GIFT OF 
 MICHAEL REESE 
 
 ,- 
 

 
SOAP-BUBBLES 
 
 AND THE 
 
 FORCES WHICH MOULD THEM, 
 
 )RNife 
 
THE ROMANCE OF SCIENCE. 
 
 SOAP-BUBBLES 
 
 AND THE 
 
 FORCES WHICH MOULD THEM 
 
 BEING A COURSE OF THREE LECTURES 
 
 DELIVERED IN THE THEATRE OF THE LONDON 
 
 INSTITUTION ON THE AFTERNOONS OF DEC. 30, 1889, 
 
 JAN. I AND 3, 1890, BEFORE A JUVENILE AUDIENCE. 
 
 BY 
 
 C. V. BOYS, A.R.S.M., F.R.S., 
 
 ASSISTANT PROFESSOR OF PHYSICS AT THE ROYAL COLLEGE OF SCIENCE, 
 SOUTH KENSINGTON. 
 
 PUBLISHED UNDER THE DIRECTION OF THE GENERAL LITERATURE 
 COMMITTEE. 
 
 XTNIVERSITT 
 
 SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE, 
 
 LONDON : NORTHUMBERLAND AVENUE, W.C. J 
 43, QUEEN VICTORIA STREET, E.G. 
 
 BRIGHTON: 129, NORTH STREET. 
 NEW YORK: E. &J. B. YOUNG & CO- 
 
 1896. 
 
TO 
 
 G. F. RO DWELL, 
 
 THE FIRST 
 SCIENCE-MASTER APPOINTED AT MARLBOROUGH COLLEGE, 
 
 BY THE AUTHOR 
 AS A TOKEN OF ESTEEM AND GRATITUDE, 
 
 AND IN THE HOPE THAT 
 
 IT MAY EXCITE IN A FEW YOUNG PEOPLE SOME SMALL 
 
 FRACTION OF THE INTEREST AND ENTHUSIASM WHICH 
 
 HIS ADVENT AND HIS LECTURES AWAKENED 
 
 IN THE AUTHOR, UPON WHOM THE LIGHT 
 
 OF SCIENCE THEN SHONE FOR 
 
 THE FIRST TIME. 
 
or THE 
 
 UNIVERSITY*; 
 
 PREFACE. 
 
 I WOULD ask those readers who have grown 
 up, and who may be disposed to find fault with 
 this book, on the ground that in so many 
 points it is incomplete, or that much is so 
 elementary or well known, to remember that 
 the lectures were meant for juveniles, and 
 for juveniles only. These latter I would urge 
 to do their best to repeat the experiments 
 described. They will find that in many cases 
 no apparatus beyond a few pieces of glass or 
 india-rubber pipe, or other simple things easily 
 obtained are required. If they will take this 
 trouble they will find themselves well repaid, 
 and if instead of being discouraged by a few 
 failures they will persevere with the best means 
 at their disposal, they will soon find more to 
 interest them in experiments in which they 
 only succeed after a little trouble than in those 
 
Vlll PREFACE. 
 
 which go all right at once. Some are so 
 simple that no help can be wanted, while some 
 will probably be too difficult, even with assist- 
 ance ; but to encourage those who wish to see 
 for themselves the experiments that I have 
 described, I have given such hints at the end 
 of the book as I thought would be most 
 useful. 
 
 I have freely made use of the published 
 work of many distinguished men, among 
 whom I may mention Savart, Plateau, Clerk 
 Maxwell, Sir William Thomson, Lord Ray- 
 leigh, Mr. Chichester Bell, and Prof. Rucker. 
 The experiments have mostly been described 
 by them, some have been taken from journals, 
 and I have devised or arranged a few. I am 
 also indebted to Prof. Rucker for the use of 
 various pieces of apparatus which had been 
 prepared for his lectures. 
 
SOAP-BUBBLES, 
 
 AND THE 
 
 FORCES WHICH MOULD THEM. 
 
 I DO not suppose that there is any one in 
 this room who has not occasionally blown a 
 common soap-bubble, and while admiring the 
 perfection of its form, and the marvellous 
 brilliancy of its colours, wondered how it is 
 that such a magnificent object can be so easily 
 produced. 
 
 I hope that none of you are yet tired of 
 playing with bubbles, because, as I hope we 
 shall see during the week, there is more in a 
 common bubble than those who have only 
 played with them generally imagine. 
 
 The wonder and admiration so beautifully 
 portrayed by Millais in a picture, copies of 
 
IO SOAP-BUBBLES, AND 
 
 which, thanks to modern advertising enterprise, 
 some of you may possibly have seen, will, I 
 hope, in no way fall away in consequence of 
 these lectures; I think you will find that it 
 will grow as your knowledge of the subject 
 increases. You may be interested to hear that 
 we are not the only juveniles who have played 
 with bubbles. Ages ago children did the 
 same, and though no mention of this is made 
 by any of the classical authors, we know that 
 they did, because there is an Etruscan vase in 
 the Louvre in Paris of the greatest antiquity, 
 on which children are represented blowing 
 bubbles with a pipe. There is however, no 
 means of telling now whose soap they used. 
 It is possible that some of you may like 
 to know why I have chosen soap-bubbles 
 as my subject ; if so, I am glad to tell you. 
 Though there are many subjects which might 
 seem to a beginner to be more wonderful, 
 more brilliant, or more exciting, there are few 
 which so directly bear upon the things which 
 we see every day. You cannot pour water 
 from a jug or tea from a tea-pot; you can- 
 not even do anything with a liquid of any 
 kind, without setting in action the forces to 
 
THE FORCES WHICH MOULD THEM. II 
 
 which I am about to direct your attention. 
 You cannot then fail to be frequently re- 
 minded of what you will hear and see in 
 this room, and, what is perhaps most im- 
 portant of all, many of the things I am 
 going to show you are so simple that you 
 will be able without any apparatus to repeat 
 for yourselves the experiments which I have 
 prepared, and this you will find more inter- 
 esting and instructive than merely listening to 
 me and watching what I do. 
 
 There is one more thing I should like to 
 explain, and that is why I am going to show 
 experiments at all. You will at once answer 
 because it would be so dreadfully dull if I 
 didn't. Perhaps it -x would. But that is not 
 the only reason. <J^\^gjE^mind you then 
 that when we want to find out anything that 
 we do not know, there are two ways of pro- 
 ceeding. _JWe_m ay either ask somebody else 
 who does know, or read^whaTthe most learned 
 men have written about it, which is a very good 
 plan if anybody happens to be able to answer 
 our question ; or else we may adopt the other 
 plan, and by arranging an experiment, try 
 for ourselves. An experiment is a question 
 
12 SOAP-BUBBLES, AND 
 
 which we ask of Nature, who is always ready 
 to give a correct answer, provided we ask 
 properly, that is, provided we arrange a proper 
 experiment. An experiment is not a conjuring 
 trick, something simply to make you wonder, 
 nor is it simply shown because it is beautiful, 
 or because it serves to relieve the monotony 
 of a lecture ; if any of the experiments I show 
 are beautiful, or do serve to make these lec- 
 tures a little less dull, so much the better; 
 but their chief object is to enable you to see 
 for yourselves what the true answers are to 
 questions that I shall ask. 
 
 Now I shall begin by performing an experi- 
 ment which you have all probably tried dozens 
 of times. I have in my hand a common 
 camers-hair brush. If you want to make the 
 hairs cling together and come to a point, you 
 wet it, and then you say the hairs cling to- 
 gether because the brush is wet. Now let us 
 try the experiment ; but as you cannot see 
 this brush across the room, I hold it in front 
 of the lantern, and you can see it enlarged 
 upon the screen (Fig. i, left hand). Now it 
 is dry, and the hairs are separately visible. I 
 am now dipping it in the water, as you can 
 
THE FORCES WHICH MOULD THEM. 13 
 
 see, and on taking it out, the hairs, as we 
 expected, cling together (Fig. i, right hand), 
 because they are wet, as we are in the habit 
 of saying. I shall now hold the brush in 
 the water, but there it is evident that the 
 
 Fig. i. 
 
 hairs do not cling at all (Fig. i, middle), 
 and yet they surely are wet now, being actually 
 in the water. It would appear then that the 
 reason which we always give is not exactly 
 correct. This experiment, which requires no- 
 thing more than a brush and a glass of 
 
water, then shows that the hairs of a brush 
 cling together not only because they are 
 wet, but for some other reason as well 
 which we do not yet know. It also shows 
 that a very common belief as to opening our 
 eyes under water is not founded on fact. It 
 is very commonly said that if you dive into 
 the water with your eyes shut you cannot see 
 properly when you open them under water, 
 because the water gums the eyelashes down 
 over the eyes ; and therefore you must dive in 
 with your eyes open if you wish to see under 
 water. Now as a matter of fact this is not 
 the case at all ; it makes no difference whether 
 your eyes are open or not when you dive in, 
 you can open them and see just as well either 
 way. In the case of the brush we have seen 
 that water does not cause the hairs to cling 
 together or to anything else when under the 
 water, it is only when taken out that this is 
 the case. This experiment, though it has not 
 explained why the hairs cling together, has at 
 any rate told us that the reason always given 
 is not sufficient. 
 
 I shall now try another experiment as simple 
 as the last. I have a pipe from which water 
 

 * 
 
 THE FORCES WHICH MOULD THEM. 15 
 
 is very slowly issuing, but it does not fall 
 away continuously ; a drop forms which slowly 
 grows until it has attained a certain definite 
 size, and then it suddenly falls away. I want 
 you to notice that every time this happens 
 the drop is always exactly the same size and 
 shape. Now this cannot be mere chance; 
 there must be some reason for the definite size, 
 and shape. Why does the water remain at 
 all? It is heavy and is ready to fall, but it 
 does not fall; it remains clinging until it is 
 a certain size, and then it suddenly breaks 
 away, as if whatever held it was not strong 
 enough to carry a greater weight. Mr. Worth- 
 ington has carefully drawn on a magnified 
 scale the exact shape of a drop of water of 
 different sizes, and these you now see upon 
 the diagram on the wall (Fig. 2). These 
 diagrams will probably suggest the idea that 
 the water is hanging suspended in an elastic 
 bag, and that the bag breaks or is torn away 
 when there is too great a weight for it to 
 carry. It is true there is no bag at all really, 
 but yet the drops take a shape which suggests 
 an elastic bag. To show you that this is no 
 fancy, I have supported by a tripod a large 
 
1 6 SOAP-BUBBLES, AND 
 
 ring of wood over which a thin sheet of india- 
 rubber has been stretched, and now on allowing 
 water to pour in from this pipe you will see the 
 rubber slowly stretching under the increasing 
 weight, and, what I especially want you to 
 
 Fig. 2. 
 
 notice, it always assumes a form like those on 
 the diagram. As the weight of water increases 
 the bag stretches, and now that there is about 
 a pailful of water in it, it is getting to a 
 state which indicates that it cannot last much 
 longer; it is like the water-drop just before 
 
THE B'oRCES WHICH MOULD THEM. 17 
 
 it falls away, and now suddenly it changes its 
 shape (Fig. 3), and it would immediately tear 
 
 Fig- 3- 
 
 itself away if it were not for the fact that india- 
 rubber does not stretch indefinitely ; after a 
 time it gets tight and will withstand a greater 
 
l8 SOAP-BUBBLES, AND 
 
 pull without giving way. You therefore see 
 the great drop now permanently hanging which 
 is almost exactly the same in shape as the 
 water-drop at the point of rupture. I shall 
 now let the water run out by means of a 
 syphon, and then the drop slowly contracts 
 again. Now in this case we clearly have a 
 heavy liquid in an elastic bag, whereas in the 
 drop of water we have the same liquid but no 
 bag that is visible. As the two drops behave 
 in almost exactly the same way, we should 
 naturally be led to expect that their form and 
 movements are due to the same cause, and that 
 the small water-drop has something holding it 
 together like the india-rubber you now see. 
 
 Let us see how this fits the first experiment 
 with the brush. That showed that the hairs 
 do not cling together simply because they are 
 wet ; it is necessary also that the brush should 
 be taken out of the water, or in other words 
 it. is necessary that the surface or the skin of 
 the water should be present to bind the hairs 
 together. If then we suppose that the surface 
 of water is like an elastic skin, then both the 
 experiments with the wet brush and with the 
 water-drop will be explained. 
 
