304 . THE PRINCIPLES OF SCIENCE. [chap. xiii. 



As regards short intervals of time, it has ah-eady been 

 stated that Sir George Airy was able to estimate one part 

 iu 8,640,000, an exactness, as he truly remarks, " almost 

 beyond conception." ^ The ratio between the mean solar 

 and the sidereal day is known to be about one part in 

 one hundred millions, or to the eighth place of decimals, 

 (p. 289). 



Determinations of weight seem to come next in exact- 

 ness, owing to the fact that repetition without error is 

 applicable to them. An ordinary good balance should 

 show about one part in 500,000 of the load. The finest 

 balance emplo5^ed by M. Stas, turned with one part in 

 825,000 of the load.^ But balances have certainly been 

 constructed to show one part in a million,^ and Eamsden is 

 said to have constructed a balance for the Koyal Society, 

 to indicate one part in seven millions, though this is hardly 

 credible. Professor Clerk Maxwell takes it for granted that 

 one part in five millions can be detected, but we ought to 

 discriminate between what a balance can do when first 

 constructed, and when in continuous use. 



Determinations of length, unless performed with extra- 

 ordinary care, are open to much error in the junction of 

 the measuring bars. Even in measuring the base line of 

 a trigonometrical survey, the accuracy generally attained 

 is only that of about one part in 60,000, or an inch in the 

 mile ; but it is said that in four measurements of a 

 baseline carried out very recently at Cape Comorin, the 

 greatest error was O'O// inch in i 68 mile, or one part in 

 1,382,400, an almost incredible degree of accuracy. Sir J. 

 Whitworth has shown that touch is even a more delicate 

 mode of measuring lengths than sight, and by means of a 

 splendidly executed screw, and a small cube of iron placed 

 between two fliat-ended iron bars, so as to be suspended 

 when touching them, he can detect a change of dimension 

 in a bar, amounting to no more than one-millionth of an 

 inch.* 



^ Philosophical Transactions, (1856), vol. cxlvi. pp. 330, 331. 

 2 First Annual Report of the Mint, p. 106. 

 ■' Jo veins, in Watts' Dictionary of Chemistry, vol. i. p. 483. 

 ^ British Assot'iation, Glasgow, 1856. Address of the President of 

 the Mechanical Section. 



