2O FORCES. 



of force. This force diminishes inversely as the square of the distance 

 between the two bodies. The power of attraction is further directly 

 proportional to the quantity of the attracting matter, though without 

 any relation to the quality of the body. The intensity of the force of 

 gravitation can be measured by the extent of the movement that it 

 communicates to a freely falling body previously supported in a vacuum 

 but deprived of its support. This figure is 9.809, because the force of 

 gravity operating for one second upon the freely falling body imparts 

 to this a velocity of 9.809 meters. 



The final velocity of the freely falling body at the end of the first second (deter- 

 mined experimentally) is designated thus, g = 9.809 meters. The velocity, v, of 

 the freely falling body is in general proportional to the time, t, occupied in falling. 



Therefore v = gt (i) , that is, at the end of the first second v = g, i = 



g = 9.809 meters. 



The distance through which the body falls, s = ^t 2 (2) ; that is, the 



distance through which a body falls is as the square of the time occupied in falling. 

 From (i) and (2) there follows (by eliminating t) v = \I 2 8 S ($}- 



The velocity is as the square root of the distance traversed in falling. 



v^ 

 thus = s (4) 



A freely falling body, and also in general every mass in movement, 

 possesses kinetic energy (actual energy) ; it is to a certain degree a reposi- 

 tory of force. The kinetic energy of a body in movement is always 

 equal to the product of its weight (determinable by scales) and the 

 height to which it would rise from earth if it were raised from the earth 

 with the velocity peculiar to it. 



If the kinetic energy of the moving body be designated W and its weight P, 

 then W = P, s; then, from (4), W = P (5). 



The kinetic energy of a body is therefore proportional to the square 

 of its velocity. 



If an accelerating force operating on a body ^(pressure, traction, or 

 tension) drives it for some distance in the direction of its activity, the 

 force thus expends work. This is equal to the product that is obtained 

 if the amount of pressure or traction that propels the body is multiplied 

 by the length of the path traversed. 



If K represents the pressure or the traction with which the force operates upon 

 the body and S the path, then the work A = KS. In the same way the attraction 

 between the earth and a body raised above it (as, for instance, a ram) is a source 

 of work. 



It is customary to express the value of K in kilograms, but, on the 

 other hand, that of S in meters. Accordingly the unit of work is the 

 kilogrammeter (according to some the grammeter), that is, the force that 

 is capable of raising i kilo (according to some i gram) to the height of 

 i meter. 



Potential Energy. Transformation of Potential Energy into Kinetic 

 Energy, and the Reverse. In addition to the kinetic energy referred 

 to, bodies may possess also mechanical potential energy. By this' 

 designation is understood an aggregation of forces that are still inhibited 

 in their free evolution, and that, further, are causes of movement, without 