THE FORCES WHICH MOULD THEM. 19 
 
 Let us therefore try another experiment to 
 see whether in other ways water behaves as if 
 it had an elastic skin. 
 
 I have here a plain wire frame fixed to a 
 stem with a weight at the bottom, and a hollow 
 glass globe fastened to it with sealing-wax. 
 The globe is large enough to make the whole 
 thing float in water with the frame up in the 
 air. I can of course press it down so that the 
 frame touches the water. To make the move- 
 ment of the frame more evident there is fixed 
 to it a paper flag. 
 
 Now if water behaves as if the surface were 
 an elastic skin, then it should resist the upward 
 passage of the frame which I am now holding 
 below the surface. I let go, and instead of 
 bobbing up as it would do if there were no such 
 action, it remains tethered down by this skin of 
 the water. If I disturb the water so as to let 
 the frame out at one corner, then, as you see, it 
 dances up immediately (Fig. 4). You can see 
 that the skin of the water must have been fairly 
 strong, because a weight of about one quarter 
 of an ounce placed upon the frame is only just 
 sufficient to make the whole thing sink. 
 
 This apparatus which was originally described 
 
SOAP-BUBBLES, AND 
 
 by Van der Mensbrugghe I shall make use of 
 again in a few minutes. 
 
 I can show you in a more striking way that 
 there is this elastic layer or skin on pure clean 
 water. I have a small sieve made of wire 
 gauze sufficiently coarse to 
 allow a common pin to be 
 put through any of the 
 holes. There are moreover 
 about eleven thousand of 
 these holes in the bottom 
 of the sieve. Now, as you 
 know, clea,n wire is wetted 
 by water, that is, if it is 
 dipped in water it comes 
 out wet ; on the other hand, 
 some materials, such as 
 paraffin wax, of which 
 paraffin candles are made, 
 are not wetted or really 
 touched by water, as you 
 may see for yourselves if you will only dip a 
 paraffin candle into water. I have melted a 
 quantity of paraffin in a dish and dipped this 
 gauze into the melted paraffin so as to coat 
 the wire all over with it, but I have shaken 
 
 Fig. 4. 
 
THE FORCES WHICH MOULD THEM. 21 
 
 it well while hot to knock the paraffin out of 
 the holes. You can now see on the screen that 
 the holes, all except one or two, are open, and 
 that a common pin can be passed through 
 readily enough. This then is the apparatus. 
 Now if waterTTas an elastic skin which it re- 
 quires force to stretch, it ought not to run 
 through these holes very readily; it ought 
 not to be able to 
 get through at all 
 unless forcedy be- 
 cause at eachTiole 
 the skin would 
 liave^jtp.-'ISe stretch- 
 ed to allow the 
 water to ger~to the 
 
 Fig. 5. 
 
 other "side. r This 
 you understand is 
 only true if the water does not wet or really 
 touch the wiret Now to prevent the water 
 that I am going to pour ' in-frnm striking the 
 bottom with so much force as to drive it 
 through, I have laid a small piece of paper 
 in the sieve, and am pouring the water on to 
 the paper, which breaks the fall (Fig. 5). I 
 have now poured in about half a tumbler of 
 
22 SOAP-BUBBLES, AND 
 
 water, and I might put in more. I take away 
 the paper but not a drop runs through. If 
 I give the sieve a jolt then the water is driven 
 to the other side, and in a moment it has all 
 escaped. Perhaps this will remind you of 
 one of the exploits of our old friend Simple 
 Simon, 
 
 11 Who went for water in a sieve, 
 But soon it all ran through." 
 
 But you see if you only manage the sieve 
 properly, this is not quite so absurd as people 
 generally suppose. 
 
 If now I shake the water off the sieve, I can, 
 for the same reason, set it to float on water, 
 because its weight is not sufficient to stretch 
 the skin of^the water through all the holes. 
 The water, therefore, remains on the other side, 
 and it floats even though, as I have already 
 said, there are eleven thousand holes in the 
 bottom, any one of which is large enough to 
 allow an ordinary pin to pass through. This 
 experiment also illustrates how difficult it is to 
 write real and perfect nonsense. 
 
 You may remember one of the stories in 
 Lear's book of Nonsense Songs. 
 
THE FORCES WHICH MOULD THEM. 
 
 23 
 
 They went to sea in a sieve, they did, 
 
 In a sieve they went to sea : 
 In spite of all their friends could say, 
 On a winter's morn, on a stormy day, 
 
 In a sieve they went to sea. 
 
 * * * * 
 
 " They sailed away in a sieve, they did, 
 
 In a sieve they sailed so fast, 
 With only a beautiful pea-green veil, 
 Tied with a riband by way of a sail, 
 
 To a small tobacco-pipe mast ; 
 
 # # * # 
 
 And so on. You see that it is quite pos- 
 sible to go to sea in 
 a sieve that is, if 
 the sieve is large 
 enough and the water 
 is not too rough and 
 that the above lines 
 are now realized in 
 every particular (Fig. 
 6). ' 
 
 I may give one more 
 example of the power 
 of this elastic skin of 
 water. If you wish 
 to pour water from a 
 tumbler into a narrow- Fig. 6. 
 
 - 
 
24 SOAP-BUBBLES, AND 
 
 necked bottle, you know how if you pour 
 slowly it nearly all runs down the side of the 
 glass and gets spilled about, whereas if you 
 pour quickly there is no room for the great 
 quantity of water to pass into the bottle all at 
 once, and so it gets spilled again. But if you 
 take a piece of stick or a glass rod, and hold it 
 against the edge of the 
 tumbler, then the water 
 runs down the rod and 
 into the bottle, and none 
 is lost (Fig. 7) ; you may 
 even hold the rod inclined 
 to one side, as I am now 
 doing, but the water runs 
 down the wet rod because 
 this elastic skin forms a 
 kind of tube which pre- 
 vents the water from escap- 
 ing. This action is often made use of in the 
 country to carry the water from the gutters 
 under the roof into a water-butt below. A 
 piece of stick does nearly as well as an iron 
 pipe, and it does not cost anything like so 
 much. 
 
 I think then I have now done enough to 
 
THE FORCES WHICH MOULD THEM. 25 
 
 show that on the surface of water there is a 
 kind of elastic skin. I do not mean that there 
 is anything that is not water on the surface, 
 but that the water while there acts in a different 
 way to what it does inside,' and that it acts as if 
 it were an elastic skin made of something like 
 very thin India- rubber, only that it is perfectly 
 and absolutely elastic, which india-rubber is not. 
 You witt now" be in a position to understand 
 how it is that in narrow tubes water does not 
 find its own levelfbut behaves in an unexpected 
 manner.- I have placed in front of the lantern 
 a dish of water coloured blue so that you may 
 the more easily see it." I shall now dip into 
 the water a very narrow glass pipe, and immedi- 
 ately the water rushes upland stands about half 
 an inch above the general levdy The tube 
 inside is wet^ The elastic skinjsf the water is 
 therefore attached to the tube,* and goes on pull- 
 ing up the water until the weight of the water 
 raised"above the general level is equal to the 
 force- exerted by the skin. If I take a tube 
 about twice as big, then this pulling action 
 which is going on all round the tube will cause 
 it to lift twice the weight of water, but this will 
 not make the water rise twice as high, because 
 
26 SOAP-BUBBLES, AND 
 
 the larger tube holds so much more water for a 
 given length than the smaller tube. It will not 
 even pull it up as high as it did in the case of 
 the smaller tube, because if it were pulled up 
 as high the weight of the water raised would 
 in that case be four times as great, and not 
 only twice as great, as you might at first think. 
 It will therefore only raise the water in the larger 
 tube to half the height, and now that the two 
 tubes are side by side you see the water in the 
 smaller tube standing twice as high as it does 
 in the larger tube. In the same way, if I were 
 to take a tube as fine as a hair the water would 
 go up ever so much higher. It is for this 
 reason that this is called Capillarity, from the 
 Latin word capillus, a hair, because the action 
 is so marked in a tube the size of a hair. 
 
 Supposing now you had a great number of 
 tubes of all sizes, and placed them in a row 
 with the smallest on one side and all the others 
 in the order of their sizes, then it is evident 
 that the water would rise highest in the smallest 
 tube and less and less high in each tube in the 
 row (Fig. 8), until when you came to a very 
 large tube you would not be able to see that 
 the water was raised at all. You can very 
 
THE FORCES WHICH MOULD THEM. 2j 
 
 easily obtain the same kind of effect by simply 
 taking two square pieces of window glass and 
 placing them face to face with a common 
 match or small fragment of anything to keep 
 them a small distance apart along one edge 
 
 Fig. 8. 
 
 while they meet together along the opposite 
 edge. An india-rubber ring stretched over 
 them will hold them in this position. I now 
 take this- pair of plates and stand it in a dish of 
 coloured water, and you at once see that the 
 water creeps up to the top of the plates on 
 
28 SOAP BUBBLES, AND 
 
 the edge where they meet, and as the distance 
 between the plates gradually increases, so the 
 height to which the water rises gradually gets 
 less, and the result is that the surface of the 
 liquid forms a beautifully regular curve which 
 
 Fig. 9. 
 
 is called by mathematicians a rectangular 
 hyperbola (Fig. 9). I shall have presently 
 to say more about this and some other curves, 
 and so I shall not do more now than state 
 that the hyperbola is formed because as the 
 width between the plates gets greater the 
 
THE FORCES WHICH MOULD THEM. 19 
 
 height gets less, or, what comes to the same 
 thing, because the weight of liquid pulled up 
 at any small part of the curve is always the 
 same. 
 
 If the plates or the tubes had been made of 
 material not wetted by water, then the effect 
 of the tension of the surface would be to drag 
 the liquid away from the narrow spaces, and 
 the more so as the spaces were narrower. As 
 it is not easy to show this well with paraffined 
 glass plates or tubes and water, I shall use 
 another liquid which does not wet or touch 
 clean glass, namely, quicksilver. As it is not 
 possible to see through quicksilver, it will not 
 do to put a narrow tube into this liquid to 
 show that the level is lower in the tube than 
 in the surrounding vessel, but the same result 
 may be obtained by having a wide and a 
 narrow tube joined together. Then, as you 
 see upon the screen, the quicksilver is lower in 
 the narrow than in the wide tube, whereas in 
 a similar apparatus the reverse is the case with 
 water (Fig. 10). 
 
 I want you now to consider what is happen- 
 ing when two flat plates partly immersed in 
 water are held close together. We have seen 
 
3O SOAP-BUBBLES, AND 
 
 that the water rises between them. Those 
 parts of these two plates, which have air 
 between them and also air outside them (in- 
 dicated by the letter a in Fig. n), are each of 
 them pressed equally in opposite directions by 
 
 Fig. 10. 
 
 the pressure of the air, and so these parts do 
 not tend to approach or to recede from one 
 another. These parts again which have water 
 on each side of each of them (as indicated by 
 the letter c) are equally pressed in opposite 
 directions by the pressure of the water, and so 
 
THE FORCES WHICH MOULD THEM. 3! 
 
 these parts do not tend to approach or to 
 recede from one another. But those parts of 
 the plates (b) which have water between them 
 and air outside would, you might think, be 
 pushed apart by the water between them with 
 a greater force than that which could be 
 exerted by the air outside, and so you might 
 
 m 
 
 Fig. II. 
 
 be led to expect that on this account a pair of 
 plates if free to move would separate at once. 
 But such an idea though very natural is wrong, 
 and for this reason. The water that is raised 
 between the plates being above the general 
 level must be under a less pressure, because, 
 as every one knows, as you go down in water 
 
3^ SOAP-BUBBLES, AND 
 
 the pressure increases, and so as you go up 
 the pressure must get less. The water then 
 that is raised between the plates is under a 
 less pressure than the air outside, and so on 
 the whole the plates are pushed together. 
 You can easily see that this is the case. I 
 have two very light hollow glass beads such 
 as are used to decorate a Christmas tree. 
 These will float in water if one end is stopped 
 with sealing-wax. These are both wetted by 
 water, and so the water between them is 
 slightly raised, for they act in the same way as 
 the two plates, but not so powerfully. How- 
 ever, you will have no difficulty in seeing that 
 the moment I leave them alone they rush 
 together with considerable force. Now if you 
 refer to the second figure in the diagram, 
 which represents two plates which are neither 
 of them wetted, I think you will see, without 
 any explanation from me, that they should be 
 pressed together, and this is made evident by 
 experiment. Two other beads which have been 
 dipped in paraffin wax so that they are neither 
 of them wetted by water float up to one another 
 again when separated as though they attracted 
 each other just as the clean glass beads did. 
 
