8 1.] INTRODUCTION. 45 



CHAPTER IV. 



STATICS. 

 I. Introduction. 



80. When a particle has two equal and opposite accelerations 

 y, y, its motion will not be changed. The same result must 

 follow when a particle is acted on by two equal and opposite 

 forces F= mj, F' = mj. Their combined effect on the particle 

 is nil, so that the particle, if originally at rest, will remain 

 at rest ; if originally moving with constant velocity in a 

 straight line, it will continue to do so ; and if originally moving 

 under the action of any other forces in any way whatever, the 

 introduction of the two equal and opposite forces will have no 

 effect on its motion. . 



We say that two equal and opposite forces acting on a particle 

 balance, or are equivalent to o, or are in equilibrium. If no 

 other forces act on the particle, the particle itself is said to be 

 in equilibrium. It must be kept in mind that equilibrium is not 

 synonymous with rest. 



81. Let us next consider any two forces F v F^ acting simul- 

 taneously on the same particle P of mass m, and let j\, j^ be 

 the accelerations produced by these forces so that 



The resultant acceleration of the particle is found by geo- 

 metrically adding the vectors j\ , j^ ; let j be their geometric 



sum. Then the force 



F=mj 





