THE PHILOSOPHICAL BASIS 21 



That the units of time cannot be regarded as 

 essentially fixed and unalterable is clear when 

 we remember that any friction on the earth, 

 such as that of the tides, is slowly prolonging 

 the day, while resistance to the bodily motion 

 of the earth round the sun would gradually 

 alter the length of the year. Such changes may 

 be appreciable only after millions of years ; but 

 their possibility shows that our time-units are 

 as arbitrary as are those of length. 



But, even though our practical units of time 

 and length are arbitrary, their statement assumes 

 that there are such things as absolute time and 

 space in which events take place. The principle 

 of relativity has now taught us that time and 

 length are always relative to some observer, 

 and that only a continuum of space-time can 

 be considered as absolute and independent. 

 Nevertheless, our present scheme of science has 

 been built up on these concepts now proved to 

 be relative, and we may continue to use them 

 as a matter of convenience. 



From the conceptions of length and time, and 

 the arbitrary units chosen to measure them, may 

 be derived the more complex ideas required for a 

 description of motion,and the derived units needed 

 to investigate it quantitatively. Thus velocity is 

 measured by the ratio of the number of units 

 of length to the number of units of time, while 

 acceleration, or the rate of change of velocity, 

 is measured by the number of units of velocity 

 gained or lost per unit of time. These relations 

 are expressed by saying that the dimensions of 

 the unit of velocity are L/T, while those of the 

 unit of acceleration are v/T or L/T^ 



