THE PHILOSOPHICAL BASIS 23 



their relative motion becomes greatly simplified 

 by assigning to each of them a certain relative 

 number to express a quantity which we may 

 term Its relative mass. Let us make the two 

 bodies, when free to move, act on each other in 

 any way, excluding the possibility of rotation, 

 for the sake of simplicity. Let us, for instance, 

 connect them by means of a long, stretched 

 elastic cord, and allow them to move each other. 

 After the action has begun, we shall find that 

 one body is, in general, moving faster than the 

 other, and that the ratio of their accelerations is 

 constant. The inverse ratio of these accelera- 

 tions is the measure of the ratio between the 

 masses of the two bodies ; the body with the 

 smaller mass is moved faster by the mutual 

 action than Is the body with the greater mass. 



We now need only to choose some mass as 

 our unit with which to compare other masses, 

 and to prove experimentally that the mass of a 

 body as thus defined Is a constant quantity, to 

 complete our preparations for using the concep- 

 tion of mass in our physical description of 

 observed phenomena. 



In all ordinary physical and chemical changes, 

 mass is found to be constant. But, when a 

 particle is travelling at speeds approaching that 

 of light, its mass, as measured by an observer at 

 rest, increases. Thus mass, like length and time, 

 is not absolute ; its value depends on its relation 

 to an observer. But with this caution we may 

 use the old concept of a constant mass with those 

 of length and time as the basis of a system of 

 physical units. 



Experience shows us that we can generalise 



