1876 RÜCKER on Bubbles
To give some perspective:
Plateau published his Statics of Liquids in 1873. (Rucker's comments about the work of M. Plateau at the end of this lecture are insightful & heartwarming. Please read them.)
C. V. Boys did not perform his Christmas Lectures or publish his Soap-Bubbles until 1889/90. Boys would almost certainly have seen this lecture by Rucker on bubbles at some point. Boy's lecture clearly was influenced by it.
Popular Science Monthly | Volume 9 | September 1876
BY PROF. RÜCKER.
IN the museum of the Louvre, in Paris, there is a vase which has by some strange chance been handed down to us through the long ages which have proved fatal to many others far more worthy of preservation than itself. It was manufactured in Italy—before the foundation of the city of Rome—by the ancient Etruscans, and it is decorated—and this is the reason I bring it to your notice this evening —with a design representing a group of children blowing bubbles. This ancient relic of those early days incontestably proves to us that the art of performing that beautiful experiment, if not with soap and water, at least with some one of the comparatively few liquids with which it can be satisfactorily undertaken, has been known at least for twenty-five hundred years. [Note from KMJ-after a lot of research I believe the Etruscan Vase - an often repeated story after Rucker's address - does not and never did exist. Others, including scientists and researchers, have looked for evidence and have not found it either. If you can prove otherwise, please let me know.] But, though generation after generation the children amused themselves with it, century after century passed away, leaving unanswered, and in all probability unthought of, the numerous questions which it cannot fail to suggest to us. Why is it so easy to blow bubbles with some liquids, and so hard to form them with others? Why does a bubble when blown at the end of an open tube gradually contract and disappear? Why, when it bursts, does it not still remain a liquid film, but is shattered to an almost imperceptible dust?
These and a hundred others remained unanswered, and, as I have said, perhaps un-put, until after the genius of Newton had attacked the far more difficult problem of the colors which bubbles display. To night, however, I hope to be able to give you the answers to some of these so long-delayed inquiries, as it is now perhaps two hundred years since men of science began to turn their attention to the phenomena of liquid bubbles, and of those properties of liquids on which they depend, and their efforts have been rewarded with no small measure of success, although it is certainly only within the time of many of us here that they have been able to give anything like a complete explanation of them all. In order, however, that we may understand how best to study the laws and constitution of a soap-bubble, it is necessary that we should in the first place clearly comprehend what it really is. We all know how soap-bubbles are ordinarily formed. A common tobacco- pipe is dipped into a mixture of soap and water, and when it is withdrawn a thin liquid film stretches across the mouth, which we can blow out into a bubble, and then shake off and detach from the tube. I will now perform the experiment of blowing a bubble before you; only, instead of employing a tobacco-pipe, I will use this glass funnel, and for the common soap and water I will substitute a mixture of Castile soap, water, and glycerine. [A large bubble was speedily blown, and it showed the usual beautiful colors. This and the succeeding experiments were dexterously and successfully performed, and were much applauded].
You now see how, by using a proper liquid, and by taking proper precautions, we are able to obtain bubbles of enormous size. But I wish you for a moment to confine your attention to the bubble, not in its full-blown beauty, as you saw it just now, but rather in that stage in which it was merely a thin film covering the mouth of the funnel. Now, this film was originally the topmost layer of that portion of the liquid inclosed by the funnel, which as I withdrew it skimmed off a thin slice from the surface—a slice so thin that had I allowed it to drain for a while its thickness would not have exceeded four millionths of an inch. But, although the total quantity of liquid contained in it was so small, the surface of the film was no less than twice the area of the orifice of this large funnel. Hence, both from the method of formation of the film and from its constitution when formed, it is evident that, if, in any respects, the surface of a liquid differs from the internal mass, if there are laws which govern and forces which are at play on the surface, the effects of which we do not recognize elsewhere, these peculiar properties must be to us of primary importance, if we would understand the theory and constitution of a soap bubble. The course which I shall adopt this evening is, in the first place, to study the laws and forces which are in operation on the surface of a liquid, and after that I shall try to show you how they may be used to explain the phenomena which we observe in the short but brilliant life of a bubble.
