GENERAL PRINCIPLES 37 



slant. This is the theorem of areas, only applicable to the case 

 of external forces with zero moment. If, however, there was 

 no external force, the sum of the areas would be zero. This 

 is the case if a man is standing upright on a perfectly smooth 

 surface ; if he wants to turn his body, one part will not turn in 

 one direction without the other turning in the opposite direction, 

 so that the sum of the described areas will be zero. If, he slides 

 one leg forward, the other will slip back and he will fall (see 

 further on, 263) 



28. Work. When a force acts either to produce or retard the 

 displacement of a body (a point or a system of points) we say 

 that it performs work. Work is the product of force by the 

 displacement / in its own direction giving 



T = F x /. 



A force of 1 kilogramme, displacing a body 1 metre on a path 

 in its direction, performs work equal to 1 kilogrammetre (sign : 

 kgm.). 



In the C.G.S. system the unit is the work done by 1 dyne for 

 1 centremetre of displacement, this unit being the erg (from 

 epyov, work). 



lr 1 



The dyne is -> the erg will be X l cm - or 

 Uol yol 



1 -' x ' Olm = of a 



that is to say, a kilogrammetre equals 0-81 x 10 7 ergs, nearly 100 



million ergs. 



A According to whether a force 



acts in the direction of the dis- 

 placement or in the opposite, it 

 _ produces either motive or re- 

 M F' .6- sistant work. As an example 



Fjo , <52 ; of resistant work may be men- 



tioned the sliding down of a 



barrel on an inclined surface, its fall being restrained by means 

 of a rope. This resistant work is also called negative work, the 

 other being said to be positive work. 



The force can have an oblique direction in relation to the dis- 

 placement. This is the case when a rope is pulling a wagon on 

 rails at an angle therewith. Then the only useful component 

 of the force is the projection of F on the line of the displacement, 

 and then 



F' = F cos a, 



