Definitions and Axioms.

114. ANY number of bodies which can in any way mutually affect each other's motion or rest, is a system of bodies.

115. Momentum is the product of the mass and the velocity of a body.

116. Force is proportional to velocity, and momentum is proportional to the product of the velocity and the mass ; hence the only difference between the equilibrium of a particle and that of a solid body is, that a particle is balanced by equal and contrary forces, whereas a body is balanced by equal and contrary momenta.

117. For the same reason, the motion of a solid body differs from the motion of a particle by the mass alone, and thus the equation of the equilibrium or motion of a particle will determine the equilibrium or motion of a solid body, if they be multiplied by its mass.

118. A moving force is proportional to the quantity of momentum generated by it.

Reaction equal and contrary to Action.

119. The law of reaction being equal and contrary to action, is a general induction from observations made on the motions of bodies when placed within certain distances of one another; the law is, that the sum of the momenta generated and estimated in a given direction is zero. It is found by experiment, that if two spheres A and B of the same dimensions and of homogeneous matter, as of gold, be suspended by two threads so as to touch one another when at rest, then if they be drawn aside from the perpendicular to equal heights and let fall at the same instant, they will strike one another centrically, and will destroy each other's motion, so as to remain at rest in the perpendicular.