Fig. 5. and Fig. 6.
Here is a toy I happened to see the other day, which will, I think, serve to illustrate our subject very well. That toy ought to lie something in this manner (fig. 5); and would do so if it were uniform in substance. But you see it does not; it will get up again. And now philosophy comes to our aid; and I am perfectly sure, without looking inside the figure, that there is some arrangement by which the centre of gravity is at the lowest point when the image is standing upright; and we may be certain, when I am tilting it over (see fig. 6), that I am lifting up the centre of gravity (a), and raising it from the earth. All this is effected by putting a piece of lead inside the lower part of the image, and making the base of large curvature; and there you have the whole secret. But what will happen if I try to make the figure stand upon a sharp point? You observe, I must get that point exactly under the centre of gravity, or it will fall over thus [endeavouring unsuccessfully to balance it]; and this you see is a difficult matter—I cannot make it stand steadily. But if I embarrass this poor old lady with a world of trouble, and hang this wire with bullets at each end about her neck, it is very evident that, owing to there being those balls of lead hanging down on either side, in addition to the lead inside, I have lowered the centre of gravity, and now she will stand upon this point (fig. 7); and what is more, she proves the truth of our philosophy by standing sideways.
Fig. 7.
Fig. 8.
I remember an experiment which puzzled me very much when a boy. I read it in a conjuring book, and this was how the problem was put to us: “How,” as the book said, “how to hang a pail of water, by means of a stick, upon the side of a table” (fig. 8). Now, I have here a table, a piece of stick, and a pail, and the proposition is, how can that pail be hung to the edge of this table? It is to be done; and can you at all anticipate what arrangement I shall make to enable me to succeed? Why, this. I take a stick, and put it in the pail between the bottom and the horizontal piece of wood, and thus give it a stiff handle—and there it is; and what is more, the more water I put into the pail the better it will hang. It is very true that before I quite succeeded I had the misfortune to push the bottoms of several pails out; but here it is hanging firmly (fig. 9), and you now see how you can hang up the pail in the way which the conjuring books require.
Fig. 9.
Again, if you are really so inclined (and I do hope all of you are), you will find a great deal of philosophy in this [holding up a cork and a pointed thin stick about a foot long]. Do not refer to your toy-books, and say you have seen that before. Answer me rather, if I ask you have you understood it before? It is an experiment which appeared very wonderful to me when I was a boy; I used to take a piece of cork (and I remember, I thought at first that it was very important that it should be cut out in the shape of a man; but by degrees I got rid of that idea), and the problem was to balance it on the point of a stick. Now, you will see I have only to place two sharp-pointed sticks one on each side, and give it wings, thus, and you will find this beautiful condition fulfilled.
Fig. 10.
We come now to another point:—All bodies, whether heavy or light, fall to the earth by this force which we call gravity. By observation, moreover, we see that bodies do not occupy the same time in falling. I think you will be able to see that this piece of paper and that ivory ball fall with different velocities to the table [dropping them]; and if, again, I take a feather and an ivory ball, and let them fall, you see they reach the table or earth at different times—that is to say, the ball falls faster than the feather. Now, that should not be so, for all bodies do fall equally fast to the earth. There are one or two beautiful points included in that statement. First of all, it is manifest that an ounce, or a pound, or a ton, or a thousand tons, all fall equally fast, no one faster than another: here are two balls of lead, a very light one and a very heavy one, and you perceive they both fall to the earth in the same time. Now, if I were to put into a little bag a number of these balls sufficient to make up a bulk equal to the large one, they would also fall in the same time; for if an avalanche fall from the mountains, the rocks, snow and ice, together falling towards the earth, fall with the same velocity, whatever be their size.
I cannot take a better illustration of this than that of gold leaf, because it brings before us the reason of this apparent difference in the time of the fall. Here is a piece of gold-leaf. Now, if I take a lump of gold and this gold-leaf, and let them fall through the air together, you see that the lump of gold—the sovereign, or coin—will fall much faster than the gold leaf. But why? They are both gold, whether sovereign or gold-leaf. Why should they not fall to the earth with the same quickness? They would do so, but that the air around our globe interferes very much where we have the piece of gold so extended and enlarged as to offer much obstruction on falling through it. I will, however, shew you that gold-leaf does fall as fast when the resistance of the air is excluded—for if I take a piece of gold-leaf and hang it in the centre of a bottle, so that the gold, and the bottle, and the air within shall all have an equal chance of falling, then the gold-leaf will fall as fast as anything else. And if I suspend the bottle containing the gold-leaf to a string, and set it oscillating like a pendulum, I may make it vibrate as hard as I please, and the gold-leaf will not be disturbed, but will swing as steadily as a piece of iron would do; and I might even swing it round my head with any degree of force, and it would remain undisturbed. Or I can try another kind of experiment:—if I raise the gold-leaf in this way [pulling the bottle up to the ceiling of the theatre by means of a cord and pulley, and then suddenly letting it fall to within a few inches of the lecture-table], and allow it then to fall from the ceiling downwards (I will put something beneath to catch it, supposing I should be maladroit), you will perceive that the gold-leaf is not in the least disturbed. The resistance of the air having been avoided, the glass bottle and gold-leaf all fall exactly in the same time.
Here is another illustration—I have hung a piece of gold-leaf in the upper part of this long glass vessel, and I have the means, by a little arrangement at the top, of letting the gold-leaf loose. Before we let it loose we will remove the air by means of an air pump, and while that is being done, let me shew you another experiment of the same kind. Take a penny-piece, or a half-crown, and a round piece of paper a trifle smaller in diameter than the coin, and try them, side by side, to see whether they fall at the same time [dropping them]. You see they do not—the penny-piece goes down first. But, now place this paper flat on the top of the coin, so that it shall not meet with any resistance from the air, and upon then dropping them you see they do both fall in the same time [exhibiting the effect]. I dare say, if I were to put this piece of gold-leaf, instead of the paper, on the coin, it would do as well. It is very difficult to lay the gold-leaf so flat that the air shall not get under it and lift it up in falling, and I am rather doubtful as to the success of this, because the gold-leaf is puckery; but will risk the experiment. There they go together! [letting them fall] and you see at once that they both reach the table at the same moment.
We have now pumped the air out of the vessel, and you will perceive that the gold-leaf will fall as quickly in this vacuum as the coin does in the air. I am now going to let it loose, and you must watch to see how rapidly it falls. There! [letting the gold loose] there it is, falling as gold should fall.
I am sorry to see our time for parting is drawing so near. As we proceed, I intend to write upon the board behind me certain words, so as to recall to your minds what we have already examined—and I put the word Forces as a heading; and I will then add, beneath, the names of the special forces according