UNITS AND STANDARDS OF MEASUREMENT. 375 



Derived Units. 



The standard units of time, space, and mass having been 

 once fixed, it becomes obvious that many kinds of magnitude 

 are naturally measured by units immediately derived from 

 one or more of the three principal ones. From the standard 

 metre of linear magnitude follows in the most obvious 

 manner the centaire or square metre, the unit of super- 

 ficial magnitude, and the litre or cube of the tenth part 

 of a metre, the standard of capacity or volume. Velocity 

 of motion, again, is expressed by the ratio of the space 

 passed over, when the motion is uniform, to the time 

 occupied ; hence the unit velocity will be that of a 

 body which passes over a unit of space in a unit of time, 

 say one metre per second. Momentum is measured by 

 the mass moving, regard being paid both to the amount 

 of matter and the velocity at which it is moving. Hence 

 the unit of momentum will be that of a unit volume of 

 matter of the unit density moving with the unit velocity, 

 or in the French system, a cubic centimetre of water of 

 the maximum density moving one metre per second. 



An accelerating force is measured by the ratio of the 

 momentum generated to the time occupied, the force 

 being supposed to act uniformly. The unit of force will 

 therefore be that which generates a unit of momentum 

 in a unit of time, or which causes, in the French system, 

 one cubic centimetre of water at maximum density to 

 acquire in one second a velocity of one metre per second. 

 The force of gravity is the most familiar kind of force, 

 and as when acting unimpeded upon any substance it 

 produces in a second a velocity of 9'8o868 .... metres 

 per second in Paris, it follows that the absolute unit 

 of force is about the tenth part of the force of gravity. 

 If we employ British weights and measures, the absolute 

 unit of force is represented by the gravity of about half 



