(61.) From the preceding details, it appears that _motion_ is not adequately estimated by _speed_ or _velocity_. For example, a certain mass A, moving at a determinate rate, has a certain quantity of motion. If another equal mass B be added to A, and a similar velocity be given to it, as much more motion will evidently be called into existence. In other words, the _two_ equal masses A and B united have _twice_ as much motion as the single mass A had when moving alone, and with the same speed. The same reasoning will show that _three_ equal masses will with the same speed have _three times_ the motion of any one of them. In general, therefore, the velocity being the same, the quantity of motion will always be increased or diminished in the same proportion as the mass moved is increased or diminished. (62.) On the other hand, the quantity of motion does not depend on the mass _only_, but also on the speed. If a certain determinate mass move with a certain determinate speed, another equal mass which moves with twice the speed, that is, which moves over twice the space in the same time, will have twice the quantity of motion. In this manner, the mass being the same, the quantity of motion will increase or diminish in the same proportion as the velocity. (63.) The true estimate, then, of the quantity of motion is found by multiplying together the numbers which express the mass and the velocity. Thus, in the example which has been last given of the impact of masses, the quantities of motion before and after impact appear to be as follow: Before Impact. | After Impact. | Mass of A 8 | Mass of A 8 Velocity of A 17 | Common velocity 14 -----------------+ -------------- Quantity of } 8 × 17[1] or 136 | Quantity of } 8 × 14 or 112 motion of A } | motion of A } -----------------+ -------------- Mass of B 6 | Mass of B 6 Velocity of B 10 | Common velocity 14 -----------------+ -------------- Quantity of } 6 × 10 or 60 | Quantity of } 6 × 14 = 84 motion of B } | motion of B } -----------------+ -------------- * The sign × placed between two numbers meant that they are to be multiplied together. By this calculation it appears that in the impact A has lost a quantity of motion expressed by 24, and that B has received exactly that amount. The effect, therefore, of the impact is a _transfer_ of motion from A to B; but no new motion is produced in the direction A C which did not exist before. This is obviously consistent with the property of inertia, and indeed an inevitable result of it. These results may be generalised and more clearly and concisely expressed by the aid of the symbols of arithmetic.