492 PHYSIOLOGICAL PHYSICS. rchap. XL. 



the resultant of the two forces OA, OB ; and if the lines 

 OA and OB represent by their lengths the magnitude 

 of the forces, then the diagonal will represent by its 

 length the magnitude of the resultant force. This is the 

 parallelogram of force. 



In a similar way one force may be made to take 

 the place of several forces. Let a parallelogram be 

 constructed on the lines representing two of the 

 forces. Take the diagonal, and with it and the line 

 representing the third force construct another paral- 

 lelogram. Its diagonal is the resultant of the three 

 forces ; with it and the line representing the fourth 

 force, the resultant of the four forces may be found, 

 and so on. 



The process of finding a single force which can be 

 substituted for more than one, is called the composi- 

 tion of forces. It is apparent also that the converse 

 of the composition of forces is true, namely, that a 

 single force can be resolved into two forces. Thus, 

 the force OR, if it be the resultant of OA and OB, can 

 be replaced by them. If it be given as a single force, 

 then, by constructing the parallelogram of which it 

 is a diagonal, it can be resolved into' two forces 

 acting at an. angle. This is called the resolution of 

 forces. 



Resultant of parallel forces. Suppose two 

 parallel forces acting on a rigid bar in the same direc- 

 tion, the resultant will be equal in magnitude to 

 their sum, and if they are equal forces they may be 

 replaced by the resultant force midway between 

 them. If they are unequal, then the point of ap- 

 plication of the resultant force will be at a distance 

 from the points of application of the two forces which 

 is inversely proportional to the magnitude of the forces ; 

 that is to say, the point of application of the resultant 

 will be nearer to the greater force. Thus, in Fig. 202, 

 the diagram to the right represents a bar AB under the 



