372 THE PRINCIPLES OF SCIENCE. 



pendulum, performed by Newton and Gauss, shows that 

 all kinds of matter equally gravitate, that is, the attractive 

 power of a substance is exactly proportional to its density. 

 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 units of mass, as indicated by the inertia and 

 gravity it possesses. To proceed in the most simple and 

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

 cubic unit of matter of the standard density. The 

 founders of the French metrical system took as their unit 

 of mass, the cubic centimetre of water, at the temperature 

 of maximum density (about 4 Centigrade). They called 

 this unit of mass the gramme, and constructed standard 

 specimens of the kilogram, which might be readily re- 

 ferred to by all who required to employ accurate weights. 

 Unfortunately, however, the determination of the bulk of 

 a given weight of water at a certain temperature is an 

 operation involving many practical and theoretical dif- 

 ficulties, and it can not be performed in the present day 

 with a greater exactness than that of about one part in 

 5000, the results of careful observers being sometimes 

 found to differ as much as one part in looo 1 . 



Weights, on the other hand, can be compared with 

 each other to at least one part in a million. Hence if 

 different specimens of the kilogram be prepared by direct 



* Clerk Maxwell's 'Theory of Heat,' p. 79. 



