Soap-Bubbles and the Forces Which Mould Them

by C. V. Boys

Now, on returning to our soap-bubbles, you may remember that I stated that the catenoid and the plane were the only figures of revolution which had no curvature, and which therefore produced no pressure. There are plenty of other surfaces which are apparently curved in all directions and yet have no curvature, and which therefore produce no pressure; but these are not figures of revolution, that is, they cannot be obtained by simply spinning a curved line about an axis. These may be produced in any quantity by making wire frames of various shapes and dipping them in soap and water. On taking them out a wonderful variety of surfaces of no curvature will be seen. One such surface is that known as the screw-surface. To produce this it is only necessary to take a piece of wire wound a few times in an open helix (commonly called spiral), and to bend the two ends so as to meet a second wire passing down the centre. The screw-surface developed by dipping this frame in soap-water is well worth seeing (Fig. 49). It is impossible to give any idea of the perfection of the form in a figure, but fortunately this is an experiment which any one can easily perform.

Fig. 50.

Then again, if a wire frame is made in the shape of the edges of any of the regular geometrical solids, very beautiful figures will be found upon them after they have been dipped in soap-water. In the case of the triangular prism these surfaces are all flat, and at the edges where these planes meet one another there are always three meeting each other at equal angles (Fig. 50). This, owing to the fact that the frame is three-sided, is not surprising. After looking at this three-sided frame with three films meeting down the central line, you might expect that with a four-sided or square frame there would be four films meeting each other in a line down the middle. But it is a curious thing that it does not matter how irregular the frame may be, or how complicated a mass of froth may be, there can never be more than three films meeting in an edge, or more than four edges, or six films, meeting in a point. Moreover the films and edges can only meet one another at equal angles. If for a moment by any accident four films do meet in the same edge, or if the angles are not exactly equal, then the form, whatever it may be, is unstable; it cannot last, but the films slide over one another and never rest until they have settled down into a position in which the conditions of stability are fulfilled. This may be illustrated by a very simple experiment which you can easily try at home, and which you can now see projected upon the screen. There are two pieces of window-glass about half an inch apart, which form the sides of a sort of box into which some soap and water have been poured. On blowing through a pipe which is immersed in the water, a great number of bubbles are formed between the plates. If the bubbles are all large enough to reach across from one plate to the other, you will at once see that there are nowhere more than three films meeting one another, and where they meet the angles are all equal. The curvature of the bubbles makes it difficult to see at first that the angles really are all alike, but if you only look at a very short piece close to where they meet, and so avoid being bewildered by the curvature, you will see that what I have said is true. You will also see, if you are quick, that when the bubbles are blown, sometimes four for a moment do meet, but that then the films at once slide over one another and settle down into their only possible position of rest (Fig. 51).

The air inside a bubble is generally under pressure, which is produced by its elasticity and curvature. If the bubble would let the air pass through it from one side to the other of course it would soon shut up, as it did when a ring was hung upon one, and the film within the ring was broken. But there are no holes in a bubble, and so you would expect that a gas like air could not pass through to the other side. Nevertheless it is a fact that gases can slowly get through to the other side, and in the case of certain vapours the process is far more rapid than any one would think possible.

Fig. 51.

Fig. 52.

Ether produces a vapour which is very heavy, and which also burns very easily. This vapour can get to the other side of a bubble almost at once. I shall pour a little ether upon blotting-paper in this bell jar, and fill the jar with its heavy vapour. You can see that the jar is filled with something, not by looking at it, for it appears empty, but by looking at its shadow on the screen. Now I tilt it gently to one side, and you see something pouring out of it, which is the vapour of ether. It is easy to show that this is heavy; it is only necessary to drop into the jar a bubble, and so soon as the bubble meets the heavy vapour it stops falling and remains floating upon the surface as a cork does upon water (Fig. 52). Now let me test the bubble and see whether any of the vapour has passed to the inside. I pick it up out of the jar with a wire ring and carry it to a light, and at once there is a burst of flame. But this is not sufficient to show that the ether vapour has passed to the inside, because it might have condensed in sufficient quantity upon the bubble to make it inflammable. You remember that when I poured some of this vapour upon water in the first lecture, sufficient condensed to so weaken the water-skin that the frame of wire could get through to the other side. However, I can see whether this is the true explanation or not by blowing a bubble on a wide pipe, and holding it in the vapour for a moment. Now on removing it you notice that the bubble hangs like a heavy drop; it has lost the perfect roundness that it had at first, and this looks as if the vapour had found its way in, but this is made certain by bringing a light to the mouth of the tube, when the vapour, forced out by the elasticity of the bubble, catches fire and burns with a flame five or six inches long (Fig. 53). You might also have noticed that when the bubble was removed, the vapour inside it began to pass out again and fell away in a heavy stream, but this you could only see by looking at the shadow upon the screen.