THE FORCES WHICH MOULD THEM. 33 
 
 If you again consider these two cases, you 
 will see that a plate that is wetted tends to 
 move towards the higher level of the liquid, 
 whereas one that is not wetted tends to move 
 towards the lower level, that is if the level of 
 the liquid on the two sides is made different 
 by capillary action. Now suppose one plate 
 wetted and the other not wetted, then, as the 
 diagram imperfectly shows, the level of the 
 liquid between the plates where it meets the 
 non-wetted plate is higher than that outside, 
 while where it meets the wetted plate it is 
 lower than that outside ; so each plate tends 
 to go away from the other, as you can see now 
 that I have one paraffined and one clean ball 
 floating in the same water. They appear to 
 repel one another. 
 
 You may also notice that the surface of the 
 liquid near a wetted plate is curved, with the 
 hollow of the curve upwards, while near a ncai- 
 wetted plate the reverse is the case. That this 
 curvature of the surface is of the first import- 
 ance I can show you by a very simple experi- 
 ment, which you can repeat at home as easily 
 as the last that I have shown. I have a clean 
 glass bead floating in water in a clean glass 
 
34 
 
 vessel, which is not quite full. The bead 
 always goes to the side of the vessel. It is 
 impossible to make it remain in the middle, it 
 always gets to one side or the other directly. 
 I shall now gradually add water until the level 
 of the water is rather higher than that of the 
 edge of the vessel. The surface is then 
 rounded near the vessel, while it is hollow near 
 the bead, and now the bead sails away towards 
 the centre, and can by no possibility be made 
 to stop near either side. With a paraffined 
 bead the reverse is the case, as you would 
 expect. Instead of a paraffined bead you may 
 use a common needle, which you will find 
 will float on water in a tumbler, if placed upon 
 it very gently. If the tumbler is not quite 
 full the needle will always go away from the 
 edge, but if rather over-filled it will work up 
 to one side, and then possibly roll over the 
 edge ; any bubbles, on the other hand, which 
 were adhering to the glass before will, the 
 instant that the water is above the edge of the 
 glass, shoot away from the edge in the most 
 sudden and surprising manner. This sudden 
 change can be most easily seen by nearly 
 filling the glass with water, and then gradually 
 
THE FORCES WHICH MOULD THEM. 35 
 
 dipping in and taking out a cork, which will 
 cause the level to slowly change. 
 
 So far I have given you no idea what force 
 is exerted by this elastic skin of water. Measure- 
 ments made with narrow tubes, with drops, 
 and in other ways, all show that it is almost 
 exactly equal to the weight of three and a 
 quarter grains to the inch. We have, more- 
 over, not yet seen whether other liquids act in 
 the same way, and if so whether in other cases 
 the strength of the elastic skin is the same. 
 
 You now see a second tube identical with 
 that from which drops of water were formed, 
 but in this case the liquid is alcohol. Now 
 that drops are forming, you see at once that 
 while alcohol makes drops which have a definite 
 size and shape when they fall away, the alcohol 
 drops are not by any means so large as the 
 drops of water which are falling by their side. 
 Two possible reasons might be given to ex- 
 plain this. Either alcohol is a heavier liquid 
 than water, which would account for the smaller 
 drop if the skin in each liquid had the same 
 strength, or else if alcohol is not heavier than 
 water its skin must be weaker than the skin of 
 water. As a matter of fact alcohol is a lighter 
 
36 SOAt>-BtJBBLES, AND 
 
 liquid than water, and so still more must the 
 skin of alcohol be weaker than that of water. 
 We can easily put this to the test of experi- 
 ment. In the game that is called the tug-of- 
 war you know well enough which side is the 
 strongest ; it is the side which pulls the other 
 over the line. Let us then make alcohol and 
 
 0-285 Inch 
 
 water play the same game. In order that you 
 may see the water, it is coloured blue. It is 
 lying as a shallow layer on the bottom of this 
 white dish. At the present time the skin of 
 the water is pulling equally in all directions, 
 and so nothing happens ; but if I pour a few 
 drops of alcohol into the middle, then at the 
 line which separates the alcohol from the water 
 
XTNIVEI 
 
 THE FORCES WHICJt MOULD fHEM. 37 
 
 we have alcohol on one side pulling in, while 
 we have water on the other side pulling out, 
 and you see the result. The water is victori- 
 ous ; it rushes away in all directions, carrying a 
 quantity of the alcohol away with it, and leaves 
 the bottom of the dish dry (Fig. 13). 
 
 Fig. 13- 
 
 This difference in the strength of the skin 
 of alcohol and of water, or of water containing 
 much or little alcohol, gives rise to a curious 
 motion which you may see on the side of a 
 wine-glass in which there is some fairly strong 
 wine, such as port. The liquid is observed to 
 
38 SOAP-BUBBLES, AND 
 
 climb up the sides of the glass, then to gather 
 into drops, and to run down again, and this 
 goes on for a long time. This is explained as 
 follows : The thin layer of wine on the side 
 of the glass being exposed to the air, loses 
 its alcohol by evaporation more quickly than 
 the wine in the glass. It therefore be- 
 comes weaker in alcohol or stronger in water 
 than that below, and for this reason it has a 
 stronger skin. It therefore pulls up more 
 wine from below, and this goes on until there 
 is so much that drops form, and it runs back 
 again into the glass, as you now see upon the 
 screen (Fig. 14). There can be no doubt 
 that this movement is referred to in Proverbs 
 xxiii. 31: "Look not thou upon the wine 
 when it is red, when it giveth his colour in 
 the cup, when it moveth itself aright." 
 
 If you remember that this movement only 
 occurs with strong wine, and that it must have 
 been known to every one at the time that these 
 words were written, and used as a test of the 
 strength of wine, because in those days every 
 one drank wine, then you will agree that this 
 explanation of the meaning of that verse is the 
 right one. I would ask you also to consider 
 
THE FORCES WHICH MOULD THEM. 39 
 
 whether it is not probable that other passages 
 which do not now seem to convey to us any 
 meaning whatever, may not in the same way 
 have referred to the common knowledge and 
 
 Fig. 14. 
 
 customs of the day, of which at the present 
 time we happen to be ignorant. 
 
 Ether, in the same way, has a skin which 
 is weaker than the skin of water. The very 
 smallest quantity of ether on the surface of 
 water will produce a perceptible effect. For 
 instance, the wire frame which I left some 
 
4O SOAP-BUBBLES, AND 
 
 time ago is still resting against the water-skin. 
 The buoyancy of the glass bulb is trying to 
 push it through, but the upward force is just 
 not sufficient. I will however pour a few 
 drops of ether into a glass, and simply pour 
 the vapour upon the surface of the water (not 
 a drop of liquid is passing over), and almost 
 immediately sufficient ether has condensed 
 upon the water to reduce the strength of the 
 skin to such an extent that the .frame jumps 
 up out of the water. 
 
 There is a well-known case in which the 
 difference between the strength of the skins 
 of two liquids may be either a source of 
 vexation or, if we know how to make use of 
 it, an advantage. If you spill grease on your 
 coat you can take it out very well with benzine. 
 Now if you apply benzine to the grease, and 
 then apply fresh benzine to that already there, 
 you have this result there is then greasy 
 benzine on the coat to which you apply fresh 
 benzine. It so happens that greasy benzine 
 has a stronger skin than pure benzine. The 
 greasy benzine therefore plays at tug-of-war 
 with pure benzine, and being stronger wins and 
 runs away in all directions, and the more you 
 
THE FORCES WHICH MOULD THEM. 41 
 
 apply benzine the more the greasy benzine 
 runs away carrying the grease with it. But 
 if you follow the directions on the bottle, and 
 first make a ring of clean benzine round the 
 grease-spot, and then apply benzine to the 
 grease, you then have the greasy benzine run- 
 ning away from the pure benzine ring and 
 heaping itself together in the middle, and 
 escaping into the fresh rag that you apply, so 
 that the grease is all of it removed. 
 
 There is a difference again between hot and 
 cold grease, as you may see, when you get 
 home, if you watch a common candle burning. 
 Close to the flame the grease is hotter than it 
 is near the outside. It has therefore a weaker 
 skin, and so a perpetual circulation is kept up, 
 and the grease runs out on the surface and 
 back again below, carrying little specks of 
 dust which make this movement visible, and 
 making the candle burn regularly. 
 
 You probably know how to take out grease- 
 stains with a hot poker and blotting-paper. 
 Here again the same kind of action is going 
 on. 
 
 A piece of lighted camphor floating in water 
 is another example of movement set up by 
 
42 SOAP-BUBBLES, AND 
 
 differences in the strength of the skin of water 
 owing to the action of the camphor. 
 
 I will give only one more example. 
 
 If you are painting in water-colours on 
 greasy paper or certain shiny surfaces the paint 
 will not lie smoothly on the paper, but runs 
 together in the well-known way ; a very little 
 ox-gall, however, makes it lie perfectly, because 
 ox-gall so reduces the strength of the skin of 
 water that it will wet surfaces that pure water 
 will not wet. This reduction of the surface 
 tension you can see if I use the same wire 
 frame a third time. The ether has now 
 evaporated, and I can again make it rest against 
 the surface of the water, but very soon after I 
 touch the water with a brush containing ox-gall 
 the frame jumps up as suddenly as before. 
 
 It is quite unnecessary that I should any 
 further insist upon the fact that the outside of 
 a liquid acts as if it were a perfectly elastic 
 skin stretched with a certain definite force. 
 
 Suppose now that you take a small quantity 
 of water, say as much as would go into a nut- 
 shell, and suddenly let it go, what will happen ? 
 Of course it will fall down and be dashed 
 against the ground. Or again, suppose you 
 
THE FORCES WHICH MOULD THEM. 43 
 
 take the same quantity of water and lay it 
 carefully upon a cake of paraffin wax dusted 
 over with lycopodium which it does not wet, 
 what will happen ? Here again the weight of 
 the drop that which makes it fall if not held 
 will squeeze it against the paraffin and make 
 it spread out into a flat cake. What would 
 happen if the weight of the drop or the force 
 pulling it downwards could be prevented from 
 acting ?, In such a case the drop would only 
 feel the effect of the elastic skin, which would 
 try to pull it into such a form as to make 
 the surface as small as possible. It would 
 in fact rapidly become a perfectly round ball, 
 because in no other way can so small a sur- 
 face be obtained. If, instead of taking so much 
 water, we were to take a drop about as large 
 as a pin's head, then the weight which tends 
 to squeeze it out or make it fall would be far 
 less, while the skin would be just as strong, 
 and would in reality have a greater moulding 
 power, though why I cannot now explain. 
 We should therefore expect that by taking a 
 sufficiently small quantity of water the mould- 
 ing power of the skin would ultimately be able 
 almost entirely to counteract the weig-ht of the 
 
44 SOAP-BUBBLES, AND 
 
 drop, so that very small drops should appear like 
 perfect little balls. If you have found any diffi- 
 culty in following this argument, a very simple 
 illustration will make it clear. You many of 
 you probably know how by folding paper to 
 make this little thing which I hold in my 
 hand (Fig. 15). It is called a cat-box, because 
 of its power of dispelling cats when it is filled 
 
 Fig. 
 
 with water and well thrown. This one, large 
 enough to hold about half a pint, is made out 
 of a small piece of the Times newspaper. 
 You may fill it with water and carry it about 
 and throw it with your full power, and the 
 strength of the paper skin is sufficient to hold 
 it together until it hits anything, when of 
 course it bursts and the water comes out. On 
 
THE FORCES WHICH MOULD THEM. 45 
 
 the other hand, the large one made out of a 
 whole sheet of the Times is barely able to 
 withstand the weight of the water that it will 
 hold. It is only just strong enough to allow 
 of its being filled and carried, and then it 
 may be dropped from a height, but you can- 
 not throw it. In the same way the weaker 
 skin of a liquid will not make a large quantity 
 take the shape of a ball, but it will mould a 
 minute drop so perfectly that you cannot tell 
 by looking at it that it is not perfectly round 
 every way. This is most easily seen with 
 quicksilver. A large quantity rolls about like 
 a flat cake, but the very small drops obtained 
 by throwing some violently on the table and 
 so breaking it up appear perfectly round. 
 You can see the same difference in the beads 
 of gold now upon the screen (Fig. 16). They 
 are now solid, but they were melted and 
 then allowed to cool without being disturbed. 
 Though the large bead is flattened by its 
 weight, the small one appears perfectly round. 
 Finally, you may see the same .thing with 
 water if you dust a little lycopodium on the 
 table. Then water falling will roll itself up 
 into perfect little balls. You may even see 
 
46 SOAP-BUBBLES, AND 
 
 the same thing on a dusty day if you water 
 the road with a water-pot. 
 