I have upon the wall a diagram on which three of the principal properties of the surface of a liquid are enunciated. That to which I wish first to draw your attention is that the surface of a liquid is in a state of tension. It is necessary that before we go any further you should have a clear comprehension of the meaning of this word "tension." I have here a piece of India-rubber, and if I stretch it with my hands I throw the whole of it into a state of tension. The peculiarity of this state is that, if I were to divide the India-rubber into two portions with a sharp knife, the parts, no matter where the incision was made, would instantly fly in opposite directions, and each would become shorter. But what each of those parts would then actually do— that is, contract or become shorter—each is now tending to do; but, since it could only become shorter by elongating the other part, and as that is pulling in an opposite direction with equal force, the two forces neutralize one another, and the whole remains in a state of rest, and also in a state of tension. If, then, we generalize from this particular instance, we may define a state of tension as follows: that a body is said to be in a state of tension when each of any two parts into which it may be divided tends to contract and to expand the other. You observe, then, that the tendency of one part to extend the other is the criterion of a state of tension; and I will now show you a couple of experiments which will, I think, enable me to prove that it exists in the surface of a liquid.
I have here a small iron ring, and stretched loosely across it, from side to side, there is a piece of cotton. I clip it into a vessel containing some of the soap-mixture I used just now, and it comes out with a film adhering to it precisely in the same way as the funnel did. I now show you upon the screen the image of the ring, with the thread stretching across it, and resting upon the thin liquid film. If what I have just been saying be true—if each portion of the film be in a state of tension— then each of the parts into which the thread divides it is tending to contract and to expand the other. Thus, the thread is acted upon by two forces: the portion of the film to the right is tending to pull it to the right, and the portion on the left is tending to pull it to the left; but, inasmuch as these two tendencies are equal and opposite, the effect upon the thread is as if they did not exist; that is to say, it will remain at rest in any position on the film. I will now move the thread about on the film with a wire, showing that it will remain wherever I place it. I distort it and put it in any position I like. Let us, however, consider what will happen if I break the film upon one side of the thread, and leave it uninjured upon the other. The surface-tension, destroyed upon one side, will remain in action in the unruptured film, and therefore we should expect the thread to be pulled toward the uninjured side. We can easily put the matter to the test of experiment. I break one side by touching it with a hot wire, and what we foresaw occurs, the thread is instantly pulled toward the side which the wire did not tear. This experiment proves that the surface of a liquid is in a state of tension. I have, however, another experiment to show you upon the same point, which will add to our knowledge upon the subject, for it will not only show that the tension exists on the surface, but that in different liquids it exists in different degrees of intensity. You now see upon the screen the image of a few drops of colored water, which are placed upon a glass plate. I dip a glass rod into some pure water, and touch the colored film with the drop which adheres to the end. As you see, nothing very particular happens. There is only a slight diminution of the blueness in the centre, owing to the fact that the colored water has been mixed with the pure water. Now, I will dip the rod into alcohol, and you will see a different result. As soon as I touch the blue water with the alcohol a motion occurs, and it moves rapidly away from the point at which the contact took place. Now, let us consider shortly what the explanation of this phenomenon is. The surface of the water and the surface of the alcohol are alike in a state of tension; but the tension of the surface of the water is greater than that at the surface of the alcohol. At the moment I put the drop of alcohol upon the water we had a small drop of alcohol surrounded by a large quantity of water, and between the two there was a line of demarkation, which we may, for simplicity's sake, liken to the thread you saw just now. When I destroyed the force of the tension in the first experiment on the one side, the force which remained on the other side pulled the thread toward it. In this case the force was acting on both sides; but the force at the surface of the water pulling away from the centre of the alcohol- drop was greater than the force at the surface of the alcohol-drop pulling toward its centre. The consequence was, that we obtained a motion in the direction in which the greater force was acting—that is, in the direction in which the water was pulling away from the centre; and this continued the water and alcohol moving farther and farther away, until the two became entirely mixed together. An experiment similar to this may be performed after dinner in the evening: When we pour some wine into a glass we generally in doing so wet the sides, and the result is, a thin film of liquid adheres to them above that portion of the glass which is filled with wine. This film soon contracts into drops, and each of these drops consists, as all wine does, of a mixture of water, alcohol, and certain other substances, the presence of which we may for the moment neglect. Alcohol, as you know, is an extremely volatile fluid, which evaporates very rapidly, and