210 



COMPOSITION AND RESOLUTION OF FORCE. 



In making the experiment, the sides A B and A D, C B and C D, are ad- 

 justed by the joints B and A to the same number of inches respectively as there 

 are ounces in the weights A and B, fig. 2. Then the diagonal A C is adjusted 

 by the loop and screw at A, to as many inches as there are ounces in the 

 weight C. This done, the point A is placed behind P, fig. %, and the paral- 

 lelogram is held upright, so that the diagonal A C shall be in the direction of 

 the vertical thread P C. The sides A B and A D will then be found to take 

 the direction of the threads P M and P N. By changing the weights and the 

 lengths of the diagonal and sides of the parallelogram, the experiment may be 

 easily varied at pleasure. 



In the examples of the composition of forces which we have here given, the 

 effects of the forces are the production of pressures ; or, to speak more cor- 

 rectly, the theorem which we have illustrated is " the composition of pres- 

 sures." For the point P is supposed to be at rest, and to be drawn or pressed 

 in the directions P M and P N. In the definition which has been given of the 

 word/or^, it is declared to include motions as well as pressures. In fact, if 

 motion be resisted, the effect is converted into pressure. The same cause, 

 acting upon a body, will either produce motion or pressure, according as the 

 body is free or restrained. If the body be free, motion ensues ; if restrained, 

 pressure, or both these effects together. It is, therefore, consistent with anal- 

 ogy to expect that the same theorems which regulate pressures will also 

 be applicable to motions, and we find accordingly a most exact corres- 

 pondence. 



Ifa body have a motion in the direction A B, and at the point P it receive 

 [ another motion, such as would carry it in the direction P C, fig. 4, were it pre- 



Fig. 4. 



viously quiescent at P, it is required to determine the direction which the 

 body will take, and the speed with which it will move, under these circum- 

 stances. 



Let the velocity with which the body is moving from A to B be such, that it 

 would move through a certain space, suppose P N, in one second of time, and 

 let the velocity of the motion impressed upon it at P be such, that, if it had no 

 previous motion, it would move from P to M in one second. From the point 

 M draw a line parallel to P B, and from N draw a line parallel to P C, and 

 suppose these lines to meet at some point, as O. Then draw the line P O. In 

 consequence of the two motions, which are at the same time impressed upon the 

 body at P, it will move in the straight line from P to O. 



Thus the two motions, which are expressed in quantity and direction by the 

 sides of a parallelogram, will, when given to the same body, produce a single 

 motion, expressed in quantity and direction by its diagonal ; a theorem which 

 is to motions exactly what the former was to pressures. 



There are various methods of illustrating experimentally the composition of 



