I will illustrate this in another way. Let _a_ and _b_, Fig. 133, be two balls of clay of equal size hanging over a graduated arc. Now if _b_ be let fall from the top of the arc, 6, on striking against _a_ it gives half of its motion to _a_, and they both move on together. But how far will they go? To 3, on the other side of the arc. Why? Let the quantity of matter in each ball be called 1, and the motion of _b_ 6. The momentum will therefore be 6. Now the momentum of the two together will be the same after the blow as that of _b_ was before it. But the quantity of matter is twice as great, and must be called 2. Therefore the motion must be represented as 3, to make the momentum 6 (2×3). But suppose that _b_ is twice as large as _a_. Falling from 6, its momentum would be represented by 12 (2×6). After it has struck _a_, the momentum of the two together would be the same as that of _b_ before the stroke; but the quantity being 3, the motion would be represented by 4. They would therefore move to 4 on the arc. 202. =Examples.=--A few examples illustrating momentum as being compounded of quantity of matter and velocity will suffice. If a musket-ball of an ounce weight were so much spent as to move with only a velocity of a foot in a second, its force would be so small that if it hit any one it would do no harm. But a cannon-ball weighing a thousand ounces moving at this slow rate would have a very great force--equal, in fact, to the momentum of an ounce ball moving 1000 feet in a second.--If a plank push a man's foot against a wharf he will scarcely feel it; but if the plank, instead of being alone, is one of a thousand planks fastened together in a raft, and the whole move with the same velocity, the force will be increased a thousand-fold, and the plank will crush the foot. So, also, if the one plank when alone should move a thousand times as fast as the whole raft, the same result would follow.--So soft a substance as a candle can be fired through a board from the momentum given to it by an immense velocity.--Perhaps there is no better example of the great force given to a substance by an enormous velocity than we have in the wind. So light a thing is air that people think of it as almost nothing. But let it be set in rapid motion, and the velocity gives to it a force, a momentum, which will drive ships upon the shore, throw over buildings, and tear up trees by the roots. In this last example we see beautifully illustrated the meaning of the expression quantity of motion. In the moving air each particle does its share of the work in the destructive effects mentioned. Each particle, therefore, may be considered as a _reservoir_ of motion, and the quantity of motion in any case depends upon the quantity which each particle has and the number of the particles.