The third law of motion tells us that action and reaction are equal and opposite, so that when two bodies come into collision the forces at work generate equal and opposite quantities of momentum. We shall best see the meaning of this law by a numerical example, bearing in mind that momentum means the product of mass into velocity. For instance, let us suppose that an inelastic body of mass 10 and velocity 20 strikes directly another inelastic body of mass 15 and velocity 15, the direction of both motions being the same. Now, it is well known that the united mass will, after impact, be moving with the velocity 17. What, then, has been the influence of the forces developed by collision? The body of greater velocity had before impact a momentum 10 × 20 = 200, while its momentum after impact is only 10 × 17 = 170; it has therefore suffered a loss of 30 units as regards momentum, or we may consider that a momentum of 30 units has been impressed upon it in an opposite direction to its previous motion. On the other hand, the body of smaller velocity had before impact a momentum 15 × 15 = 225, while after impact it has 15 × 17 = 255 units, so that its momentum has been increased by 30 units in its previous direction. The force of impact has therefore generated 30 units of momentum in two opposite directions, so that, taking account of direction, the momentum of the system is the same before and after impact; for before impact we had a momentum of 10 × 20 + 15 × 15 = 425, while after it we have the united mass 25 moving with the velocity 17, giving the momentum 425 as before. 125. But while the momentum is the same before and after impact, the visible energy of the moving mass is undoubtedly less after impact than before it. To see this we have only to turn to the expression of Art. 28, from which we find that the energy before impact was as follows:--Energy in kilogrammetres = (_m v_²)/(19 · 6) = (10 × 20² + 15 × 15²)/19·6 = 376 nearly; while that after impact = (25 × 17²)/19·6 = 368 nearly. 126. The loss of energy will be still more manifest if we suppose an inelastic body in motion to strike against a similar body at rest. Thus if we have a body of mass 20 and velocity 20 striking against one of equal mass, but at rest, the velocity of the double mass after impact will obviously be only 10; but, as regards energy, that before impact will be (20 × 20²)/19·6 = ⁸⁰⁰⁰⁄₁₉·6 while that after impact will be (40 × 10²)/19·6 = ⁴⁰⁰⁰⁄₁₉·6 or only half the former.