I must not, however, leave the subject of gravitation, without telling you something about its laws and regularity; and first, as regards its power with respect to the distance that bodies are apart. If I take one of these balls and place it within an inch of the other, they attract each other with a certain power. If I hold it at a greater distance off, they attract with less power; and if I hold it at a greater distance still, their attraction is still less. Now this fact is of the greatest consequence; for, knowing this law, philosophers have discovered most wonderful things. You know that there is a planet, Uranus, revolving round the sun with us, but eighteen hundred millions of miles off; and because there is another planet as far off as three thousand millions of miles, this law of attraction, or gravitation, still holds good--and philosophers actually discovered this latter planet, Neptune, by reason of the effects of its attraction at this overwhelming distance. Now I want you clearly to understand what this law is. They say (and they are right) that two bodies attract each other _inversely as the square of the distance_--a sad jumble of words until you understand them; but I think we shall soon comprehend what this law is, and what is the meaning of the “inverse square of the distance.” [Illustration: Fig. 11.] I have here (fig. 11) a lamp A, shining most intensely upon this disc, B, C, D; and this light acts as a sun by which I can get a shadow from this little screen, B F (merely a square piece of card), which, as you know, when I place it close to the large screen, just shadows as much of it as is exactly equal to its own size. But now let me take this card E, which is equal to the other one in size, and place it midway between the lamp and the screen: now look at the size of the shadow B D--it is four times the original size. Here, then, comes the “inverse square of the distance.” This distance, A E, is _one_, and that distance, A B, is _two_; but that size E being _one_, this size B D of shadow is _four_ instead of _two_, which is the _square_ of the distance; and, if I put the screen at one-third of the distance from the lamp, the shadow on the large screen would be _nine_ times the size. Again, if I hold this screen _here_, at B F, a certain amount of light falls on it; and if I hold it nearer the lamp at E, _more_ light shines upon it. And you see at once how much--exactly the quantity which I have shut off from the part of this screen, B D, now in shadow; moreover, you see that if I put a single screen here, at G, by the side of the shadow, it can only receive _one-fourth_ of the proportion of light which is obstructed. That, then, is what is meant by the _inverse_ of the square of the distance. This screen E is the brightest, because it is the nearest; and there is the whole secret of this curious expression, _inversely as the square of the distance_. Now, if you cannot perfectly recollect this when you go