therefore above the surface of the liquid there is a small atmosphere of alcohol formed by evaporation from the wine. This evaporation goes on in the drops as well as in the main body of the wine, but more rapidly at the upper surface of a drop than at the lower; the reason being that the lower part is more completely immersed in the little cloud of alcohol which hangs over the wine itself. A drop is thus formed composed in the upper part of water, with comparatively little alcohol, and in the lower part of water with a larger proportion of alcohol. The experiment I have just shown proves that the tension in the upper part must be greater than that in the more alcoholic or lower portion of the drop. Hence you may often see drops of wine actually running up the side of a glass, in obedience to a force exerted in an upward direction, by the greater surface-tension of the portion containing the larger percentage of water. A very important deduction may be made from the fact that the surface of a liquid is in a state of tension. You saw in the first experiment that, as soon as the film on the one side of the thread was broken, that on the other side contracted very rapidly, and took up a form with as small a surface as was possible under the circumstances. If we were to generalize from this particular instance, we should be led to the conclusion that, because the surface of a liquid is in a state of tension, and thus each part of it is tending to contract, therefore it will always assume a shape which will have the smallest possible surface. I will now show an experiment to illustrate this fact. I have here a tube formed of four plane pieces of glass, through which I shall be able to send light, and so show you the image of its contents on the screen. It forms, in fact, a little box of glass, the ends of which are open, one of them being considerably narrower than the other. I now put the larger end of this tube into a mixture of soap and water, and I withdraw it with a film adhering to it. This film has a tendency to assume that shape which has the smallest possible surface; and evidently, by moving up the tube toward the narrow end, its surface can be made smaller than it is at present. You now see on the screen an image of the tube. I move it for a moment in order to form the film. You now see the image of the film, and I think you will observe that it is slowly moving up the tube, and therefore that its surface is becoming smaller and smaller. The experiment might be prolonged until the film burst; but, at all events, you have there sufficient proof that it moves into a position in which its surface is diminished. And, further, inasmuch as the image of the tube is turned upside down on the screen, what appeared, to you to be a motion from above to below was, in fact, a motion from below to above; the film was in reality moving upward, although to you it appeared to be moving down. It was really raising its own weight instead of being pulled down by it. We have thus now established this quality of liquids, namely, that their surfaces tend to become as small as possible, and we may extend the law to another and very interesting case.
Let me suppose for a moment that I take a mass of clay: it is evident that I could mould it into an infinite number of different forms; each of these forms might have precisely the same volume, might occupy exactly the same space, but they might all have very different surfaces. For instance, if I took a rolling-pin and rolled the clay out into a thin disk, and then compressed it into a round ball, it is evident that, although the volume might be precisely the same in the two cases, the area of the surface would be much greater in the disk than in the ball. Now, in the experiment I showed you last, the film moved up the tube, because it had a tendency to diminish its surface as far as possible; but, if I had continued the experiment longer—if I had allowed the film to move up to the narrowest part of the tube, it would, even then, only in part have satisfied this tendency, and not have done so completely—it would have attained the smallest surface possible under the circumstances, though not the smallest possible surface. The reason why it would not have done so is this: that forces were acting upon it other than that which tended to make it contract, for it was also affected by the force of adhesion to the sides of the glass tube; and, as a matter of fact, liquids are ordinarily subjected to the action of no less than three distinct sets of forces. The first of these is the attractive influence of the earth, or the weight of the liquid; the second is the adhesion of the liquid to the sides of any solid vessel in which it may be contained; and the third class comprises those forces which are at play in the liquid itself. It is evident, then, that the form which a liquid takes will not be due to any one of these, but to all three. The form which it would assume if left to the action of its molecular forces will be modified in the first place by its weight, and in the next by the adhesion to the sides of the solid vessel. Hence the question arises, if we take a liquid free from both these disturbing forces—free from the attractive influence of the earth, or practically so, and free also from the force of adhesion to the side of the solid vessel—which of all the possible shapes into which I might mould my mass of clay would the liquid assume so as to have the smallest possible surface? This question we are able to answer very easily by means of experiment, and the method by which we do so depends upon the application of an extremely simple principle. When we place a stone in a mass of water we have, in order to immerse it entirely, to push aside, to remove to the right and left, a certain quantity of water, the volume of which is precisely equal to the volume of the stone; and the stone