 If it were not for the weight of liquids, that 
 is the force with which they are pulled down 
 towards the earth, large drops would be as 
 
 Fig. 16. 
 
 perfectly round as small ones. This was first 
 beautifully shown by Plateau, the blind experi- 
 mentalist, who placed one liquid inside another 
 which is equally heavy, and with which it does 
 not mix. Alcohol is lighter than oil, while 
 water is heavier, but a suitable mixture of alcohol 
 
THE FORCES WHICH MOULD THEM. 47 
 
 and water is just as heavy as oil, and so oil does 
 not either tend to rise or to fall when immersed 
 in such a mixture. I have in front of the 
 lantern a glass box containing alcohol and 
 water, and by means of a tube I shall slowly 
 allow oil to flow in. You see that as I remove 
 the tube it becomes a perfect ball as large as a 
 walnutr There are now two or three of these 
 balls of oil all perfectly round. I want you to 
 notice that when I hit them on one side the 
 large balls recover their shape slowly, while the 
 small ones become rooHid again much more 
 quickly. Thsre is a v^ry beautiful effect which 
 can be produced with this apparatus, and though 
 it is not necessary to refer to it, it is well 
 worth while now that the apparatus is set up 
 to show it to you. In the middle of the box 
 there is an axle with a disc upon it to which I 
 can make the oil adhere. Now if I slowly turn 
 the wire and disc the oil will turn also. As I 
 gradually increase the speed the oil tends to fly 
 away in all directions, but the elastic skin 
 retains it. The result is that the ball becomes 
 flattened at its poles like the earth itself. On 
 increasing the speed, the tendency of the oil to 
 get away is at last too much for the elastic skin, 
 
48 SOAP-BUBBLES, AND 
 
 and a ring breaks away (Fig. 17), which almost 
 immediately contracts again on to the rest of 
 the ball as the speed falls. If I turn it suffi- 
 ciently fast the ring breaks up into a series of 
 balls which you now see. One cannot help 
 
 Fig. 17. 
 
 being reminded of the heavenly bodies by this 
 beautiful experiment of Plateau's, for you see a 
 central body and a series of balls of different 
 sizes all travelling round in the same direction 
 (Fig. 1 8) ; but the forces which are acting in 
 
THE FORCES WHICH MOULD THEM. 49 
 
 the two cases are totally distinct, and what you 
 see has nothing whatever to do with the sun 
 and the planets. 
 
 We have thus seen that a large ball of liquid 
 can be moulded by the elasticity of its skin if 
 
 Fig. 18. 
 
 the disturbing effect of its weight is neutral- 
 ized, as in the last experiment. This disturbing 
 effect is practically of no account in the case 
 of a soap-bubble, because it is so thin that it 
 hardly weighs anything. You all know, of 
 
5<D SOAP-BUBBLES. 
 
 course, that a soap-bubble is perfectly round, 
 and now you know why; it is because the 
 elastic film, trying to become as* small as it 
 can, must take the form which has the smallest 
 surface for its content, and that form is the 
 sphere. I want you to notice here, as with the 
 oil, that a large ^bubble oscillates" much more 
 slowly than a small one when knocked out of 
 shape with a-bat^covered with baize or wool. 
 
 The chief result that I have endeavoured to 
 make clear to-day is this. The outside of a 
 liquid acts as if it were an elastic skin, which 
 will, as far as it is able, so mould the liquid 
 within it that it shall be as small as possi 
 Generally the weight of liquids, especially wl 
 there is a large quantity, is too much for the 
 feebly elastic skin, and its power may not be 
 noticed. The disturbing effect of weight is got 
 rid of by immersing one liquid in another 
 which is equally heavy with which it do v es" not 
 mix, and it is hardly noticed when very small 
 drops are examined, or when a bubble is blown, 
 for in these cases the weight is almost nothing, 
 while the elastic power of the skin is just as 
 great as ever. 
 
LECTURE II. 
 
 I DID not in the last lecture by any direct 
 experiment show that a soap-film or bubble is 
 really elastic, like a pjece of stretched india- 
 rubber* 
 
 A, soap-^bubble^ consisting, as it does, of a thin 
 layer of liquid, which must have of course both 
 an inside and an outside surface or skin, must 
 be elastic, and this is easily shown in many 
 ways. Perhaps the easiest way is to tie a 
 thread across a ring rather loosely, and then to 
 dip the ring into soap water. On taking it 
 out there is a film stretched over the ring, in 
 which the thread moves about quite freely, as 
 you can see upon the screen. But if I break 
 the film on one side, then immediately the 
 thread is pulled by the film on the other side 
 as far as it can go, and it is now tight (Fig. 
 19). You will also notice that it is part of a 
 perfect circle, because that form makes the 
 
space on one side as great, and therefore on 
 the other side, where the film is, as small, 
 as possible. Or again, in this second ring the 
 thread is double for a short distance in the 
 middle. If I break the film between the 
 
 Fig. 19. 
 
 threads they are at once pulled apart, and are 
 pulled into a perfect circle (Fig. 20), because 
 that is the form which makes the space within 
 it as great as possible, and therefore leaves the 
 space outside it as small as possible. You will 
 also notice, that though the circle will not 
 
THE FORCES WHICH MOULD THEM. 53 
 
 allow itself to be pulled out of shape, yet it 
 can move about in the ring quite freely, because 
 such a movement does not make any difference 
 to the space outside it. 
 
 I have now blown a bubble upon a ring 
 
 Fig. 20. 
 
 of wire. I shall hang a small ring upon it, 
 and to show more clearly what is happening, 
 I shall blow a little smoke into the bubble. 
 Now that I have broken the film inside the lower 
 ring, you will see the smoke being driven out 
 and the ring lifted up, both of which show the 
 
54 
 
 SOAP-BUBBLES, AND 
 
 elastic nature of the film. Or again, I have 
 blown a bubble on the end of a wide pipe ; on 
 holding the open end of the pipe to a candle 
 flame, the outrushing air blows out the flame 
 at- once, which shows that the soap-bubble is 
 
 Fig. 21. 
 
 acting like an elastic bag (Fig. 21). You 
 now see that, owing to the elastic skin of a 
 soap-bubble, the air inside is under pressure 
 and will get out if it can. Which would you 
 think would squeeze the air inside it most, a 
 large or a small bubble ? We will find out by 
 
THE FORCES WHICH MOULD THEM. 55 
 
 trying, and then see if we can tell why. You 
 now see two pipes each with a tap. These are 
 joined together by a third pipe in which there 
 is a third tap. I will first blow one bubble 
 and shut it off with the tap I (Fig. 22), and 
 
 Fig. 22. 
 
 then the other, and shut it off with the tap 2. 
 They are now nearly equal in size, but the air 
 cannot yet pass from one to the other because 
 the tap 3 is turned off. Now if the pressure 
 in the largest one is greatest it will blow 
 air into the other when I open this tap 9 
 
56 SOAP-BUBBLES, AND 
 
 until they are equal in size; if, on the other 
 hand, the pressure in the small one is greatest, 
 it will blow air into the large one, and will itself 
 get smaller until it has quite disappeared. We 
 will now try the experiment. You see imme- 
 diately that I open the tap 3 the small bubble 
 shuts up and blows out the large one, thus 
 showing that there is a greater pressure in a 
 small than in a large bubble. The directions 
 in which the air and the bubble move is in- 
 dicated in the figure by arrows. I want you 
 particularly to notice and remember this, 
 because this is an experiment on which a 
 great deal depends. To impress this upon 
 your memory I shall show the same thing in 
 another way. There is in front of the lantern 
 a little tube shaped like a U half filled with 
 water. One end of the U is joined to a pipe on 
 which a bubble can be blown (Fig. 23). You 
 will now be able to see how the pressure 
 changes as the bubble increases in size, because 
 the water will be displaced more when the pres- 
 sure is more, and less when it is less. Now 
 that there is a very small bubble, the pressure 
 as measured by the water is about one quarter 
 of an inch on the scale. The bubble is grow- 
 
THE FORCES WHICH MOULD THEM. 57 
 
 ing and the pressure indicated by the water in 
 the gauge is falling, until, when the bubble is 
 double its former size, the pressure is only 
 half what it was ; and this is always true, the 
 
 Fig. 23. 
 
 smaller the bubble the greater the pressure. 
 As the film is always stretched with the same 
 force, whatever size the bubble is, it is clear 
 that the pressure inside can only depend upon 
 the curvature of a bubble. In the case of 
 
58 
 
 lines, our ordinary language tells us, that the 
 larger a circle is the less is its curvature; a 
 piece of a small circle is said to be a quick 
 or a sharp curve, while a piece of a great 
 circle is only slightly curved ; and if you 
 take a piece of a very large circle indeed, then 
 you cannot tell it from a straight line, and you 
 say it is not curved at all. With a part of the 
 surface of a ball it is just the same the larger 
 the ball the less it is curved ; and if the ball is 
 very large indeed, say 8000 miles across, you 
 cannot tell a small piece of it from a true 
 plane. Level water is part of such a surface, 
 and you know that still water in a basin appears 
 perfectly flat, though in a very large lake or the 
 sea you can see that it is curved. We have ] 
 seen that in large bubbles the pressure is little I 
 and the curvature is little, while in small bubbles i 
 the pressure is great and the curvature is great. 
 The pressure and the curvature rise and fall 
 together. We have now learnt the lesson 
 which the experiment of the two bubbles, one 
 blown out by the other, teaches us. 
 
 A ball or sphere is not the only form which 
 you can give to a soap-bubble. If you take 
 a bubble between two rings, you can pull it 
 
THE FORCES WHICH MOULD THEM. 
 
 59 
 
 out until at last it has the shape of a round 
 straight tube or cylinder as it is called. We 
 have spoken of the curvature of a ball or 
 sphere ; now what is the curvature of a cylinder ? 
 Looked at sideways, the edge of the wooden 
 cylinder upon the table appears straight, i. e. 
 not curved at all ; but looked at from above 
 
 SIDE 
 
 VIEW 
 
 Fig. 24. 
 
 it appears round, and is seen to have a definite 
 curvature (Fig. 24). What then is the curva- 
 ture of the surface of a cylinder? We have 
 seen that the pressure in a bubble depends upon 
 the curvature when they are spheres, and this 
 is true whatever shape they have. If, then, we 
 find what sized sphere will produce the same 
 pressure upon the air inside that a cylinder 
 does, then we shall know that the curvature of 
 
60 SOAP-BUBBLES, AND 
 
 the cylinder is the same as that of the sphere 
 which balances it. Now at each end of a 
 short tube I shall blow an ordinary bubble, 
 but I shall pull the lower bubble by means 
 of another tube into the cylindrical form, and 
 finally blow in more or less air until the sides 
 
 Fig. 25. 
 
 of the cylinder are perfectly straight. That is 
 now done (Fig. 25), and the pressure in the 
 two bubbles must be exactly the same, as there 
 is a free passage of air between the two. On 
 measuring them you see that the sphere is 
 exactly double the cylinder in diameter. But 
 
THE FORCES WHICH MOULD THEM. 6 1 
 
 this sphere has only half the curvature that a 
 sphere half its diameter would have. Therefore 
 the cylinder, which we know has the same 
 curvature that the large sphere has, because 
 the two balance, has only half the curvature of 
 a sphere of its own diameter, and the pressure 
 in it is only half that in a sphere of its own 
 diameter. 
 
