Experimental Comparlfon of Standard Meafures, 



245 



The mean of thefe feven feet is - =1 1,99982 



And the greateft error in thefe divifions - = ,0008 



And the mean probable error - - =: ,0004. 



(§. 51.) Left, however, it fliould be fufpe£ted, that Mr. Troughton's fcale, with which 

 I have made thefe comparifons, is not fufiiciently correifl for this apparent preference, I will 

 now give the refult of my examination of that fcale, from one end to the other. I fet the 

 microfcopes to an interval of nearly 6 inches, corre<St]y fpeaking it was 6,00013 "iches, 

 taken from a mean of the whole fcale i and, comparing this interval fucceflively, I found as 

 follows : 



inches. 



- - = 6,00025* - _ _ 



- - = 6,00013 - - - ,00000 



_ - = 6,00020 - - - - + ,00007 



- - = 6,00000 _ - _ — ,00013 



- - = 6,00007 " " " ,00006 



- - =: 6,00033 - - - + ,00020 



- - = 5-99980 - - - — ,00033 



- - = 6,00020 - - - ^ ,00007 

 - := 6,00010 - - - — ,00003 



- - = 6,00023 - - - + ,00010 



inches, inches. 



viz, from o to 6 

 6 to 12 

 12 to 18 

 18 to 24 

 24 to 30 

 30 to 36 

 36 to 42 

 42 to 48 

 48 to 54 

 54 to 60 



Mean of all 



Error, or difference 

 from the mean. 

 + ,00012 



- - rr 6,00013 



From whence it appears that the greateft probable error, without a palpable miftake, in Mr. 

 Troughton's divifions, is = ,00033 '"ch; againft which the chance is 9 to i ; and the 

 mean probable error = ,00016; and that it is 4 to i the error doth not exceed to 5^15 '"ch. 



This accuracy is about three times as great as that of Mr. Bird's fcales, and about equal 

 to that of the divifions of my equatorial inftrument, made by Ramfden, in 1791. See 

 Phil.Tranf. for 1793. 



(§. 52.) I now proceed to the examination of the ftandard rod of Henry VIT. which is 

 an odtangular brafs bar, of about ' an inch in diameter, with one of the fides rudely divided, 

 into halves, thirds, quarter, eighths, and fixteenths; and the firft foot into inches. Each end 



is fealed with a crowned old Englifti H /sj^A and from hence is concluded to be of the 



time of King Henry VII. viz. about 1490, but is now become wholly obfolete, fince the 



J" 



• It is not pretended, that in this and the foregoing obfervations, the quantity of any interval can be de- 

 termined to the precifion of the onc-hunJretl-thoufandih part of an inch; but it is prefumed, tliat with the 

 affiftance of the microfcopes, the ten-thoufandth part of an inch becomes vifible ; and, as a mean is taken 

 from 3 or 4 times reading off the tiiicrometer at each trial, it has been deemed not unreafonable to fet down 

 the quantities to five places of decimals. 



Vol. III. — September 1799. Kk . ■ introdudion 