sinks to the bottom, because its own weight is greater than the weight of the water which it has so displaced. A piece of cork, on the other hand, would rise to the surface, because its weight is less than the weight of the water equal in volume to itself. If we could obtain a body the weight of which was precisely the same as the weight of the water it displaced, it would have no tendency to sink or swim, but would remain at rest in any part of the water into which we might choose to place it. Hence this body would be practically free from the attractive influence of the earth, and we should have succeeded in neutralizing the force of gravity, since a body having no tendency to rise or fall might be considered as removed to such a distance from the earth as to have no weight. Of course, this conclusion is independent of the fact whether the body introduced into the water is a liquid or a solid, and we may substitute for the water any other liquid; but, if we employ two liquids, they must satisfy the following conditions: In the first place, they must not mix together, as wine and water do, but must remain separate, like water and oil. In the second place, the weight of any volume of one must be exactly equal to that of the same volume of the other; and, in the third place, the two liquids must have, when in contact. no chemical effect upon each other. Could two such liquids be found, a small quantity of the one introduced into a mass of the second would be a state eminently favorable for determining the shape which it would assume under the influence of its surface-tension alone. It would, as I have pointed out, be free from the attraction of the earth, and it would also be free from the force of adhesion to the sides of a solid vessel. It would, however, be extremely difficult to find two liquids which would satisfy these conditions; but, although we cannot find them to our hand, we are able to manufacture them. Water is a liquid which is heavier than oil, and alcohol is on the other hand lighter than oil; and, if we mingle water and alcohol, we may make a mixture, the weight of any given volume of which is precisely equal to that of the same volume of oil, and by introducing a few drops of oil into the mass of alcohol and water of the right density we ought to succeed in observing the form which a liquid assumes under the influence of its surface- tension alone. You now see upon the screen the image of a mass of oil in a mixture of alcohol and water of the kind I have just described; and you see that our question is at once answered—the oil assumes a spherical form. From this we learn that a liquid, if left to the action of its surface-forces alone, will become a sphere. But inasmuch as the effect of the attractive influence of the earth, or the weight of the liquid, increases with the quantity we use, while on the other hand the surface-tension, or its own moulding molecular force, remains precisely the same, we should, if we use a large quantity of liquid, expect the weight to be the particular force which determined its shape; and if we employ a small mass of liquid, then the surface-tension, growing proportionately greater, would become the more important.
Thus it follows that, although we have to use the most accurate adjustment in order to obtain a sphere of oil an inch in diameter, every rain-drop, every dew-drop, and every soap-bubble, is in itself almost a mathematically accurate sphere. It is very possible, of course, to make a liquid assume any number of other shapes you please, but I wish now to draw your attention to the fact that we are able to give it another very simple form, namely, that of a cylinder: and I will show you upon the screen the conversion of a spherical soap-bubble into a cylinder. You now see the image of a glass funnel. I take another of precisely the same dimensions, and blow upon it a small bubble, which I make adhere to the first, and then I draw it out into a very accurate cylinder. This proves that the form of a quantity of liquid may, under proper conditions, be cylindrical; but if we make the cylinder of such dimensions that the length is very considerable in proportion to the breadth, then the liquid will only retain the cylindrical form for a very short time indeed. The slightest jar or disturbance of any kind will of course make it deviate from its shape, and that deviation when once begun is continued, as it were, by the liquid of its own accord. The series of transformations through which the cylinder will go, I have represented for you in the diagram. At the top is the long cylinder, which represents the liquid in its first state. Assuming that it is slightly disturbed, you see that it swells out in some places and contracts in others; and the elevations and depressions grow greater and greater, until the mass of the liquid becomes, as in the lower figures, little more than a series of balls tied together by very fine liquid threads. The transformation does not end here; the threads are soon broken, and thus what was originally a continuous cylinder is transformed into a series of alternately large and small spheres. I shall have to make use of this particular transformation of the cylinder later in my lecture; but I wish for the moment to call attention to the fact that one very interesting instance of it is observed whenever water flows out from the bottom of a vessel through a small circular hole. In such a case the form of the column of water would be approximately that of a long cylinder. But, as I have already pointed out, this is a state of what is called unstable equilibrium—of equilibrium which may exist for an instant, but not for a longer time. Hence the above series of transformations are gone through. We have alternately contraction and elevation; these go on until at length the falling column of water is broken up into a falling column of drops.
