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. 



