322 THE PRINCIPLES OF SCIENCE. [CHAP. 



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' 80868 . . 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 

 an ounce, since the force of gravity of any portion of 

 matter acting upon that matter during one second, pro- 

 duces a final velocity of 32' 1889 feet per second or about 

 32 units of velocity. Although from its perpetual action 

 and approximate uniformity we find in gravity the most 

 convenient force for reference, and thus habitually employ 

 it to estimate quantities of matter, we must remember 

 that it is only one of many instances of force. Strictly 

 speaking, we should express weight in terms of force, but 

 practically we express other forces in terms of weight. 



We still require the unit of energy, a more com- 

 plex notion. The momentum of a body expresses the 

 quantity of motion which belongs or would belong to the 

 aggregate of the particles ; but when we consider how this 

 motion is related to the action of a force producing or 

 removing it, we find that the effect of a force is pro- 

 portional to the mass multiplied by the square of the 

 velocity and it is convenient to take half this product 

 as the expression required. But it is shown in books 

 upon dynamics that it will be exactly the same thing if 

 we define energy by a force acting through a space. The 



