24 THE HUMAN MOTOR 



18. Mass. It is said that two bodies have the same mass when, 

 under the action of equal forces, they take the- same acceleration. 

 If their acceleration is different, the masses of the bodies are 

 correspondingly different ; in general terms the mass is pro- 

 portional to the acceleration, and 

 F F F 



--/. A=A -,=A -> 



m m m 



or 



m f m' f. 



- = -I' - =r 1 * I 



m' f m" f 



and also for the forces F and F' producing the same acceleration 

 /on the masses m and m' : 



F , F' . , F m' 



= /; = /; from which = e tc. 



mm' F' m 



It follows that F = mf, that is to say : The force is the pro- 

 duct of the mass and the acceleration ; and can be measured 

 by the product. 



The intensity of gravity, which is also a force, will be P = mg, 

 where P is the weight of a body. In the same manner the 

 acceleration of gravity being constant, P' = m'g, P" = m"g. 



Thus the weights of bodies are in proportion to the masses. 



In the formula P = mg, if the unit of mass m = 1, then P = g, 

 and the intensity of gravity will be that of the acceleration, g 

 due to gravity. At Paris, g = 9-80978 metres, or approxi- 

 mately 9-81 metres per second. In the C.G.S. system the unit 

 of mass is denned as the mass of a cubic centimetre of water 

 at a temperature of 4 centigrade, which is called the gramme. 

 The unit of length is the centimetre. 



It follows that the force of the weight : p = mg, will be : 

 p = Igr x 980-97 centimetres = 980'97 gramme centimetres. 



The unit of force in the C.G.S. System is, therefore the 



gramme-centimetre, or the dyne ; it is the fraction - or 7^-. 



g yyi 



of a gramme. The value of g being constant, the gramme 

 becomes the unit of force or weight. The unit of time being 

 the second, we have the C.G.S. system, which is almost 

 universal for scientific measurements. 



The definition F = mg or Mf, that has been given for any force, 

 can be compared with that given above ( 11) ; one is dynamic, 

 the other static. As for the word mass, it does not connote 

 either physics or metaphysics. If mass is defined as the quantity 



