XIV.] UNITS AND STANDARDS OF MEASUEEMENT. 313 



higher powers of measurement, would detect errors in 

 the copies of the standard, but the standard itself would 

 be unimpeached, and would, as it were, become by degrees 

 more and more accurately known. Unfortunately to con- 

 struct and preserve a metre or yard is also a task which 

 is either impossible, or what comes nearly to the same 

 thing, cannot be shown to be possible. Passing over the 

 practical difficulty of defining the ends of the standard 

 length with complete accuracy, whether by dots or lines 

 on the surface, or by the terminal points of the bar, we 

 have no means of proving that substances remain of in- 

 variable dimensions. Just as we cannot tell whether the 

 rotation of the earth is uniform, except by comparing it 

 with other moving bodies, believed to be more uniform 

 in motion, so we cannot detect the change of length in a 

 bar, except by comparing it with some other bar sup- 

 posed to be invariable. But how are we to know which 

 is the invariable bar ? It is certain that many rigid 

 and apparently invariable substances do change in di- 

 mensions. The bulb of a thermometer certainly contracts 

 by age, besides undergoing rapid changes of dimensions 

 when warmed or cooled through ioo° Cent. Can we 

 be sure that even the most solid metallic bars do not 

 slightly contract by age, or undergo variations in their 

 structure by change of temperature. Fizeau was induced 

 to try whether a quartz crystal, subjected to several 

 hundred alternations of temperature, would be modified in 

 its physical properties, and he was unable to detect any 

 change in the coefficient of expansion.^ It does not 

 follow, however, that, because no apparent change was 

 tli.scovered in a quartz crystal, newly-constructed bars of 

 ineral would undergo no change. 



The best principle, as it seems to me, upon which the 

 perpetuation of a standard of length can be rested, is that, 

 if a variation of length occurs, it will in all probability be 

 of different amount in different substances. If then a 

 great number of standard metres were constructed of all 

 kinds of dilfcrent metals and alloys ; hard rocks, such as 

 granite, serjieutine, slate, quartz, limestone ; artificial 

 Bubstances, such as porcelain, glass, &c., &c., careful 



* Philosophical Magazine, (1868), 4tli Series, vol. xxxvi. p. 52. 



