144 THE REALITIES OF MODERN SCIENCE 



centimeter which we used in Chapter IX, is conse- 

 quently not invariable. We need an absolute unit, 

 and we shall now derive it from the three fundamental 

 units of length, mass and time. 



Since the p.e. which is available for conversion into 

 kinetic energy when 1 gram falls 1 cm. depends upon 

 the locality, the k.e. which is acquired is similarly 

 dependent. If a gram in falling 1 cm. acquires a 

 greater k.e. in one locality than in another it must 

 also have acquired a greater velocity. That is, it is 

 accelerated more and the value of g should be higher. 

 Let us therefore measure energy in such a unit that the 

 numeric expressing 1 gram-cm, shall be proportional 

 to the acceleration at the given locality. We have 

 already seen that the increase in energy is proportional 

 to the total distance traversed and to the mass of the 

 displaced body. Hence, let us write as the defining 

 equation of the unit of energy 



W 8 -W = mas (7) 



when W is the initial energy of a body of mass m 

 which, after traveling a distance s with a uniform 

 acceleration of a, has a final energy W s . 



We now apply the method of Chapter X by placing 

 m = 1 gram, s = 1 cm., and a = 1cm./ 1 sec. 2 , then W s W 

 is one unit of energy. Unit energy is that expended 

 upon (and hence that acquired by) 1 gram in moving 

 1 cm. with an acceleration of 1 cm. per sec. per sec. 

 This unit is so frequently used that it has been given a 

 convenient name, viz. the "erg" from the same Greek 

 root as "energy." 



If a in equation (7) has the special value of g then 



