VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 311 



The greatest error in this scale appears to be about = .00 1 2 



And the mean probable error = .0006. 



The Royal Society's scale, compared, was as follows : 58 inches on Mr. Bird's 

 were equal to 57,99912 inches on Mr. Troughton's , thermometer 50°.5 ; 



viz. Mr. Bird's measure was shortest .00088 



Or shorter on 36 inches 00054 



32 inches on the same were equal to 31 .99967 



viz. Mr. Bird's was shortest by 00033 



Or, on 36 inches, by 00037 



The mean of these two comparisons is 00045 



And, by so much, is Mr. Bird's scale shorter, in 3 feet, than Troughton's. 



Inches. 



And 12 inches, or 1st foot, of the Royal Society's scale, is . . = 12.00013 ' 



2d foot of ditto = 11.99957 



3d foot of ditto =12.00027 ^ ,, , , iU 



aiu c 4. c At.,. .,' nnn i v on Troughton's scale : the 



££*£•& :::::::::::::::::::: = WS f th ™-* t51 °- 



6th foot of ditto = 11.99823 



7th foot of ditto = 12.0000Q_ 



The mean of these 7 feet is =11 .99982 



And the greatest error in these divisions = .0008 



And the mean probable error = .0004. 



Lest however it should be suspected that 

 Mr. Troughton's scale, with which I have made 

 these comparisons, is not sufficiently correct for 

 this apparent preference, I will now give the 

 result of my examination of that scale, from 

 one end to the other. I set the microscopes 

 to an interval of nearly 6 inches, correctly 

 speaking, it was 6.00013 inches, taken from a 

 mean of the whole scale ; and, comparing this 

 interval successively, I found as annexed. Mean of a11 = 6.00013. 



Whence it appears, that the greatest probable error, without a palpable mistake, 

 in Mr. Troughton's divisions, is = .00033 inch ; against which, the chance is 9 to 

 1 ; and the mean probable error = .0001 6 ; and that it is 4 to 1 the error doth 

 not exceed 1 00 9 00 inch. This accuracy is about 3 times as great as that of Mr. 

 Bird's scales, and about equal to that of the divisions of my equatorial instrument, 

 made by Mr. Ramsden, in 1791. 



I now proceed to the examination of the standard rod of Henry 7th, which is 

 an octangular brass bar, of about 4- an inch in diameter, with one of the sides 

 rudely divided, into halves, thirds, quarters, 8ths, and l6ths ; and the first foot into 

 inches. Each end is sealed with a crowned old English H, and hence is • 

 concluded to be of the time of King Henry 7th, viz. about 1490, but is 

 now become wholly obsolete, since the introduction of the standard of Queen 