 I must now make one more step in explain- 
 ing this question of curvature. Now that the 
 cylinder and sphere are balanced I shall blow 
 in more air, making the sphere larger; what 
 will happen to the cylinder ? The cylinder is, 
 as you see, very short ; will it become blown 
 .out too, or what will happen r Now that I am 
 blowing in air you see the sphere enlarging, 
 thus relieving the pressure ; the cylinder 
 develops a waist, it is no longer a cylinder, 
 the sides are curved inwards. As I go on blow- 
 ing and enlarging the sphere, they go on falling 
 inwards, but not indefinitely. If I were to blow 
 the upper bubble till it was of an enormous 
 size the pressure would become extremely 
 small. Let us make the pressure nothing at 
 all at once by simply breaking the upper 
 bubble, thus allowing the air a free passage 
 
62 SOAP-BUBBLES, AND 
 
 from the inside to the outside of what was the 
 cylinder. Let me repeat this experiment on 
 a larger scale. I have two large glass rings, 
 between which I can draw out a film of the 
 
 Fig. 26. 
 
 same kind. Not only is the outline of the 
 soap-film curved inwards, but it is exactly the 
 same as the smaller one in shape (Fig. 26). 
 As there is now no pressure there ought to be 
 
THE FORCES WHICH MOULD THEM. 63 
 
 no curvature, if what I have said is correct. 
 But look at the soap-film. Who would 
 venture to say that that was not curved ? and 
 yet we had satisfied ourselves that the pres- 
 sure and the curvature rose and fell together. 
 We now seem to have come to an absurd 
 conclusion. Because the pressure is reduced 
 to nothing we say the surface must have no 
 curvature, and yet a glance is sufficient to 
 show that the film is so far curved as to have 
 a most elegant waist. Now look at the plaster 
 model on the table, which is a model of a 
 mathematical figure which also has a waist. 
 
 Let us therefore examine this cast more in 
 detail. I have a disc of card which has exactly 
 the same diameter as the waist of the cast. I 
 now hold this edgeways against the waist 
 (Fig. 27), and though you can see that it does 
 not fit the whole curve, it fits the part close to 
 the waist perfectly. This then shows that this 
 part of the cast would appear curved inwards 
 if you looked at it sideways, to the same extent 
 that it would appear curved outwards if you 
 could see it from above. So considering the 
 waist only, it is curved both towards the inside 
 and also away from the inside according to the 
 
64 SOAP-BUBBLES, AND 
 
 way you look at it, and to the same extent. 
 The curvature inwards would make the pres- 
 sure inside less, and the curvature outwards 
 would make it more, and as they are equal 
 they just balance, and there is no pressure at 
 all. If we could in the same way examine the 
 
 Fig. 27. 
 
 bubble with the waist, we should find that this 
 was true not only at the waist but at every part 
 of it. Any curved surface like this which at 
 every point is equally curved opposite ways, 
 is called a surface of no curvature, and so what 
 seemed an absurdity is now explained. Now 
 this surface, which is the only one of the kind 
 
THE FORCES WHICH MOULD THEM. 65 
 
 symmetrical about an axis, except a flat sur- 
 face, is called a catenoid, because it is like a 
 chain, as you will see directly, and, as you 
 know, catena is the Latin for a chain. I shall 
 now hang a chain in a loop from a level stick, 
 and throw a strong light upon it, so that you 
 can see it well (Fig. 28). This is exactly the 
 
 Fig. 28. 
 
 same shape as the side of a bubble drawn 
 out between two rings, and open at the end 
 to the air. 1 
 
 Let us now take two rings, and having placed 
 a bubble between them, gradually alter the 
 pressure. You can tell what the pressure is 
 
 1 If the reader finds these geometrical relations too 
 difficult to follow, he or she should skip the next pages, 
 and go on again at " We have found . . ." p. 7 7. 
 
66 SOAP-BUBBLES, AND 
 
 by looking at the part of the film which 
 covers either ring, which I shall call the cap. 
 This must be part of a sphere, and we know 
 that the curvature of this and the pressure 
 inside rise and fall together. I have now 
 adjusted the bubble so that it is a nearly 
 
 perfect sphere. If 
 I blow in more air 
 the caps become 
 more curved, show- 
 ing an increased 
 pressure, and the 
 Fig 29 sides bulge out even 
 
 more than those of 
 
 a sphere (Fig. 29). I have now brought the 
 whole bubble back to the spherical form. A 
 little increased pressure, as shown by the 
 increased curvature of the cap, makes the 
 sides bulge more; a little less pressure, as 
 shown by the flattening of the caps, makes 
 the sides bulge less. Now the sides are 
 straight, and the cap, as we have already 
 seen, forms part of a sphere of twice the 
 diameter of the cylinder. I am still further 
 reducing the pressure until the caps are plane, 
 that is, not curved at all. There is now no 
 
THE FORCES WHICH MOULD THEM. 67 
 
 pressure inside, and therefore the sides have, 
 as we have already seen, taken the form of a 
 hanging chain ; and now, finally, the pressure 
 inside is less than that outside, as you can 
 see by the caps being drawn inwards, and the 
 sides have even a smaller waist than the cate- 
 noid. We have now seen seven curves as we 
 gradually reduced the pressure, namely 
 
 1. Outside the sphere. 
 
 2. The sphere. 
 
 3. Between the sphere and the cylinder. 
 
 4. The cylinder. 
 
 5. Between the cylinder and the catenoid. 
 
 6. The catenoid. 
 
 7. Inside the catenoid. 
 
 Now I am not going to say much more 
 about all these curves, but I must refer to the 
 very curious properties that they possess. In 
 the first place, they must all of them have the 
 same curvature in every part as the portion of 
 the sphere which forms the cap ; in the second 
 place, they must all be the curves of the least 
 possible surface which can enclose the air and 
 join the rings as well. And finally, since they 
 pass insensibly from one to the other as the 
 pressure gradually changes, though they are 
 
68 SOAP-BUBBLES, AND 
 
 distinct curves there must be some curious and 
 intimate relation between them. Tl though 
 it is a little difficult, I shall explain. If I were 
 to say that these curves are the roulettes of 
 the conic sections I suppose I should alarm 
 you, and at the same time explain nothing, so 
 I shall not put it in that way ; but instead, I 
 shall show you a simple experiment which will 
 throw some light upon the subject, which you 
 can try for yourselves at home. 
 
 I have here a common bedroom candlestick 
 with a flat round base. Hold the candlestick 
 exactly upright near to a white wall, then you 
 will see the shadow of the base on the wall 
 below, and the outline of the shadow is a 
 symmetrical curve, called a hyperbola. Gradu- 
 ally tilt the candle away from the wall, you 
 will then notice the sides of the shadow 
 gradually branch away less and less, and when 
 you have so far tilted the candle away from 
 the wall that the flame is exactly above the 
 edge of the base, and you will know when 
 this is the case, because then the falling grease 
 will just fall on the edge of the candlestick and 
 splash on to the carpet, I have it so now, 
 the sides of the shadow near the floor will be 
 
THE FORCES WHICH MOULD THEM. 69 
 
 almost parallel (Fig. 30), and the shape of the 
 shadov '11 have become a curve, known as a 
 parabola; and now when the candlestick is 
 still more tilted, so that the grease misses the 
 
 Fig. 30. 
 
 base altogether and falls in a gentle stream 
 upon the carpet, you will see that the sides of 
 the shadow have curled round and met on the 
 wall, and you now have a curve like an oval, 
 except that the two ends are alike, and this is 
 
70 SOAP-BUBBLES, AND 
 
 called an ellipse. If you go on tilting the 
 candlestick, then when the candle is just 
 level, and the grease pouring away, the shadow 
 will be almost a circle ; it would be an exact 
 circle if the flame did not flare up. Now 
 if you go on tilting the candle, until at last 
 the candlestick is upside down, the curves 
 already obtained will be reproduced in the 
 reverse order, but above instead of below you. 
 You may well ask what all this has to do 
 with a soap-bubble. You will see in a moment. 
 When you light a candle, the base of the 
 candlestick throws the space behind it into 
 darkness, and the form of this dark space, 
 which is everywhere round like the base, and 
 gets larger as you get farther from the flame, 
 is a cone, like the wooden model on the table. 
 The shadow cast on the wall is of course the 
 part of the wall which is within this cone. It 
 is the same shape that you would find if you 
 were to cut a cone through with a saw, and 
 so these curves which I have shown you are 
 called conic sections. You can see some of 
 them already made in the wooden model on 
 the table. If you look at the diagram on the 
 wall (Fig. 31), you will see a complete cone at 
 
THE FORCES WHICH MOULD THEM, 
 
 first upright 
 (A) 3 then being 
 gradually tilted 
 over into the 
 positions that 
 I have speci- 
 fied. The black 
 line in the 
 upper part of 
 the diagram 
 shows where 
 the cone is cut 
 through, and 
 the shaded area 
 below shows 
 the true shape 
 of these shad- 
 ows, or pieces 
 cut off, which 
 are called sec- 
 tions. Now in 
 each of these 
 sections there 
 are either one 
 or two points, 
 each of which 
 
72 SOAP-BUBBLES, AND 
 
 is called a focus, and these are indicated by 
 conspicuous dots. In the case of the circle 
 (D Fig. 31), this point is also the centre. Now 
 if this circle is made to roll like a wheel 
 along the straight line drawn just below it, a 
 pencil at the centre will rule the straight line 
 which is dotted in the lower part of the figure ; 
 but if we were to make wheels of the shapes of 
 any of the other sections, a pencil at the focus 
 would certainly not draw a straight line. 
 What shape it would draw is not at once 
 evident. First consider any of the elliptic 
 sections (C, E, or F) which you see on either 
 side of the circle. If these were wheels, and 
 were made to roll, the pencil as it moved along 
 would also move up and down, and the line it 
 would draw is shown dotted as before in the 
 lower part of the figure. In the same way the 
 other curves, if made to roll along a straight 
 line, would cause pencils at their focal points 
 to draw the other dotted lines. 
 
 We are now almost able to see what the 
 conic section has to do with a soap-bubble. 
 When a soap-bubble was blown between two 
 rings, and the pressure inside was varied, its 
 outline went through a series of forms, some 
 
THE FORCES WHICH 
 
 of which are represented by the dotted lines 
 in the lower part of the figure, but in every 
 case they could have been accurately drawn by 
 a pencil at the focus of a suitable conic section 
 made to roll on a straight line. I called one 
 of the bubble forms, if you remember, by its 
 name, catcnoid ; this is produced when there 
 is no pressure. The dotted curve in the second 
 figure B is this one; and to show that this 
 catenary can be so drawn, I shall roll upon a 
 straight edge a board made into the form of 
 the corresponding section, which is called a 
 parabola, and let the chalk at its focus draw 
 its curve upon the black board. There is 
 the curve, and it is as I said, exactly the curve 
 that a chain makes when hung by its two ends. 
 Now that a chain is so hung you see that it 
 exactly lies over the chalk line. 
 
 All this is rather difficult to understand, 
 but as these forms which a soap-bubble takes 
 afford a beautiful example of the most im- 
 portant principle of continuity, I thought it 
 would be a pity to pass it by. It may be put 
 in this way. A series of bubbles may be blown 
 between a pair of rings. If the pressures are 
 different the curves must be different. In 
 
74 SOAP-BUBBLES, AND 
 
 blowing them the pressures slowly and continu- 
 ously change, and so the curves cannot be alto- 
 gether different in kind. Though they may 
 be different curves, they also must pass slowly 
 and continuously one into the other. We find 
 the bubble curves can be drawn by rolling 
 wheels made in the shape of the conic sections 
 on a straight line, and so the conic sections, 
 though distinct curves, must pass slowly and 
 continuously one into the other. This we saw 
 was the case, because as the candle was slowly 
 tilted the curves did as a fact slowly and in- 
 sensibly change from one to the other. There 
 was only one parabola, and that was formed 
 when the side of the cone was parallel to the 
 plane of section, that is when the falling grease 
 just touched the edge of the candlestick; 
 there is only one bubble with no pressure, the 
 catenoid, and this is drawn by rolling the para- 
 bola. As the cone is gradually inclined more, 
 so the sections become at first long ellipses, 
 which gradually become more and more round 
 until a circle is reached, after which they 
 become more and more narrow until a line is 
 reached. The corresponding bubble curves 
 are produced by a gradually increasing pressure, 
 
THE FORCES WHICH MOULD THEM. 75 
 
 and, as the diagram shows, these bubble curves 
 are at first wavy (C), then they become straight 
 when a cylinder is formed (D), then they be- 
 come wavy again (E and F), and at last, when 
 the cutting plane, i. e. the black line in the 
 upper figure, passes through the vertex of the 
 cone the waves become a series of semicircles, 
 indicating the ordinary spherical soap-bubble. 
 Now if the cone is inclined ever so little more a 
 new shape of section is seen (G), and this being 
 rolled, draws a curious curve with a loop in it ; 
 but how this is so it would take too long to 
 explain. It would also take .too long to trace 
 the further positions of the cone, and to trace 
 the corresponding sections and bubble curves 
 got by rolling them. Careful inspection of the 
 diagram may be sufficient to enable you to 
 work out for yourselves what will happen in all 
 cases. I should explain that the bubble sur- 
 faces are obtained by spinning the dotted lines 
 about the straight line in the lower part of 
 Fig. 31 as an axis. 
 
