310 PHILOSOPHICAL TRANSACTIONS. [ANNO 1798. 



Appendix. — Since writing the preceding Memoir, I have had an opportunity 

 of examining 3 other scales, divided into inches, or equal parts, of considerable 

 authority in this country, having been executed by the late Mr. J. Bird. I have 

 also compared the old standard in the Exchequer, of the time of Hen. 7th, and 

 which is considered to be the most ancient authority of this sort now subsisting. 

 The first of those scales belonged to the late General Roy, and was purchased by 

 him at the sale of Mr. Short's, the celebrated optician ; it was used by him in his 

 operations of measuring a base line on Hounslow Heath. It was originally the 

 property of Mr. G. Graham, has the name of Jon. Sisson engraven on it, but is 

 known to have been divided by Mr. Bird, who then worked with old Mr. Sisson. 

 It is 42 inches long, divided into lOths, with a vernier of 100 at one end, and of 

 50 at the other, giving the subdivisions of 500ths and lOOOths, of an inch. 



The 2d is in the possession of Alex. Aubert, Esq. and formerly belonged to Mr. 

 Harris, of the Tower ; contains 6o inches, divided into lOths, with a vernier, like 

 that of the preceding. It is 1 inch broad, and 0.2 thick. The 3d was presented 

 by Alex. Aubert, Esq. and the late Adm. Campbell, Mr. Bird's executors, to the 

 b. s., in whose custody it now remains. It consists of a brass rod, 92.4 inches 

 long, 0.57 inch broad, and 0.3 inch thick ; bearing a scale of 90 inches, or equal 

 parts, each subdivided into 10, with a vernier at the commencement, being a scale 

 of 100 divisions to 10 J tenths. This has been called Mr. Bird's own scale, viz. 

 made for his own use ; and was the instrument with which it is said he laid off 

 the divisions of his 8-feet mural quadrants. It is probable that Mr. Bird made 

 many more of these scales, now in the hands of private persons. 



In comparing General Roy's (Bird's) scale with Mr. Troughton's, I found 42 

 inches of the former were = 42.00010 inches on Troughton's; the thermometer 

 51°.7 ; 36 inches were consequently = 36.00008. 



Inches. 

 And 12 inches on the 1st foot were equal to the 12 inches from 12 to 24 on ) __ _ 03 __ 



Troughton's scale j ■- ,yyy ' 



The 2d foot + .0006 12.0006 



The 3d foot - .0004 1 1.9996 



The last foot + .0006 12.0006 



The mean foot, therefore, in General Roy's scale, taken from 4 different feet, compared ) J2 00012 



with Troughton's, between the 12th and 24th inch, is as 12 to j 



That is, General Roy's scale is longest on 1 foot by so much, and longer on 3 foot by 00036 



And the greatest probable error from the inequality in the divisions is about .0005 



And the mean probable error about .' .0003 



Mr. Aubert's scale, compared with Mr. Troughton's, was as follows : 58 inches 

 were equal to 57.9982 inches on Troughton's ; thermometer at 51°.0; viz. Mr. 

 Bird's measure was shortest .0018 ; or, shortest on 36 inches = .0012, 



Inches. 



And 12 inches, or 1st foot, on Mr. Aubert's = 1 1.9999") 



2d foot, = 12.0005 on Mr. Troughton's scale, 



3d foot, 11.99£)6 I from 6 inches to 18 inches; 



4th foot, *. 12.0019 [ the thermometer being at 



5th foot, , 12.0006 50°.0. 



Therefore the mean foot is ,. 12.0005 j 



