It is obvious, therefore, from the preceding examples, that it is not impossible to construct a weighing apparatus with ordinary and very inexpensive objects. We can, in the same way, show that it is possible to perform instructive experiments with no appliances at all, or, at any rate, with common things, such as everyone has at hand. The lamented Balard, whose loss science has had recently to deplore, excelled in chemical experiments without a laboratory; fragments of broken glass or earthenware were used by him for improvising retorts, bottles and vases for forming precipitates, and carrying on many important operations.
Scheele also operated in like manner; he knew how to make great discoveries with the humblest appliances and most slender resources. One cannot too earnestly endeavour to imitate such leaders, both in teaching others and instructing oneself.
The laws relating to the weight of bodies, the centre of gravity, and stable or unstable equilibrium, may be easily taught and demonstrated by means of a number of very familiar objects. By putting into the hands of a child a box of soldiers cut in elder-wood, the end of each fixed into half a bullet, we provide him with the means of making some easy experiments on the centre of gravity. According to some authorities on equilibrium, it is not impossible, with a little patience and delicacy of manipulation, to keep an egg balanced on one of its ends. This experiment should be performed on a perfectly horizontal surface, a marble chimney-piece, for example. If one can succeed in keeping the egg up, it is, according to the most elementary principles of physics, because the vertical line of the centre of gravity passes through the point of contact between the end of the egg and the surface on which it rests.
Fig. 21.—Experiment on “centre of gravity.”
Fig. 21 reproduces a curious experiment in equilibrium, which is performed with great facility. Two forks are stuck into a cork, and the cork is placed on the brim of the neck of a bottle. The forks and the cork form a whole, of which the centre of gravity is fixed over the point of support. We can bend the bottle, empty it even, if it contains fluid, without the little construction over its mouth being in the least disturbed from its balance. The vertical line of the centre of gravity passes through the point of support, and the forks oscillate with the cork, which serves as their support, thus forming a movable structure, but much more stable than one is inclined to suppose. This curious experiment is often performed by conjurors, who inform their audience, that they will undertake to empty the bottle without disturbing the cork. If a woodcock has been served for dinner, or any other bird with a long beak, take off the head at the extreme end of the neck; then split a cork so that you can insert into it the neck of the bird, which must be tightly clipped to keep it in place; two forks are then fixed into the cork, exactly as in the preceding example, and into the bottom of the cork a pin is inserted. This little contrivance is next placed on a piece of money, which has been put on the opening of the neck of the bottle, and when it is fairly balanced, we give it a rotatory movement, by pushing one of the forks as rapidly as we please, but as much as possible without any jerk (fig. 22). We then see the two forks, and the cork surmounted by the woodcock’s head, turning on the slender pivot of a pin. Nothing can be more comical than to witness the long beak of the bird turning round and round, successively facing all the company assembled round the table, sometimes with a little oscillation, which gives it an almost lifelike appearance. This rotatory movement will last some time, and wagers are often laid as to which of the company the beak will point at when it stops. In laboratories, wooden cylinders are often to be seen which will ascend an inclined plane without any impulsion. This appears very surprising at first, but astonishment ceases when we perceive that the centre of gravity is close to the end of the cylinder, because of a piece of lead, which has been fixed in it.
Fig. 22.—Another experiment on the same subject.
Fig. 23.—Automatic puppets.
Fig. 23 gives a very exact representation of a plaything which was sold extensively on the Boulevards at Paris at the beginning of the New Year. This little contrivance, which has been known for some time, is one of the most charming applications of the principles relating to the centre of gravity. With a little skill, any one may construct it for himself. It consists of two little puppets, which turn round axles adapted to two parallel tubes containing mercury. When we place the little contrivance in the position of fig. 24, the mercury being at a, the two dolls remain motionless, but if we lower the doll S, so that it stands on the second step (No. 2) of the flight, as indicated in fig. 25, the mercury descends to b at the other end of the tube; the centre of gravity is suddenly displaced; the doll R then accomplishes a rotatory movement, as shown by the arrow in fig. 25, and finally alights on step No. 3. The same movement is also effected by the doll S, and so on, as many times as there are steps. The dolls may be replaced by a hollow cylinder of cartridge paper closed at both ends, and containing a marble; the cylinder, when placed vertically on an inclined plane, descends in the same way as the puppets. The laws of equilibrium and displacement of the centre of gravity, are rigorously observed by jugglers, who achieve many wonderful feats, generally facilitated by the rotatory motion given to the bodies on which they operate, which brings into play the centrifugal force. The juggler who balances on his forehead a slender rod, on the end of which a plate turns round, would never succeed in the experiment if the plate did not turn on its axis with great rapidity. But by quick rotation the centre of gravity is kept near the point of support. We need hardly remark, too, that it is the motion of a top that tends to keep it in a vertical position.
Fig. 24.—First position of the puppets.
Fig. 25.—Second position of the puppets.
Many experiments in mechanical physics may occur to one’s mind. To conclude the enumeration of those we have collected on the subject, I will describe the method of lifting a glass bottle full of water by means of a simple wisp of straw. The straw is bent before being passed into the bottle of water, so that, when it is lifted, the centre of gravity is displaced, and brought directly under the point of suspension. Fig. 26 shows the method of operation very plainly. It is well to have at hand several pieces of straw perfectly intact, and free from cracks, in case the experiment does not succeed with the first attempt.
Having now seen how this point we call the centre of gravity acts, we may briefly explain it.
Fig. 26.—Lifting a bottle with a single straw.
The centre of gravity of a body is that point in which the sum of the forces of gravity, acting upon all the particles, may be said to be united. We know the attraction of the earth causes bodies to have a property we call Weight. This property of weight presses upon every particle of the body, and acts upon them as parallel forces. For if a stone be broken all the portions will equal the weight of the stone; and if some of them be suspended, it will be seen that they hang parallel to each other, so we may call these weights parallel forces united in the whole stone, and equal to a single resultant. Now, to find the centre of gravity, we must suspend the body, and it will hang in a certain direction. Draw a line from the point of suspension, and suspend the body again: a line drawn from that point of suspension will pass through the same place as the former line did, and so on. That point is the centre of gravity of that suspended body. If the form of it be regular, like a ball or cylinder, the centre of gravity is the same as the mathematically central point. In such forms as pyramids it will be found near the largest mass; viz., at the bases, about one-fourth of the distance between the apex and the centre of gravity of the base.
When the centre of gravity of any body is supported, that body cannot fall. So the well-known leaning towers are perfectly safe, because their lines of direction