 As you will soon find out if you try, you 
 cannot make with a soap-bubble a great length 
 of any of these curves at one time, but you 
 may get pieces of any of them with no more 
 
76 SOAP-BUBBLES, AND 
 
 apparatus than a few wire rings, a pipe,, and a 
 little soap and water. You can even see the 
 whole of one of the loops of the dotted curve 
 of the first figure (A), which is called a nodoid, 
 not a complete ring, for that is unstable, but a 
 part of such a ring. Take a piece of wire or a 
 match, and fasten one end to a piece of lead, so 
 that it will stand upright in a dish of soap 
 water, and project half an inch or so. Hold 
 with one hand a sheet of glass resting on the 
 match in middle, and blow a bubble in the 
 water against the match. As soon as it 
 touches the glass plate, which should be 
 wetted with the soap solution, it will become 
 a cylinder, which will meet the glass plate in 
 a {rue circle. Now very slowly incline the 
 plate. The bubble will at once work round 
 to the lowest side, and try to pull itself away 
 from the match stick, and in doing so it will 
 develop a loop of the nodoid, which would be 
 .exactly true in form if the match or wire were 
 slightly bent, so as to meet both the glass and 
 the surface of the soap water at a right angle. 
 I have described this in detail, because it is 
 not generally known that a complete loop of 
 the nodoid can be made with a soap-bubble. 
 
THE FORCES WHICH MOULD THEM. 77 
 
 We have found that the pressure in a short 
 cylinder gets less if it begins to develop a 
 waist, and greater if it begins to bulge. Let us 
 therefore try and balance one with a bulge 
 against another with a waist. Immediately that 
 I open the tap and let the air pass, the one 
 
 Fig. 32. 
 
 with a bulge blows air round to the one with 
 a waist and they both become straight. In 
 Fig. 32 the direction of the movement of the 
 air and of the sides of the bubble is indi- 
 cated by arrows. Let us next try the same 
 
78 SOAP-BUBBLES, AND 
 
 experiment with a pair of rather longer cylinders, 
 say about twice as long as they are wide. 
 They are now ready, one with a bulge and one 
 with a waist. Directly I open the tap, and let 
 the air pass from one to the other, the one with 
 
 Fig. 33- 
 
 a waist blows out the other still more (Fig. 33), 
 until at last it has shut itself up. It there- 
 fore behaves exactly in the opposite way that 
 the short cylinder did. If you try pairs of 
 cylinders of different lengths you will find that 
 the change occurs when they are just over one 
 
THE FORCES WHICH MOULD THEM. 
 
 79 
 
 and a half times as long as they are wide. 
 Now if you imagine one of these tubes joined 
 on to the end of the other, you will see that a 
 cylinder more than about three times as long 
 as it is wide cannot last more than a moment; 
 because if one end were to 
 contract ever so little the 
 pressure there would increase, 
 and the narrow end would 
 blow air into the wider end _ 
 (Fig. 34), until the sides of 
 the narrow end met one 
 another. The exact length 
 of the longest cylinder that <~ 
 is stable, is a little more than 
 three diameters. The cylinder 
 just becomes unstable when 
 its length is equal to its cir- 
 cumference, and this is 3* 
 
 *ia* ^*t* 
 
 diameters almost exactly. 
 
 I will gradually separate these rings, keep- 
 ing up a supply of air, and you will see 
 that when the tube gets nearly three times 
 as long as it is wide it is getting very diffi- 
 cult to manage, and then suddenly it grows 
 a waist nearer one end than the other, and 
 
8o SOAP-BUBBLES, AND 
 
 breaks off forming a pair of separate and 
 unequal bubbles. 
 
 If now you have a cylinder of liquid of great 
 length suddenly formed and left to itself, it 
 clearly cannot retain that form. It must break 
 up into a series of drops. Unfortunately the 
 changes go on so quickly in a falling stream 
 of water that no one by merely looking at it 
 could follow the movements of the separate 
 drops, but I hope to be able to show to you 
 in two or three ways exactly what is happen- 
 ing. You may remember that we were able 
 to make a large drop of one liquid in another, 
 because in this way the effect of the weight was 
 neutralized, and as large drops oscillate or 
 change their shape much more slowly than 
 small, it is more easy to see what is happen- 
 ing. I have in this glass box water coloured 
 blue on which is floating paraffin, made heavier 
 by mixing with it a bad-smelling and dangerous 
 liquid called bisulphide of carbon. 
 
 The water is only a very little heavier than 
 the mixture. If I now dip a pipe into the 
 water and let it fill, I can then raise it and 
 allow drops to slowly form. Drops as large 
 as a shilling are now forming, and when each 
 
THE FORCES WHICH MOULD THEM. 8 1 
 
 one has reached its full size, a neck forms 
 above it, which is drawn out by the falling 
 drop into a little cylinder. 
 You will notice that the liquid 
 of the neck has gathered it- 
 self into a little drop which 
 falls away just after the large 
 drop. The action is now 
 going on so slowly that you 
 can follow it. Fig. 35 con- 
 tains forty-three consecutive 
 views of the growth and fall of 
 the drop taken photographic- Sce Dia Z ram at 
 ally at intervals of one-twen- the end of the 
 tieth of a second. For the Book. 
 
 use to which this figure is to 
 be put, see page 149. If I 
 again fill the pipe with water, 
 and this time draw it rapidly 
 out of the liquid, I shall leave 
 behind a cylinder which will 
 break up into balls, as you 
 can easily see (Fig. 36). I 
 should like now to show^you, 
 as I have this apparatus^in its 
 place, that you can blow bubbles of water 
 
8 2 SOAP-BUBBLES, AND 
 
 containing paraffin in the paraffin mixture, 
 
 to 
 
 
 
THE FORCES WHICH MOULD THEM. 83 
 
 and you will see some which have other 
 bubbles and drops of one or other liquid inside 
 again,, One of these compound bubble drops 
 is now resting stationary on a heavier layer of 
 liquid, so that you can see it all the better 
 
 Fig. 37- 
 
 - 37). If I rapidly draw the pipe out of 
 the box I shall leave a long cylindrical bubble 
 of water containing paraffin, and this, as was 
 the case with the water-cylinder, slowly breaks 
 up into spherical bubbles. 
 
 Having now shown that a very large liquid 
 
84 SOAP-BUBBLES, AND 
 
 cylinder breaks up regularly into drops, I shall 
 next go the other extreme, and take as an 
 example an excessively fine cylinder. You see 
 
 Fig. 38. 
 
 a photograph of a spider on her geometrical 
 web (Fig. 38). If I had time I should like 
 to tell you how the spider goes to work to 
 make this beautiful structure, and a great deal 
 

 
 HE FORCES WHICH MOULD THEM. 85 
 
 about these wonderful creatures, but I must do 
 no more than show you that there are two 
 kinds of web those that point outwards, which 
 are hard and smooth, and those that go round 
 and round, which are very elastic, and which 
 are covered with beads of a sticky liquid. 
 Now there are in a good web over a quarter 
 of a million of these beads which catch the 
 flies for the spider's dinner. A spider makes 
 a whole web in an hour, and generally has to 
 make a new one every day. She would not 
 be able to go round and stick all these in 
 place, even if she knew how, because she would 
 not have time. Instead of this she makes use 
 of the way that a liquid cylinder breaks up 
 into beads as follows. She spins a thread, 
 and at the same time wets it with a sticky 
 liquid, which of course is at first a cylinder. 
 This cannot remain a cylinder, but breaks up 
 into beads, as the photograph taken with a 
 microscope from a real web beautifully shows 
 (Fig. 39). You see the alternate large and 
 small drops, and sometimes you even see extra 
 small drops between these again. In order 
 that you may see exactly how large these 
 beads really are, I have placed alongside a 
 
86 
 
 scale of thousandths of an inch, 
 which was photographed at the 
 same time. To prove to you that 
 this is what happens, I shall now 
 show you a web that I have made 
 myself by stroking a quartz fibre 
 with a straw dipped in castor-oil. 
 The same alternate large and 
 small beads are again visible just 
 as perfect as they were in the 
 spider's web. In fact it is impos- 
 sible to distinguish between one 
 of my beaded webs and a spider's 
 by looking at them. -And there 
 is this additional similarity my 
 webs are just as good as a spider's 
 for catching flies. You might 
 say that a large cylinder of water 
 in oil, or a microscopic cylinder 
 on a thread, is not the same as 
 an ordinary jet of water, and that 
 you would like to see if it be- 
 
 5 10 
 
 Scale of thousanbths of an Inch 
 
THE FORCES WHICH MOULD THEM. 87 
 
 haves as I have described. The next photo- 
 graph (Fig. 40), taken by the light of an 
 instantaneous electric spark, 
 and magnified three and a 
 quarter times, shows a fine 
 column of water falling from 
 a jet. You will now see that 
 it is at first a cylinder, that 
 as it goes down necks and 
 bulges begin to form, and at 
 last beads separate, and you 
 can see the little drops as well. 
 The beads also vibrate, be- 
 coming alternately long and 
 wide, and there can be no 
 doubt that the sparkling por- 
 tion of a jet, though it ap- 
 pears continuous, is really 
 made up of beads which pass 
 so rapidly before the eye that 
 it is impossible to follow 
 them. (I should explain that 
 for a reason which will ap- 
 pear later, I made a loud note 
 by whistling into a key at the 
 time that this photograph was taken.) 
 
88 
 
 Lord Rayleigh has shown that in a stream 
 of water one twenty-fifth of an inch in diameter, 
 necks impressed upon the stream, even though 
 imperceptible, develop a thousandfold in depth 
 every fortieth of a second, and thus it is not 
 difficult to understand that in such a stream 
 the water is already broken through before it 
 has fallen many inches. He has also shown 
 that free water drops vibrate at a rate which 
 may be found as follows. A drop two inches 
 in diameter makes one complete vibration in 
 one second. If the diameter is reduced to one 
 quarter of its amount, the time of vibration 
 will be reduced to one-eighth, or if the diameter 
 is reduced to one-hundredth, the time will be 
 reduced to one-thousandth, and so on. The 
 same relation between the diameter and the 
 time of breaking up applies also to cylinders. 
 We can at once see how fast a bead of water 
 the size of one of those in the spider's web 
 would vibrate if pulled out of shape, and let 
 go suddenly. If we take the diameter as being 
 one eight-hundredth of an inch, and it is 
 really even finer, then the bead would have a 
 diameter of one sixteen-hundredth of a two- 
 inch bead, which makes one vibration in one 
 
THE FORCES WHICH MOULD THEM. 89 
 
 second. It will therefore vibrate sixty-four 
 thousand times as fast, or sixty-four thousand 
 times a second. Water-drops the size of the 
 little beads, with a diameter of rather less than 
 one three-thousandth of an inch, would vibrate 
 half a million times a second, under the sole 
 influence of the feebly elastic skin of water ! 
 We thus see how powerful is the influence of 
 the feebly elastic water-skin on drops of water 
 that are sufficiently small. 
 
