314 THE PRINCIPLES OF SCIENCE. [CHAP. 



comparison would show from time to time the comparative 

 variations of length of these different substances. The 

 most variable substances would be the most divergent, and 

 the standard would be furnished by the mean length 

 of those which agreed most closely with each other just 

 as uniform motion is that of those bodies which agree 

 most closely in indicating the efflux of time. 



The Terrestrial Standard. 



The second method assumes that the globe itself is a 

 body of invariable dimensions and the founders of the me- 

 trical system selected the ten-millionth part of the dis- 

 tance from the equator to the pole as the definition of the 

 metre. The first imperfection in such a method is that the 

 earth is certainly not invariable in size ; for we know 

 that it is superior in temperature to surrounding space, and 

 must be slowly cooling and contracting. There is much 

 reason to believe that all earthquakes, volcanoes, mountain 

 elevations, and changes of sea level are evidences of this 

 contraction as asserted by Mr. Mallet. 1 But such is the 

 vast bulk of the earth and the duration of its past exis- 

 tence, that this contraction is perhaps less rapid in propor- 

 tion than that of any bar or other material standard which 

 we can construct. 



The second and chief difficulty of this method arises 

 from the vast size of the earth, which prevents us from 

 making any comparison with the ultimate standard, ex- 

 cept by a trigonometrical survey of a most elaborate and 

 costly kind. The French physicists, who first proposed 

 the method, attempted to obviate this inconvenience by 

 carrying out the survey once for all, and then constructing 

 a standard metre, which should be exactly the one ten 

 millionth part of the distance from the pole to the 

 equator. But since all measuring operations are merely 

 approximate, it was impossible that this operation could be 

 perfectly achieved. Accordingly, it was shown in 1838 

 that the supposed French metre was erroneous to the con- 

 siderable extent of one part in 5527. It then became 

 necessary either to alter the length of the assumed metre, 



1 Proceedings of ilie Royal Society, 2oth June, 1872, vol. xx. p. 438. 



