376 THE PRINCIPLES OF SCIENCE. 



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 presence 

 and approximate uniformity we find in gravity the most 

 convenient force for reference, and thus habitually employ 

 it to estimate quantities of matter or mass, we must re- 

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

 Strictly speaking, we should express weight in terms of 

 force, but practically we express all 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 most 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 certain space. 

 The natural unit of energy will then be that which over- 

 comes a unit of force acting through a unit of space ; when 

 we lift one kilogram through one metre, against gravity, 

 we therefore accomplish 9*80868 . . . . units of work, 

 that is, we turn so many units of potential energy ex- 

 isting in the muscles, into potential energy of gravitation. 

 In lifting one pound through one foot there is in like 

 manner a conversion of 32-1889 units of energy. Accord- 

 ingly the unit of energy will be that required to lift a 

 kilogram through about one tenth part of a metre against 

 gravity, or, in the English system, to lift one pound through 

 the thirty-second part of a foot. 



Every person is at perfect liberty to measure and record 



