24 Mr, Smeaton’s Obfervations on the 
fize, is capable of all attainable exaCtnefs ; and would be as 
much to be depended on as. any of thofe now in being of eight 
feet. By adopting, quadrants of this fmaller fize, we fiiall of 
courfe get rid of ^-Ifhs of the prefent weight ; and confequently 
of much cumber, unhandinefs, and derangement, that muft arife 
from that weight, as well as the fear of totally difcompofing 
them, if ever moved out of their place. 
It now comes to be time to open a principle upon which there 
is a profpeCt of effecting fiich an improvement. I have ftiewn 
that a 4000th part of an inch is the ultimatum that we are to 
expeCt from fight, though aided by glafles, when obferving the 
divifions of an inftrument. But in the XLVIllth volume of 
the Philofophical TranfaCtions for the year 1754, I have (hewn 
the mechanifmof a new pyrometer , and experiments made there- 
with ; whereby it appears, that, upon the principle of contact , a 
24,000th part of an inch is a very definite quantity. I remem- 
bered very well that I did not then go to the extent of what I 
might have aflerted, being willing to keep within the bounds 
of credibility : but on occafion of the prefent fubjeCt, I have re- 
examined this inftrument, and find myfelf very well authorifed 
to fay, that a 60,000th part of an inch, with fuch an inftru- 
ment, is a more definite and certain quantity than a 4000th 
part of an inch is to the fight , conditioned as above fpecified. 
The certainty of contaCt is, therefore, fifteen times greater than 
that of vifion, when applied to the divifions of an inftrument ; 
and if this principle of certainty in contaCt did not take place 
even much beyond the limit I have now affigned, we never 
fnould have feen thofe exquifite mirrors for reflecting telefcopes ? 
that have already been produced. 
Thefe reflections apply immediately to my prefent fubjeCt, as 
Hindley’s method of divifion proceeds wholly by contact, and 
2 that 