We must now, however, pass on to another property of the surfaces of liquids, namely, that they press on the liquid, or air which they contain, in much the same way as a blown-out bladder presses on the air within it. I will show you an experiment illustrating this in the following way: If a bubble presses on the air within, then it is evident that, if we made a hole in its side, the tendency of the compressed air would be immediately to escape through the hole, and we should have a current of air flowing out of the bubble, which would thus become smaller. I will blow a bubble at one end of a glass tube, and leave the tube open at the other end; we shall thus have a small hole formed in one side of the bubble, which, if our theory is correct, will gradually contract and disappear. You now see on the screen images of the ends of two tubes. I have the power of cutting off one tube entirely from access to the other; and I do so now, so that you will, if you please, consider for the purposes of this experiment that tube only as existing at the extremity of which I shall blow the bubble. You now see the image of the soap- bubble, which as long as the tube is closed remains unaltered in size; I open it, and it now at once contracts and disappears. This, then, conclusively proves that the air in the bubble was compressed. I will now go a step farther, and show that the amount of this compression depends on the size of the bubble. If it be large, the air is not so much compressed as if it be small. Let us consider what would happen if I formed bubbles at the two ends of a tube. If they were of the same size, evidently—the one pressing the air in one direction, and the other pressing it in the other with equal force no effect would follow. If, however, one bubble were smaller than the other, and what I have said be true, the small one would compress the air within it, and drive it from left to right (say) with greater force than the other would tend to drive it from right to left: hence the air would flow from the small bubble to the large one; the large one would increase, and the small one diminish. The smaller the bubble, the more the air would be compressed; and thus the current would become greater and greater, until at last we should see the small bubble entirely disappear, the large one having absorbed all the air which it previously contained. I will try to show you this on the screen; first disconnecting the two tubes, I blow at their ends bubbles of unequal size. I will now place them in communication, so that the air can pass from the one to the other. You see, the small bubble contracts and the large one expands, and we thus learn that the pressure of the smaller or more curved bubble upon the air is greater than that of the less curved one.
I now come to the third property of liquids of which I wish to speak; and that is, that the surface of a liquid is generally either more or less viscous than the interior. With reference to the word viscous, you will find a familiar example of two liquids which differ very much in this property of viscosity in treacle and water. Take a vessel of treacle and bring it nearer and nearer—still no effect. I bring it so near that you can see its shadow, and still the magnet remains absolutely motionless. On the surface of the liquid, then, we have found that the little magnet is totally insensible to the attractive force of this large one. You may say that the same would happen in the case of glycerine or treacle. It might; but now comes the extraordinary part of the experiment. I pour in some more saponine and water, until the little magnet lies a quarter of an inch below its surface; I then bring the large magnet near, and you see the result.
