'INTRODUCTION. xxiii 



i.e., at the end of the 1st sec., V = g, I = g 9 '809 M the distance traversed 



a = |* 2 .......... (2); 



i.e., the distances are as the square of the times. Hence, from (1) and (2) it follows 

 (by eliminating t) that 



V = V2^~ r ...... (3). 



The velocities are as the square roots of the distances traversed 



Therefore, ~- = s ........... (4). 



The freely falling body, and in fact every freely moving body, possesses 

 kinetic energy, and is in a certain sense a magazine of energy. The 

 kinetic energy of any moving body is always equal to the product of 

 its weight (estimated by the balance), and the height to which it 

 would rise from the earth, if it were thrown from the earth with its 

 own velocity. 



Let W represent the kinetic energy of the moving body, and P its weight, then 

 W =1 P.s, so that from (4) it follows that 



Hence, the kinetic energy of a body is proportional to the square of 

 its velocity. 



Work. If a force (pressure, strain, tension) be so applied to a body 

 as to move it, a certain amount of work is performed. The amount of 

 work is equal to the product of the amount of the pressure or strain 

 which moves the body, and of the distance through which it is moved. 



Let K represent the force acting on the body, and S the distance, then the 

 work W = K S. The attraction between the earth and any body raised above it 

 is a source of work. 



It is usual to express the value of K in kilogrammes, and S in 

 metres, so that the " unit of work" is the kilogramme-metre, i.e., the force 

 which is required to raise 1 kilo, to the height of 1 metre. 



2. Potential Energy. The transformation of Potential into Kinetic 

 energy, and conversely : Besides kinetic energy, there is also " potential 

 energy," or energy of position. By this term are meant various forms 

 of energy, which are suspended in their action, and which, although 

 they may cause motion, are not in themselves motion. A coiled watch- 

 spring kept in this position, a stone resting upon a tower, are instances 

 of bodies possessing potential energy, or the energy of position. It 

 requires merely a push to develop kinetic from the potential energy, 

 or to transform potential into kinetic energy. 