 I shall now cause a small fountain to play, 
 and shall allow the water as it falls to patter 
 upon a sheet of paper. You can see both the 
 fountain itself and its shadow upon the screen. 
 You will notice that the water comes out of the 
 nozzle as a smooth cylinder, that it presently 
 begins to glitter, and that the separate drops 
 scatter over a great space (Fig. 41). Now why 
 should the drops scatter ? All the water comes 
 out of the jet at the same rate and starts in 
 the same direction, and yet after a short way the 
 separate drops by no means follow the same 
 paths. Now instead of explaining this, and 
 then showing experiments to test the truth of 
 the explanation, I shall reverse the usual order, 
 and show one or two experiments first, which 
 
90 SOAP-BUBBLES, AND 
 
 I think you will all agree are so like magic, so 
 wonderful are they and yet so simple, that if 
 they had been performed a few hundred 
 years ago, the rash person who showed them 
 
 Fig. 41. 
 
 might have run a serious risk of being burnt 
 alive. 
 
 You now see the water of the jet scattering 
 in all directions, and you hear it making a 
 pattering sound on the paper on which it falls. 
 I take out of my pocket a stick of sealing-wax 
 and instantly all is changed, even though I am 
 
THE FORCES WHICH MOULD THEM. 9! 
 
 some way off and can touch nothing. The 
 water ceases to scatter ; it travels in one con- 
 tinuous line (Fig. 42), and falls upon the paper 
 making a loud rattling noise which must re- 
 mind you of the rain of a thunder-storm. 
 
 Fig. 42. 
 
 I come a little nearer to the fountain and the 
 water scatters again, but this time in quite a 
 different way. The falling drops are much 
 larger than they were before. Directly I hide 
 the sealing-wax the jet of water recovers its old 
 
92 SOAP-BUBBLES, AND 
 
 appearance, and as soon as the sealing-wax is 
 taken out it travels in a single line again. 
 
 Now instead of the sealing-wax I shall take 
 a smoky flame easily made by dipping some 
 cotton-wool on the end of a stick into benzine, 
 and lighting it. As long as the flame is held 
 away from the fountain it produces no effect, 
 but the instant that I bring it near so that the 
 water passes through the flame, the fountain 
 ceases to scatter ; it all runs in one line and falls 
 in a dirty black stream upon the paper. Ever 
 so little oil fed into the jet from a tube as 
 fine as a hair does exactly the same thing. 
 
 I shall now set a tuning-fork sounding at the 
 other side of the table. The fountain has not 
 altered in appearance. I now touch the stand 
 of the tuning-fork with a long stick which rests 
 against the nozzle. Again the water gathers 
 itself together even more perfectly than before, 
 and the paper upon which it falls is humming 
 out a note which is the same as that produced 
 by the tuning-fork. If I alter the rate at 
 which the water flows you will see that the 
 appearance is changed again, but it is never 
 like a jet which is not acted upon by a musical 
 sound. Sometimes the fountain breaks up 
 
THE FORCES WHICH MOULD THEM. 
 
 93 
 
 into two or three and sometimes many more 
 distinct lines, as though it came out of as many 
 tubes of different sizes and pointing in slightly 
 different directions (Fig. 43). The effect of 
 different notes could be very easily shown if 
 any one were to sing to the piece of wood by 
 
 43- 
 
 which the jet is held. I can make noises of 
 different pitches, which for this purpose are 
 perhaps better than musical notes, and you 
 can see that with every new noise the fountain 
 puts on a different appearance. You may well 
 
94 SOAP-BUBBLES. 
 
 wonder how these trifling influences sealing- 
 wax, the smoky flame, or the more or less 
 musical noise should produce this mysterious 
 result, but the explanation is not so difficult 
 as you might expect. 
 
 I hope to make this clear when we meet 
 again. 
 
LECTURE III. 
 
 AT the conclusion of the last lecture I 
 showed you some curious experiments with a 
 fountain of water, which I have now to explain. 
 Consider what I have said about a liquid 
 cylinder. If it is a little more than three 
 times as long as it is wide, it cannot retain its 
 form ; if it is made very much more than three 
 times as long, it will break up into a series of 
 beads. Now, if in any way a series of necks 
 could be developed upon a cylinder which were 
 less than three diameters apart, some of them 
 would tend to heal up, because a piece of a 
 cylinder less than three diameters long is stable. 
 If they were about three diameters apart, the 
 form being "then unstable, the necks would get 
 more pronounced in time^ and would at last 
 break through, so that beads would be formed. 
 If necks were made at distances more than 
 three diameters apart, then the cylinder would 
 go on breaking up by the narrowing of these 
 
96 SOAP-BUBBLES, AND 
 
 necks, and it would most easily break up into 
 drops when the necks were just four and a half 
 diameters apart. In other words, if a fountain 
 were to issue from a nozzle held perfectly still, 
 the water would most easily break into beads at 
 the distance of four and a half diameters apart, 
 but it would break up into a greater number 
 closer together, or a smaller number further 
 apart, if by slight disturbances of the jet very 
 slight waists were impressed upon the issuing 
 cylinder of water. When you make a fountain 
 play from a jet which you hold as still as 
 possible, there are still accidental tremors of all 
 kinds, which impress upon the issuing cylinder 
 slightly narrow and wide places at irregular dis- 
 tances, and so the cylinder breaks up irregu- 
 larly into drops of different sizes and at differ- 
 ent distances apart. Now these drops, as they 
 are in the act of separating from one another, 
 and are drawing out the waist, as you have 
 seen, are being pulled for the moment towards 
 one another by the elasticity of the skin of the 
 waist ; and, as they are free in the air to move 
 as they will, this will cause the hinder one to 
 hurry on, and the more forward one to lag 
 behind, so that unless they are all exactly 
 
THE FORCES WHICH MOULD THEM. 97 
 
 alike both in size and distance apart they will 
 many of them bounce together before long. 
 You would expect when they hit one another 
 afterwards that they would join, but I shall be 
 able to show you in a moment that they do 
 not ; they act like two india-rubber balls, and 
 bounce away again. Now it is not difficult to 
 see that if you have a series of drops of differ- 
 ent sizes and at irregular distances bouncing 
 against one another frequently, they will tend 
 to separate and to fall, as we have seen, on all 
 parts of the paper down below. What did 
 the sealing-wax or the smoky flame do ? and 
 what can the musical sound do to stop this 
 from happening? Let me first take the 
 sealing-wax. A piece of sealing-wax rubbed 
 on your coat is electrified, and will attract light 
 bits of paper up to it. The sealing-wax acts 
 electrically on the different water-drops, causing 
 them to attract one another, feebly, it is true, 
 but with sufficient power where they meet to 
 make them break through the air-film between 
 them and join. To show that this is no fancy, 
 I have now in front of the lantern two foun- 
 tains of clean water coming from separate 
 bottles, and you can see that they bounce 
 
9 8 
 
 apart perfectly (Fig. 44). To show that they 
 do really bounce, I have coloured the water in 
 the two bottles differently. The sealing-wax 
 is now in my pocket ; I shall retire to the other 
 side of the room, and the instant it appears 
 
 Fig. 44. 
 
 the jets of water coalesce (Fig. 45). This 
 may be repeated as often as you like, and 
 it never fails. These two bouncing jets are in 
 fact one of the most delicate tests for the pre- 
 sence of electricity that exist. You are now 
 able to understand the first experiment. The 
 
THE FORCES WHICH MOULD THEM. 99 
 
 separate drops which bounced away from one 
 another, and scattered in all directions, are 
 unable to bounce when the sealing-wax is held 
 up, because of its electrical action. They 
 therefore unite, and the result is, that instead 
 
 Fig- 45- 
 
 of a great number of little drops falling all 
 over the paper, the stream pours in a single 
 line, and great drops, such as you see in a 
 thunder-storm, fall on the top of one another. 
 There can be no doubt that it is for this reason 
 that the drops of rain in a thunder-storm are 
 
100 
 
 so large. This experiment and its explanation 
 are due to Lord Rayleigh. 
 
 The smoky flame, as lately shown by Mr. 
 Bidwell, does the same thing. The reason 
 probably is that the dirt breaks .through the 
 air-film, just as dust in the air will make the 
 two fountains join as they did when they were 
 electrified. However, it is possible that oily 
 matter condensed on the water may have some- 
 thing to do with the effect observed, because 
 oil alone acts quite as well as a flame, but the 
 action of oil in this case, as when it smooths 
 a stormy sea, is not by any means so easily 
 understood. 
 
 When I held the sealing-wax closer, the 
 drops coalesced in the same way ; but they 
 were then so much more electrified that they 
 repelled one another as similarly electrified 
 bodies are known -to do, and so the electrical 
 scattering was produced. 
 
 .You possibly already see why the tuning- 
 fork made the drops follow in one line, but 
 I shall explain. A musical note is, as is well 
 known, caused by a rapid vibration ; the more 
 rapid the vibration the higher is the pitch of 
 the note. For instance, I have a tooth-wheel 
 
THE FORCES WHICH MOULD THEM. IOI 
 
 which I can turn round very rapidly if I wish. 
 Now that it is turning slowly you can hear 
 the separate teeth knocking against a card that 
 I am holding in the other hand. I am now 
 turning faster, and the card is giving out a 
 note of a low pitch. As I make the wheel 
 turn faster and faster, the pitch of the note 
 gradually rises, and it would, if I could only 
 turn fast enough, give so high a note that 
 we should not be able to hear it. A tuning- 
 fork vibrates at a certain definite rate, and 
 therefore gives a definite note. The fork now 
 sounding vibrates 128 times in every second. 
 The nozzle, therefore, is made to vibrate, but 
 almost imperceptibly, 128 times a second, and 
 to impress upon the issuing cylinder of water 
 128 imperceptible waists every second. Now 
 it just depends what size the jet is, and how 
 fast the water is issuing, whether these waists 
 are about four and a half diameters apart 
 in the cylinder. If the jet is larger, the water 
 must pass more quickly, or under a greater 
 pressure, for this to be the case ; if the jet is 
 finer, a smaller speed will be sufficient. If it 
 should happen that the waists so made are 
 anywhere, about four diameters apart, then 
 
IO2 SOAP-BUBBLES, AND 
 
 even though they are so slightly developed 
 that if you had an exact drawing of them, you 
 would not be able to detect the slightest change 
 of diameter, they will grow at a great speed, 
 and therefore the water column will break up 
 regularly, every drop will be like the one 
 behind it, and like the one in front of it, and 
 not all different, as is the case when the break- 
 ing of the water merely depends upon acci- 
 dental tremors. If the drops then are all alike 
 in every respect, of course they all follow the 
 same path, and so appear to fall in a continuous 
 stream. If the waists are about four and a 
 half diameters apart, then the jet will break up 
 most easily ; but it will, as I have said, break 
 up under the influence of a considerable range 
 of notes, which cause the waists to be formed 
 at other distances, provided they are more 
 than three diameters apart. If two notes are 
 sounded at the same time, then very often 
 each will produce its own effect, and the result 
 is the alternate formation of drops of different 
 sizes, which then make the jet divide into two 
 separate streams. In this way, three, four, or 
 even many more distinct streams may be 
 produced. 
 
