36 FORCE AND MOTION. 



82. Parallelogram of Forces. In the diagram, 

 let AB and AC represent 



O- 



two forces acting upon the 

 point A. Draw the two 

 dotted lines to complete the 

 parallelogram. From A, the 

 point of application, draw 

 the diagonal AD. This 

 diagonal will be a complete graphic representa- 

 tion of the resultant. In such cases the two given 

 forces are called components. The resultant of any two 

 components may always be determined in this way. If 

 two forces, such as those represented in the diagram, act 

 simultaneously upon a body at A, that body will move 

 over the path represented by AD, and come to rest at D. 



(a.) Suppose that instead of acting simultaneously, these forces 

 act successively. If AC act first for a given time, it would move the 

 body to C. If then the other force act for an equal time it would 

 move it to the right a distance represented by AB or its equal CD, 

 and the body be left at D as before. If the force represented by AB 

 acted first and the force represented by AC then acted for an equal 

 time, the body would evidently be left at D. Thus we see that these 

 two forces produce the same effect whether they act simultaneously 

 or successively. 



83. Experimental Verification. This prin- 

 ciple of the parallelogram of forces may be verified by 

 the apparatus represented in Fig. 10. ABCD is a very 

 light wooden frame, jointed so as to allow motion at its 

 four corners. The lengths of opposite sides are equal ; the 

 lengths of adjacent sides are in the ratio of two to three. 

 From the corners B and C, light, flexible silk cords pass 

 over the pulleys M and N, and carry weights, W and w, 

 of 90 and 60 ounces respectively, the ratio between the 



