' 43 



therefore, if the whole set of divisions on the limb could be preserved true to 

 this aliquot part of an inch, the 8-feet quadrants of Greenwich might be ex- 

 pected to be true to half a second. How far they are from this, I do not 

 exactly know ; but I have reason to think they vary from it some seconds : nay 

 I believe it is generally allowed that our largest quadrants, even when executed 

 by the accurate hand of Mr. Bird, do not exceed those of a less size, by the 

 same hand, in proportion to their increase of radius : nor can it well be ex- 

 pected that they should ; since, as the weight necessarily increases in a triplicate 

 ratio of the radius, the great weight of the Greenwich quadrants in moving and 

 fixing them, as they could not be divided in their place, may easily derange the 

 framing ; or even the internal elasticity of the materials may give way, by a 

 change of position, to so minute a quantity as a 4000th part of an inch. It 

 therefore appears to me, that since the divisions of a quadrant of 4 feet radius 

 are more than sufficient, and even those of 3 feet admit of all the distinctness 

 that in other respects is wanted, a 3 -feet quadrant, in point of size, is capable 

 of all attainable exactness ; and would be as much to be depended on as any of 

 those now in being of 8 feet. By adopting quadrants of this smaller size, we 

 shall of course get rid of -ff of the present weight ; and consequently of much 

 cumber, unhandiness, and derangement, that must arise from that weight, as 

 well as the fear of totally discomposing them, if ever moved out of their place. 



It is now time to open a principle on which there is a prospect of effecting 

 such an improvement. I have shown that a 4000th part of an inch is the ulti- 

 matum that we are to expect from sight, though aided by glasses, when ob- 

 serving the divisions of an instrument. But in the 48th volume of the Philos. 

 Trans, for the year 1754, I have shown the mechanism of anew pyrometer, and 

 experiments made with it, by which it appears that, on the principle of contact, 

 a '24,000th part of an inch is a very definite quantity. I remembered very well 

 that I did not then go to the extent of what I might have asserted, being wil- 

 ling to keep within the bounds of credibility : but on occasion of the present 

 subject, I have re-examined this instrument, and find myself very well autho- 

 rized to say, that a 6o,OOOth part of an inch, with such an instrument, is a 

 more definite and certain quantity, than a 4000th part of an inch is to the sight, 

 conditioned as above specified. The certainty of contact is therefore 15 times 

 greater than that of vision, when applied to the divisions of an instrument : and 

 if this principle of certainty in contact did not take place even much beyond the 

 limit I have now assigned, we never should have seen those exquisite mirrors for 

 reflecting telescopes, that have already been produced. 



These reflections apply immediately to my present subject, as Hindley*s 

 method of division proceeds wholly by contact, and that of the firmest kind ; 

 there being scarcely need of magnifying glasses in any part of the operation. 



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