G. J.Stoney— Conversion of British into Metrical Measures. 357 



Combining this datum with Clarke's value for the yard, viz. : 



yard = 914-39180 mm., 



and Miller's value for the lb. avoirdupois, viz. : 



lb. = 453-59265 grammes, 

 we find 



gallon = 4543-58 cubic centimetres. 



= 4544 (1 - -000,09), 



so that the error involved in taking 4544 as the number of cc. in 

 a gallon is less than one part in 10,000. Now the density of water 

 is not known to this degree of accuracy, and accordingly no expe- 

 rimental determinations that have been made are competent to 

 detect the difference. It is, accordingly, legitimate to neglect it 

 and to use the convenient number- 4544 as the number of cubic 

 centimetres in a gallon. 



We thus find that we may take as our fundamental units — 



Authority. 



Yard = 914*4 millimetres, with an error 

 which is less than a fifth-metret 1 in a 

 metre, Clarke. 



Lb. = 453*6 grammes, with an error of 

 about 7 milligrammes, i.e. a little more 

 than the tenth of a grain in the lb., . Miller. 



n n azu vi n l ■ ( Clarke, Miller, 



Gallon = 4o44 cc, with an error that is 



, ,, ,. ,. , . , ... < Royal Commission 



less than a cubic centimetre in ten litres. „,«■•« 



( of 1816. 



Now the first of these numbers happens to be divisible in suc- 

 cession by 3, by 12, and by 2 ; the second by 7 and by 8 ; and the 



the density of water within the limits of the probable error. And, finally, the volume 

 of the solid must be determined which has to be weighed successively in water and air. 

 This determination is a very difficult one, and probably would not admit with the 

 utmost care of a smaller probable error than one or two parts in 10,000. 



The solid used in the later determination was a round cylinder with flat ends. I 

 would suggest as a better form a cube or tetrahedron, the faces of which could be 

 polished flat, and the flatness tested optically. This would ascertain that they had the 

 intended flatness within about two seventh-metrets. (The seventh -metret is the ten- 

 millionth of a metre.) 



1 The fifth-metret is the hundred-thousandth of a metre. 