It moves almost as freely as in the air itself. Hence we have a 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, a vessel of water, pour the liquids out, and note the different way in which they behave; the water flows out smoothly, one part slipping over another, whereas the treacle comes out in a great rolling mass, which seems to stick to the sides of the vessel. Again, put a spoon into a vessel of water, and move it through the liquid, you will find little resistance to its motion, the water seems to flow away to make room for it and closes in again immediately behind. Try the same experiment with the treacle and you will find the resistance very much increased; in front of the spoon a little heap of liquid gathers, which subsides but slowly, and there is a depression behind which is as slowly filled up. It is evident that there is some difference between the interior constitutions of the treacle and the water; and that difference consists in this, that the particles of which the treacle is composed move among themselves with very much less facility than do those of the water. The fact, then, of one part of a liquid moving more or less easily among the other parts is that which distinguishes one from another in respect to their viscosity. In a very viscous body, like treacle, the parts move with difficulty; and in a non-viscous liquid, like water, they move with comparative ease. The fact which I wish to impress upon you this evening is, not that one kind of liquid differs from another; but that one part of a liquid may differ from another in respect of viscosity; and that as a general rule the surface is more or less viscous than the interior. I will now show you an experiment which will illustrate this fact in a very striking way. I have in a glass vessel a little magnet, which, when I bring near to it a large magnet, will easily and readily follow its motions. The vessel also contains a mixture of water and a substance called saponine. This saponine is extracted from the horse-chestnut, and is, as far as I know, chiefly interesting on account of the extraordinary effect it produces on water when mixed with it. In making the mixture, I have added only one part of saponine to sixty of water, and, to look at, it retains the properties of water; it is colorless; it has none of the viscosity of treacle. In fact, the saponine has next to no effect on the interior parts of the water, but it has a most extraordinary and marked effect on the surface; and that I will now try to illustrate. You now see upon the screen the image of the magnet, and the vessel at the bottom of which there is the mixture of saponine and water. The magnet is at present about an eighth of an inch above the liquid. I bring near the large magnet, and you see how easily it follows its motions. I will now pour in some of my mixture until the magnet lies upon the surface, and I then again bring the large magnet near it. It is now upon the surface of the mixture, and you can see some of the bubbles formed as I pour the liquid in. I bring the large magnet as near as it was at first and am moving it, but it produces no effect. I 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 would press upon the plate; but the plate would be able to resist the pressure, and the bubble would remain a hemisphere with a flat base. If, on the other hand, the bubble were formed on the surface of a liquid, there would be precisely the same pressure on the bottom, only it would be acting on a medium which would give way to it; the liquid, therefore, would yield to the pressure of the air, and we should have the bubble as it were a little buried in the liquid by its own pressure. As the pressure increases with the smallness of the bubble, we should expect a small bubble to be very deeply buried, and a large bubble to be slightly buried. I will now pour into the cell, the image of which you see, a small quantity of liquid, and blow in it a very small bubble. You now see the images of two bubbles which have risen to the surface, and that they are very much buried in the liquid by virtue of their pressure. I will now blow a large bubble. You see that within it the surface of the liquid is very much less depressed. I will blow a still larger one. Now I have succeeded in blowing a very large bubble, and the lower part of it is not appreciably depressed. I will now blow a great number of bubbles in contact, and will then point out one or two facts. You now see that odd network which represents a great number of bubbles. There are two points I wish you to notice. In the first place, when two bubbles meet, the surface between them may be either plane or curved. It is plane if both bubbles are of equal size, and therefore compress the air within them with equal force; but, if they are unequal, the smaller bubble, compressing the air more strongly, indents the larger, and the surface which divides them is curved. Notice also another very curious point, namely, that in no case do more than three bubbles meet in a point, excepting for an instant. This follows from the law that a large number of bubbles, as well as each one, will assume the smallest possible surface. I cannot go into the proof of this, but it follows from the law I have already given you. As the bubbles form, collapse, and disappear, you see that they always so arrange themselves that no more than three shall ever meet in a point.
