312 THE PRINCIPLES OF SCIENCE. [CHAP. 



The Unit of Space and the Bar Standard. 



Next in importance after the measurement of time is 

 that of space. Time comes first in theory, because pheno- 

 mena, our internal thoughts for instance, may change in 

 time without regard to space. As to the phenomena 

 of outward nature, they tend more and more to resolve 

 themselves into motions of molecules, and motion cannot 

 be conceived or measured without reference both to time 

 and space. 



Turning now to space measurement, we find it almost 

 equally difficult to fix and define once and for ever, a unit 

 magnitude. There are three different modes in which 

 it has been proposed to attempt the perpetuation of a 

 standard length. 



(1) By constructing an actual specimen of the standard 

 yard or metre, in the form of a bar. 



(2) By assuming the globe itself to be the ultimate 

 standard of magnitude, the practical unit being a sub- 

 multiple of some dimension of the globe. 



(3) By adopting the length of the simple seconds pen- 

 dulum, as a standard of reference. 



At first sight it might seem that there was no great 

 difficulty in this matter, and that any one of these methods 

 might serve well enough; but the more minutely we 

 inquire into the details, the more hopeless appears to be 

 the attempt to establish an invariable standard. We must 

 in the first place point out a principle not of an obvious 

 character, namely, that the standard length must be defined 

 by one single object. 1 To make two bars of exactly the 

 same length, or even two bars bearing a perfectly defined 

 ratio to each other, is beyond the power of human art. If 

 two copies of the standard metre be made and declared 

 equally correct, future investigators will certainly discover 

 some discrepancy between them, proving of course that they 

 cannot both be the standard, and giving cause for dispute 

 as to what magnitude should then be taken as correct. 



If one invariable bar could be constructed and main- 

 tained as the absolute standard, no such inconvenience 

 could arise. Each successive generation as it acquired 



1 See Harris' Essay upon Money and Coins, part. ii. [1758] p. 127. 



