22 



THE HUMAN MOTOR 



The reduction of a system of forces to a general resultant and 

 a resultant moment, shows that the equilibrium of a solid de- 

 mands six conditions and six equations. 



16. Parallel Forces. If two divergent forces, F x and F 2 , 

 change their direction and become parallel (fig. 40), the point 

 of convergence is infinity and the resultant will be at a point 



Fio. 40. 



FM 41 



in the straight line AB, which joins the points of application 

 of F, and F 2 . This resultant will be equal to the sum of the 



two forces if they have the same 

 direction, to their difference if 

 they are unequal and in opposite 

 directions (fig. 41). It will have 

 a direction parallel to them, and 

 it will divide the line AB into 

 segments, inversely proportional 

 to these forces. Thus 



-.d 



Fio. 42. 





CB 

 CA 



The point C is said to be the centre of parallel forces. 



If the two forces are equal and in a contrary direction, their 

 resultant is zero : Fj = F x ' and F l F' x = (fig. 42) ; they 

 are said to form a couple. The couple tends to produce a move- 

 ment of rotation ; it possesses a moment, and it is easily seen 

 that the moment of Fj' in relation to the point A is 



F\ xd 



That of F! in relation to the same point A is zero : so that 

 the moment of the couple is the product of one of the two forces 

 by the distance d. This moment is shown, for example, when 

 two horses are harnessed to a cart : also in an auger and a cork- 

 screw. The moment is represented by a vector AM perpendicular 



