Suppose two balls of equal magnitude, A and B (fig. 14). These being of equal magnitude, attract each other with equal force, and will meet, if not opposed, at a point (M) half-way between the two. But they do not meet, because the attraction of the earth is greater than the attraction they relatively and collectively exercise towards each other. But if the size of the balls be different, the attraction of the greater will be more evident, as shown below, where the points of meeting are indicated respectively (figs. 15 and 16). These experiments will illustrate the phenomena of _falling bodies_. Gravity is the cause of this, because every object on the surface of the earth is very much smaller than the earth itself, and therefore all bodies _fall_ towards the centre of the earth. A certain time is thus occupied, and we can find the _velocity_ or rapidity of a falling body very easily. On the earth a body, if let fall, will pass through a space sixteen feet in the first second; and as the attraction of the earth still continues and is exercised upon a body already in rapid motion, this rate of progress must be proportionately increased. Just as when steam is kept up in an engine running down hill, the velocity of the train will rapidly increase as it descends the gradient. [Illustration: Figs. 15 and 16.] A body falling, then, descends sixteen feet in the first second, and for every succeeding second it assumes a greater velocity. The distance the body travels has been calculated, and the space it passes through has been found to _increase in proportion to the square of the time it takes to fall_. For instance, suppose you drop a stone from the top of a cliff to the beach, and it occupies two seconds in falling, if you multiply 2 × 2, and the result by sixteen, you will find how high the cliff is: in this (supposed) case it is (omitting decimals) sixty-four feet high. The depth of a well can also be ascertained in the same way, leaving out the effect of air resistance. But if we go up into the air, the force of gravity will be diminished. The attraction will be less, because we are more distant from the centre of the earth. This decrease is scarcely, if at all, perceptible, even on very high mountains, because their size is not great in comparison with the mass of the earth’s surface. The rule for this is _that gravity decreases in proportion to the square of the distance_. So that if at a certain distance from the earth’s surface the force of attraction be 1, if the distance be _doubled_ the attraction will be only _one quarter_ as much as before—not one-half.