Now, then, we have got our bubble on the surface of the liquid. Let us consider what will happen to it after that. Evidently the liquid of which it is composed will run down the sides by virtue of its own weight; but there will be a certain resistance to this motion, greater or less as the viscosity of the surface is great or small. Hence, there are two different dangers which may beset the bubble. The first of these is, that when the surface-viscosity is small, then the liquid runs down the sides of the bubble very easily; the consequence is, the bubble becomes very thin and bursts. There is, however, an opposite danger which may imperil the bubble when the surface-viscosity is great; and that is, that the liquid does not flow down in a straight line or regular curve, but in irregular masses, which every now and then tear away from each other. Now, these ruptures make little holes in the surface of the liquid; and when a hole is made the surface-tension tends to tear the liquid away, and to make it bigger. If the liquid has a very considerable surface- tension, the small holes in the surface may be so instantly turned into large ones that the bubble may burst. This is, however, less likely to occur when the surface-viscosity is small than when it is great, because in that case the liquid flowing in from all sides can more easily fill up the hole, and restore the damage done, before it becomes dangerously large. The best kind of bubble for lasting is one in which the surf ace- viscosity is tolerably large, so that the sides of the bubble may not become thin too quickly, and in which the surface-tension is not too great, so that any small fractures which occur may not be instantly enlarged. When we find a liquid which has these two properties, we have all the requisites for making good bubbles; but sooner or later a hole is made, and then the bubble bursts, and in a way which is probably very different from what, a priori, we should expect. In the first place, the orifice which has been formed becomes rapidly larger, the surface-tension which acts all round its edges and pulls the film away from its centre tending to enlarge it. Secondly, the surface of the liquid is necessarily very much curved all round the hole, and a greater pressure is therefore excited at that part by the surface on the liquid which forms the interior of the film than elsewhere. Hence the liquid becomes heaped up around the hole into a ring which is thicker than the rest of the bubble, though its thickness is very small compared with the diameter of the hole. The liquid in the ring is thus in circumstances somewhat similar to that in the long cylinder we have already studied — it undergoes a similar series of transformations and is broken up into drops which are flung away from the bubble. Another ring is instantly formed and as instantly broken, and the process is repeated again and again with inconceivable rapidity, until in a very small fraction of a second a little cloud, composed of the numerous minute drops which have been formed, is all that remains of the bubble.
I must now draw to a close. I have discussed with you, as well as I could in the short space of time allotted to me, the history of a bubble from its birth, in the bosom of the liquid, to its dissolution in the air above. The facts and experiments I have brought to your notice have been, I hope, in themselves sufficient to attract you; but I think they will acquire an additional interest if, before we part, I tell you something about the man to whom we owe most of our knowledge on the subject of my lecture. I mean M. Plateau, the Professor of Physics in the Belgian University of Ghent. This gentleman began his studies on liquids when a young man, and was already well known for his success in scientific investigation, when a misfortune overtook him which one would have thought would have put an end to his further researches. He became hopelessly blind. A misfortune like this would have crushed a weaker man; but in the case of M. Plateau it served to show the genuine metal he was made of. He spent the long hours of darkness, not in useless repining, or vain regrets, but in endeavoring to advance the knowledge of his race by pondering over the unsolved problems connected with the subjects he understood so well, and in devising experiments, often of the most exquisite ingenuity, for putting his theories and conclusions to the test. These, which he could no longer perform for himself, were undertaken for him by a devoted band of friends, among whom was his own son; and the result has been, not merely a very large addition to our knowledge of the properties of the surfaces of liquids, but, what is perhaps far more important, the presentation to the world of a spectacle of victory over almost overwhelming obstacles such as it has seldom seen. It is not well that our knowledge of scientific facts should be entirely divorced from an acquaintance with the lives and labors of their discoverers, or that we should come to regard them simply as a sort of revelation made to a fortunate few, to the rich inheritance of which we have been lucky enough to succeed. The men who built up the pile of modern science were not of those who sit still and wait with folded hands for some inspiration, they know not whence; rather they performed their tasks, and won success amid difficulties and discouragements to which we in happier times are strangers. But, while rightly ready to pay our homage to the great achievements of the past, we should ever be watchful to honor duly deeds which will cast a lustre upon our own time;. and among these the life-work of M. Plateau holds in some respects a position second to none. Others may deserve a higher place for the number, or practical or scientific importance, of their discoveries, but none have more honestly earned the praise due to those who have done what they could; and the world, which is so apt to appropriate the work and forget the worker, should be taught at all events to remember this, that we owe some of the most charming experiments in the whole range of physics to one who himself has never beheld many of them, and of whom, with respect to the rest, we must in all sadness say, he "shall see them again no more forever."
1. A lecture delivered in the Hulme Town-Hall, Manchester, on Wednesday, November 3, 1875.