“Every change of motion must be proportional to the impressed force, and must be in the direction of that straight line in which the force is impressed.” III. “Action must always be equal and contrary to reaction; or the actions of two bodies upon each other must be equal, and directed towards contrary sides.” When _inertia_ and _force_ are defined, the first law becomes an identical proposition. The second law cannot be rendered perfectly intelligible until the student has read the chapter on the composition and resolution of forces, for, in fact, it is intended as an expression of the whole body of results in that chapter. The third law has been explained in the present chapter, as far as it can be rendered intelligible in the present stage of our progress. We have noticed these formularies more from a respect for the authorities by which they have been proposed and adopted, than from any persuasion of their utility. Their full import cannot be comprehended until nearly the whole of elementary mechanics has been acquired, and then all such summaries become useless. * * * * * (71.) The consequences deduced from the consideration of the quality of inertia in this chapter, will account for many effects which fall under our notice daily, and with which we have become so familiar, that they have almost ceased to excite curiosity. One of the facts of which we have most frequent practical illustration is, that the quantity of motion or _moving force_, as it is sometimes called, is estimated by the velocity of the motion, and the weight or mass of the thing moved conjointly. If the same force impel two balls, one of one pound weight, and the other of two pounds, it follows, since the balls can neither give force to themselves, nor resist that which is impressed upon them, that they will move with the same force. But the lighter ball will move with twice the speed of the heavier. The impressed force which is manifested by giving velocity to a double mass in the one, is engaged in giving a double velocity to the other. If a cannon-ball were forty times the weight of a musket-ball, but the musket-ball moved with forty times the velocity of the cannon-ball, both would strike any obstacle with the same force, and would overcome the same resistance; for the one would acquire from its velocity as much force as the other derives from its weight. A very small velocity may be accompanied by enormous force, if the mass which is moved with that velocity be proportionally great. A large ship, floating near the pier wall, may approach it with so small a velocity as to be scarcely perceptible, and yet the force will be so great as to crush a small boat. A grain of shot flung from the hand, and striking the person, will occasion no pain, and indeed will scarcely be felt, while a block of stone having the same velocity would occasion death.