51, 52] PRINCIPLES OF MECHANICS. UNITS AND DIMENSIONS. 97 



The factors m^ ra 2 , are called the masses of the bodies 1 and 2. 

 This gives us a means of comparing masses. If we make two 

 bodies act upon each other in any manner, their masses are 

 inversely proportional to the accelerations they have at the same 

 instant. The vector whose components are 



is called the impressed force acting on the mass ra. If the quantities 

 X, Y, Z are given functions, the above are called the differential 

 equations of motion of the material point m. 



52. Units. The specification of any quantity, scalar or vector, 

 involves two factors, first a numerical quantity (integer, fraction 

 or irrational) or numeric, and secondly a concrete quantity in terms 

 of which all quantities of that kind are numerically expressed, 

 called a unit. The simplest unit is that of the geometrical 

 quantity ; length. We shall adopt as the unit of length the centi- 

 meter, defined as the one-hundredth part of the distance at tem- 

 perature zero degrees Centigrade, and pressure 760 millimeters 

 of mercury, between two parallel lines engraved on a certain bar 

 of platinum-iridium alloy, deposited in a vault in the laboratory of 

 the " Comitd International des Poids et Mesures" at Sevres, near 

 Paris. This bar is known as the "Metre Prototype" and serves as 

 the basis of length measurements for the civilized world (except 

 the British Empire and Russia*). 



It was proposed by Maxwell to use a natural unit of length, 

 namely the length of a wave of light corresponding to some well- 

 defined line in the spectrum of some element, at a definite tem- 

 perature and pressure, as it is extremely probable that such a 

 wave-length is extremely constant. Measurements were carried 

 out at Sevres by Michelson, with this end in view, which established 

 the ratio between the above meter and the wave-length in air of 

 a red cadmium ray as l,553,164f. 



* The United States yard is defined as 3600/3937 metres. 

 t Michelson, Journal de Physique, Jan. 1894. 

 W. E. 7 



