most convincing proof that the surface-viscosity of this solution is very much greater than the viscosity of the interior of liquid; and that the resistance offered to motion by the surface is many times larger than that experienced by moving bodies in the interior.
Another experiment will illustrate this enormous surface-viscosity of the mixture of saponine and water in a still more striking way. I have already explained to you that it we blow a bubble at the end of an open tube, the bubble will gradually contract until all the air is expelled. What, however, will occur if, instead of simply allowing the bubble to drive the air out, I suck the end of the tube and draw it out more quickly? I will first perform the experiment on some of the soap and water I have used before, and you will see that, although the bubble will contract more rapidly than before, it will retain throughout the whole of the experiment its spherical form. I will now repeat the same experiment with saponine and water. In this case, on account of the great viscosity of this thin film it will be unable to follow the retreating air as quickly as it must do to retain its spherical form; the consequence is, it will be unable to retain that form, and it will therefore collapse and wrinkle up into a purse-shaped bag.
I hope I have succeeded in proving to you that these three properties of liquid surfaces exist. I must now go on to explain how they can be applied to the theory of soap-bubbles. Let us suppose, in the first place, that a bubble is rising in a vessel of water. It will tend to assume a spherical form; but as it rises to the surface it will be flattened in the direction in which it is moving, and, instead of being a perfect sphere, it will be longer in one direction than the other. Evidently, as it moves, it has to displace the water in front of it, which flows away to the right and left out of the way of the bubble. But, as I have explained, all liquids offer a certain amount of resistance to the motion of one part upon another; and, although the resistance offered by water is extremely small, it must be taken into consideration. The liquid, therefore, has to flow out of the way of the advancing bubble, and to overcome the resistance offered to its motion; but as the bubble rises nearer to the surface it moves faster and faster, and therefore the water must be removed from its path more and more quickly. But the resistance offered to its motion becomes greater the faster it moves; hence you have the bubble rising more quickly, the water being obliged to get more quickly out of the way, and finding more and more difficulty in doing so, and having, when the bubble gets very near the surface, less space between the bubble and the surface to flow away in. The result is, that the water cannot get out of the way, and therefore the bubble carries it up with it and forms a thin liquid film, which we see as foam upon the surface, through which the bubbles of air are rising. Supposing the bubble thus formed were placed upon a solid plate, it would have the form of half a sphere; and, as the bubble compresses the air in it, the air
