FORCE, A SPACE RATE OF ENERGY 147 



for accelerating the body will be less than mg and may 

 even be zero, as was the case in the experiment of 

 Joule described on page 112. The value mg is thus the 

 maximum force which can be called into play by allow- 

 ing the potential energy to decrease. This maximum 

 force which a body can exert in free fall is called its 

 weight. The weight of 1 gram is then g dynes, or 

 approximately 980 dynes, depending upon the locality. 



This inexact use of the word " force" as meaning 

 " weight," that is, the maximum space rate at which 

 energy will be released if gravitational tractation is 

 allowed, persists in the language of physics. There 

 is no serious objection to this use provided that it 

 does not encourage an attitude of considering force 

 as a cause instead of a rate. Energy is the cause in 

 terms of which we must seek to explain all physical 

 phenomena. 



The rigorous quantitative meaning which modern 

 physics has given to " force" leads to the same numeri- 

 cal measure as Newton selected and stated in his 

 second law. This law says that "rate of change of 

 quantity of motion is proportional to the force and takes 

 place in the straight line in which the force acts." To- 

 day "quantity of motion" is called "momentum." It 

 is measured by the product of mass and velocity. Since 

 only the velocity changes and since the rate of change 

 of velocity is acceleration, the rate of change of momen- 

 tum is the product of mass and acceleration. From 

 equation (8) it is evident that the two definitions are 

 equivalent, for the left-hand member expresses our 

 present definition and the right-hand the Newtonian 

 definition. 



