(1.) _Conservation of Momentum._—What is understood by this is a mere direct consequence of Newton’s _first_ interpretation of his Third Law of Motion, viz., that _Action and Reaction are equal and opposite_. In this _first_ interpretation Newton tells us to consider actions and reactions as forces proper, or (their equivalents) quantities of motion. This is the term employed by Newton; but we now designate it _momentum_, and measure it by the product of the mass and the velocity of a body. Stated in its simplest form, this law asserts that the momentum of a system of bodies, measured in any direction whatever, is not altered by their mutual action, whether that action be of the nature of traction, attraction, repulsion, or impact. And we see at once from this third law of motion that it must be so, because the change of momentum, in any direction, of any one part of the system, per unit of time, is the measure of the force acting on that part in that direction. Whatever momentum in this particular direction is gained by one member of the system must have been lost by other members, but not from their whole momentum, merely from the part of it in this direction. It thus appears that the (algebraic) sum of the momenta generated by the mutual actions of the system is zero. These momenta are in fact _directed magnitudes_ (like the forces of which they are the measure), and are therefore capable of _cancelling one another_ when their numerical amounts are equal and their directions are opposite. In this sense the conservation is of the same nature as that of the imagined electric or magnetic fluids, where no portion whatever of one kind can be produced without the simultaneous appearance of an equal quantity of the other, a quantity just capable of neutralising it. This is obviously not in any sense analogous to the Conservation of Matter of which we have just spoken. As an illustration take a loaded cannon. Before firing, neither cannon nor ball had momentum. After firing, the ball has a certain momentum, the cannon (in virtue of its recoil) an _equal_ and opposite momentum. If we could exactly reverse the motions of the cannon and ball just as they separate, the impact between them would just reduce each to rest, and no momentum would be left. Considered separately after the discharge, each has momentum, but _in the complete system_ of cannon and ball there is no momentum—there being equal quantities of positive and negative, in the same line. In fact momentum cannot be produced or destroyed _in any system as a whole_. This is the Conservation referred to. It is as if a man always when he received a sum of money fell to the same amount in debt—the state of his affairs, as shown by his books, would of course not be altered.