xiv.] UNITS AND STAND AEDS OF MEASUREMENT. 317 



Thus the force required to set a body in motion varies 

 both according to the bulk of the matter, and also accord- 

 ing to its quality. Two cubic inches of iron of uniform 

 quality, will require twice as much force as one cubic inch 

 to produce a certain velocity in a given time ; but one cubic 

 inch of gold will require more force than one cubic inch of 

 iron. There is then some new measurable quality in 

 matter apart from its bulk, which we may call density, and 

 which is, strictly speaking, indicated by its capacity to 

 resist and absorb the action of force. For the unit of 

 density we may assume that of any substance which is uni- 

 form in quality, and can readily be referred to from time to 

 time. Pure water at any definite temperature, for instance 

 that of snow melting under inappreciable pressure, fur- 

 nishes an invariable standard of density, and by compar- 

 ing equal bulks of various substances with a like bulk of 

 ice-cold water, as regards the velocity produced in a unit 

 of time by the same force, we should ascertain the densities 

 of those substances as expressed in that of water. Practi- 

 cally the force of gravity is used to measure density ; for a 

 beautiful experiment with the pendulum, performed by 

 Newton and repeated by Gauss, shows that all kinds of 

 matter gravitate equally. Two portions of matter then 

 which are in equilibrium in the balance, may be assumed 

 to possess equal inertia, and their densities will therefore 

 be inversely as their cubic dimensions. 



Unit of Mass. 



Multiplying the number of units of density of a portion 

 of matter, by the number of units of space occupied by it, 

 we arrive at the quantity of matter, or, as it is usually 

 called, the unit of mass, as indicated by the inertia and 

 gravity it possesses. To proceed in the most simple 

 manner, the unit of mass ought to be that of a cubic unit 

 of matter of the standard density ; but the founders of 

 the metrical system took as their unit of mass, the cubic 

 centimetre of water, at the temperature of maximum 

 density (about 4 Cent.). /They called this unit of mass 

 the gramme, and constructed standard specimens of the 

 kilogram, which might be readily referred to by all who 

 required to employ accurate weights. Unfortunately the 



