CHAPTER XIV. 



UNITS AND STANDARDS OF MEASUREMENT. 



INSTRUMENTS of measurement are, as we have seen, 

 only means of comparison between one magnitude and 

 another, and as a general rule we must assume some 

 one arbitrary magnitude, in terms of which all results 

 of measurement are to be expressed. Mere ratios be- 

 tween any series of objects will never tell us their 

 absolute magnitudes ; we must have at least one ratio 

 for each, and we must have one absolute quantity. The 

 number of ratios n are expressible in n equations, which 

 will contain at least n + i quantities, so that if we 

 employ them to make known n magnitudes, we must 

 have one magnitude known. Hence, whether we are 

 measuring time, space, density, weight, mass, energy, or 

 any other physical quantity, we must refer to some con- 

 crete standard, some actual object, which if once lost and 

 irrecoverable, all our measures lose their absolute mean- 

 ing. This concrete standard is in all, except two, cases 

 absolutely arbitrary in point of theory, and its selection 

 a question of practical convenience. 



Of the two cases in which a natural standard unit is 

 ready made for us, one case is that of number itself. 

 Abstract number needs no special unit ; for any object 

 by existing or being thought of as separate from other 

 objects (p. 176), furnishes us with a unit, and is the only 

 standard required. 



