COMPOSITION AND RESOLUTION OF FORCE. 



211 



motion. An ivory ball, being placed upon a perfectly level, square table, at 

 one of the corners, and receiving two equal impulses, in the directions of the 

 sides of the table, will move along the diagonal. Apparatus for this experiment 

 differ from each other only in the way of communicating the impulses to the 

 ball. 



As two motions simultaneously communicated to a body are equivalent to a 

 single motion in an intermediate direction, so also a single motion may be me- 

 chanically replaced by two motions in directions expressed by the sides of any 

 parallelogram, whose diagonal represents the single motion. This process is 

 " the resolution of motion," and gives considerable clearness and facility to 

 many mechanical investigations. 



It is frequently necessary to express the portion of a given force, which acts 

 in some given direction different from the immediate direction of the force it- 

 self. Thus, if a force act from A, fig. 5, in the direction A C, we may require 



Fig. 5. 



to estimate what part of that force acts in the direction A B. If the force be a 

 pressure, take as many inches, A P, from A, on the line A C, as there are 

 ounces in the force, and from P draw P M perpendicular to A B ; then the 

 part of the force which acts along A B will be as many ounces as there are 

 inches in A M. The force A B is mechanically equivalent to two forces, ex- 

 pressed by the sides A M and A N of the parallelogram ; but A N, being per- 

 pendicular to A B, can have no effect on a body at A, in the direction of A B, 

 and therefore the effective part of the force A P, in the direction A B, is ex- 

 pressed by A M. 



Any number of forces acting on the same point of a body may be replaced 

 by a single force which is mechanically equivalent to them, and which is, 

 therefore, their resultant. This composition may be effected by the successive 

 application of the parallelogram of forces. Let the several forces be called A, 

 B, C, D, E, &c. Draw the parallelogram whose sides express the forces A 

 and B, and let its diagonal be A'. The force expressed by A' will be equiva- 

 lent to A and B. Then draw the parallelogram whose sides express the forces 

 A' and C, and let its diagonal be B'. This diagonal will express a force me- 

 chanically equivalent to A' and C. But A' is mechanically equivalent to A and 

 B, and therefore B' is mechanically equivalent to A, B, and C. Next construct 

 a parallelogram whose sides express the forces B' and D, and let its diagonal 

 be C 7 . The force expressed by C' will be mechanically equivalent to the forces 

 B 7 and D ; but the force B 7 is equivalent to A, B, C, and therefore C 7 is equiv- 

 alent to A, B, C, and D. By continuing this process, it is evident that a sin- 

 gle force may be found which will be equivalent to, and may be always substi- 

 tuted for, any number of forces which act upon the same point. 



If the forces which act upon the point neutralize each other, so that no mo- 

 tion can ensue, they are said to be in equilibrium. 



Examples of the composition of motion and pressure are continually present- 

 ing themselves. They occur in almost every instance of motion or force which 

 falls under our observation. The difficulty is to find an example which, strictly 

 speaking, is a simple motion. 