THE FORCES WHICH MOULD THEM. 103 
 
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 a 
 
 o 
 
 ( 
 
 o 
 
 % 
 
 t& 
 
 '-"' U 
 
 o a 
 
 Q 
 
 e 
 
 o 
 
 & o 
 
 o 
 O 
 
 O 
 
 O o 
 
 O 
 
 9 
 O 
 
 o 
 
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104 SOAP-RUBBLES, AND 
 
 I can now show you photographs of some 
 of these musical fountains, taken by the instan- 
 taneous flash of an electric spark, and you can 
 see the separate paths described by the drops 
 of different sizes (Fig. 46). In one photograph 
 there are eight distinct fountains all breaking 
 from the same jet, but following quite distinct 
 paths, each of which is clearly marked out by a 
 perfectly regular series of drops. You can also 
 in these photographs see drops actually in the 
 act of bouncing against one another, and flat- 
 tened when they meet, as if they were india- 
 rubber balls. In the photograph now upon 
 the screen the effect of this rebound, Which 
 occurs at the place marked with a cross, is to 
 hurry on the upper and more forward drop, 
 and to retard the other one, and so to make 
 them travel with slightly different velocities 
 and directions. It is for this reason that they 
 afterwards follow distinct paths. The smaller 
 drops had no doubt been acted on in a similar 
 way, but the part of the fountain where this 
 happened was just outside the photographic 
 plate, and so there is no record of what 
 occurred. The very little drops of which I 
 have so often spoken are generally thrown out 
 
THE FORCES WHICH MOULD THEM. 105 
 
 from the side of a fountain of water under the 
 influence of a musical sound, after which they 
 describe regular little curves of their own, quite 
 distinct from the main stream. They, of 
 course, can only get out sideways after one or 
 two bouncings from the regular drops in front 
 and behind. You can easily show that they 
 are really formed below the place where they 
 first appear, by taking a piece of electrified 
 sealing-wax and holding it near the stream 
 close to the nozzle and gradually raising it. 
 When it comes opposite to the place where the 
 little drops are really formed, it will act on 
 them more powerfully than on the large drops, 
 and immediately pull them out from a place 
 where the moment before none seemed to 
 exist. They will then circulate in perfect 
 little orbits round the sealing-wax, just as the 
 planets do round the sun ; but in this case, 
 being met by the resistance of the air, the 
 orbits are spirals, and the little drops after 
 many revolutions ultimately fall upon the wax, 
 just as the planets would fall into the sun after 
 many revolutions, if their motion through space 
 were interfered with by friction of any kind. 
 There is only one thing needed to make the 
 
IO6 SOAP-BUBBLES, AND 
 
 demonstration of the behaviour of a musical 
 jet complete, and that is, that you should your- 
 selves see these drops in their different posi- 
 tions in an actual fountain of water. Now if I 
 were to produce a powerful electric spark, then 
 it is true that some of you might for an instant 
 catch sight of the drops, but I do not think that 
 most would see anything at all. But if, instead 
 of making merely one flash, I were to make 
 another when each drop had just travelled to 
 the position which the one in front of it occu- 
 pied before, and then another when each drop 
 had moved on one place again, and so on, then 
 all the drops, at the moments that the flashes 
 of light fell upon them, would occupy the same 
 positions, and thus all these drops would appear 
 fixed in the air, though of course they really are 
 travelling fast enough. If, however, I do not 
 quite succeed in keeping exact time with my 
 flashes of light, then a curious appearance will 
 be produced. Suppose, for instance, that the 
 flashes of light follow one another rather too 
 quickly, then each drop will not have had quite 
 time enough to get to its proper place at each 
 flash, and thus at the second flash all the drops 
 will be seen in positions which are just behind 
 
THE FORCES WHICH MOULD THEM. 107 
 
 those which they occupied at the first flash, 
 and in the same way at the third flash they 
 will be seen still further behind their former 
 places, and so on, and therefore they will 
 appear to be moving slowly backwards ; where- 
 as if my flashes do not follow quite quickly 
 enough, then the drops will, every time that 
 there is a flash, have travelled just a little too 
 far, and so they will all appear to be moving 
 slowly forwards. Now let us try the experi- 
 ment. There is the electric lantern sending a 
 powerful beam of light on to the screen. This 
 I bring to a focus with a lens, and then let it 
 pass through a small hole in a piece of card. 
 The light then spreads out and falls upon the 
 screen. The fountain of water is between the 
 card and the screen, and so a shadow is cast 
 which is conspicuous enough. Now I place 
 just behind the card a little electric motor, 
 which will make a disc of card which has six 
 holes near the edge spin round very fast. 
 The holes come one after the other opposite 
 the hole in the fixed card, and so at every 
 turn six flashes of light are produced. When 
 the card is turning about 21 J times a second, 
 then the flashes will follow one another at the 
 
108 SOAP-BUBBLES, AND 
 
 right rate. I have now started the motor, 
 and after a moment or two I shall have 
 obtained the right speed, and this I know by 
 blowing through the holes, when a musical 
 note will be produced, higher than the fork if 
 the speed is too high, and lower than the 
 fork if the speed is too low, and exactly the 
 same as the fork if it is right. 
 
 To make it still more evident when the 
 speed is exactly right, I have placed the tuning- 
 fork also between the light and the screen, so 
 that you may see it illuminated, and its shadow 
 upon the screen. I have not yet allowed the 
 water to flow, but I want you to look at the 
 fork. For a moment I have stopped the 
 motor^ so that the light may be steady, and 
 you can see that the fork is in motion because 
 its legs appear blurred at the ends, where of 
 course the motion is most rapid. Now the 
 motor is started, and almost at once the fork 
 appears quite different. It now looks like 
 a piece of india-rubber, slowly opening and 
 shutting, and now it appears quite still, but the 
 noise it is making shows that it is not still by 
 any means. The legs of the fork are vibrating, 
 but the light only falls upon them at regular 
 
THE FORCES WHICH MOULD THEM. 109 
 
 intervals, which correspond with their move- 
 ment, and so, as I explained in the case of the 
 water-drops, the fork appears perfectly still. 
 Now the speed is slightly altered, and, as I 
 have explained, each new flash of light, coming- 
 just too soon or just too late, shows the fork 
 in a position which is just before or just behind 
 that made visible by the previous flash. You 
 thus see the fork slowly going through its 
 evolutions, though of course in reality the legs 
 are moving backwards and forwards 128 times 
 a second. By looking at the fork or its 
 shadow, you will therefore be able to tell 
 whether the light is keeping exact time with 
 the vibrations, and therefore with the water- 
 drops. 
 
 Now the water is running, and you see all 
 the separate drops apparently stationary, strung 
 like pearls or beads of silver upon an invisible 
 wire (see Frontispiece). If I make the card 
 turn ever so little more slowly, then all the 
 drops will appear to slowly march onwards, and 
 what is so beautiful, but I am afraid few will 
 see this, each little drop may be seen to gradu- 
 ally break off', pulling out a waist which becomes 
 a little drop, and then when the main drop is 
 
110 SOAP-BUBBLES, AND 
 
 free it slowly oscillates, becoming wide and long, 
 or turning over and over, as it goes on its way. 
 If it so happens that a double or multiple jet is 
 being produced, then you can see the little 
 drops moving up to one another, squeezing each 
 other where they meet and bouncing away 
 again. Now the card is turning a little too 
 fast and the drops appear to be moving back- 
 wards, so that it seems as if the water is coming 
 up out of the tank on the floor, quietly going 
 over my head, down into the nozzle, and 
 so back to the water-supply of the place. 
 Of course this is not happening at all, as you 
 know very well, and as you will see if I simply 
 try and place my finger between two of these 
 drops. The splashing of the water in all direc- 
 tions shows that it is not moving quite so 
 quietly as it appears. There is one more thing 
 that I would mention about this experiment. 
 Every time that the flashing light gains or 
 loses one complete flash, upon the motion of 
 the tuning-fork, it will appear to make one 
 complete oscillation, and the water-drops will 
 appear to move back or on one place. 
 
 I must now come to one of the most 
 beautiful applications of these musical jets 
 
THE FORCES WHICH MOULD THEM. Ill 
 
 to practical purposes which it. is possible to 
 -imagine, and what I shall now show are a few 
 out of a great number of the experiments of 
 Mr. Chichester Bell, cousin of Mr. Graham 
 Bell, the inventor of the telephone. 
 
 To begin with I have a very small jet of 
 water forced through the nozzle at a great 
 pressure, as you can see if I point it towards 
 the ceiling, as the water rises eight or ten feet. 
 If I allow this stream of water to fall upon 
 an india-rubber sheet, stretched over the end 
 of a tube as big as my little finger, then the 
 little sheet will be depressed by the water, and 
 the more so if the stream is strong. Now 
 if I hold the jet close to the sheet the smooth 
 column of liquid will press the sheet steadily, 
 and it will remain quiet ; but if I gradually 
 take the jet further away from the sheet, then 
 any waists that may have been formed in the 
 liquid column, which grow as they travel, will 
 make their existence perfectly evident. When 
 a wide part of the column strikes the sheet it 
 will be depressed rather more than usual, and 
 when a narrow part follows, the depression will 
 be less. In other words, any very slight 
 vibration imparted to the jet will be magnified 
 
I I 2 SOAP-BUBBLES, AND 
 
 by the growth of waists, and the sheet of india- 
 rubber will reproduce the vibration, but on a 
 magnified scale. Now if you remember that 
 sound consists of vibrations, then you will 
 understand that a jet is a machine for magnify- 
 ing sound. To show that this is the case I am 
 now directing the jet on to the sheet, and you 
 can hear nothing; but I shall hold a piece of 
 wood against the nozzle, and now, if on the 
 whole the jet tends to break up at any one rate 
 rather than at any other, or if the wood or the 
 sheet of rubber will vibrate at any rate most 
 easily, then the first few vibrations which cor- 
 respond to this rate will be 'imparted to the 
 wood, which will impress them upon the nozzle 
 and so upon the cylinder of liquid, where they 
 will become magnified ; the result is that the 
 jet immediately begins to sing of its own 
 accord, giving out a loud note (Fig. 47). 
 
 I will now remove the piece of wood. On 
 placing against the nozzle an ordinary lever 
 watch, the jolt which is imparted to the case 
 at every tick, though it is so small that you 
 cannot detect it, jolts the nozzle also, and thus 
 causes a neck to form in the jet of water which 
 will grow as it travels, and so produce a loud 
 
THE FORCES WHICH MOULD THEM. 113 
 
 tick, audible in every part of this large room 
 (Fig. 48). Now I want you to notice how the 
 vibration is magnified by the action I have 
 described. I now hold the nozzle close to the 
 rubber sheet, and you can hear nothing. As I 
 
 Fig- 47 
 
 gradually raise it a faint echo is produced, 
 which gradually gets louder and louder, until 
 at last it is more like a hammer striking an 
 anvil than the tick of a watch. 
 
 I shall now change this watch for another 
 
 H 
 
I 14 SOAP-BUBBLES, AND 
 
 which, thanks to a friend, I am able to use. 
 This watch is a repeater, that is, if you press 
 upon a nob it will strike, first the hour, then 
 the quarters, and then the minutes. I think the 
 
 Fig. 48. 
 
 water-jet will enable you all to hear what time 
 it|is. Listen ! one, two, three, four ; . , . ting- 
 tang, ting-tang; . . . one, two, three, four, five, 
 six. Six minutes after half-past four. You 
 notice that not only did you hear the number 
 of strokes, but the jet faithfully reproduced the 
 
THE FORCES WHICH MOULD THEM. 115 
 
 musical notes, so that you could distinguish one 
 note from the others. 
 
 I can in the same way make the jet play a 
 tune by simply making the nozzle rest against 
 a long stick, which is pressed upon a musical- 
 box. The musical-box is carefully shut up in 
 a double box of thick felt, and you can hardly 
 hear anything ; but the moment that the nozzle 
 is made to rest against the stick and the water is 
 directed upon the india-rubber sheet, the sound 
 of the box is loudly heard, I hope, in every part 
 of the room. It is usual to describe a fountain 
 as playing, but it is now evident that a fountain 
 can even play a tune. There is, however, one 
 peculiarity which is perfectly evident. The jet 
 breaks up at certain rates more easily than at 
 others, or, in other words, it will respond to 
 certain sounds in preference to others. You 
 can hear that as the rnusical-box plays, certain 
 notes are emphasized in a curious way, pro- 
 ducing much the *same effect that follows if 
 you lay a penny upon the upper strings of a 
 horizontal piano. 
 
 Now, on returning to our soap-bubbles, you 
 may remember that I stated that the cate- 
 noid and the plane were the only figures of 
 
Il6 SOAP-BUBBLES, AND 
 
 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 curva- 
 ture, 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- 
 Fig. 49- 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 clipping this frame 
 in soap-water is well worth seeing (Fig. 49). 
 It is impossible to give any idea of the per- 
 
THE FORCES WHICH MOULD THEM. 1IJ 
 
 fection of the form in a figure, but fortunately 
 this is an experiment which any one can easily 
 perform. 
 
 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 
 
 Fig. 50- 
 
 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" 
 
n8 
 
 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. 
 
THE FORCES WHICH MOULD THEM. 
 
 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 
 
I2O SOAP-BUBBLES, AND 
 
 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. 
 Ether produces a vapour which is very heavy,, 
 
 Fig- 5'- 
 
 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 blot- 
 ting-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 
 
THE FORCES WHICH MOULD THEM. 121 
 
 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 
 
 Fig. 52- 
 
122 
 
 SOAP-BUBBLES, AND 
 
 to the other side. However, I can see whether 
 this is the true explanation or not by blow- 
 ing 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 
 
 Fig- 53- 
 
 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 
 
THE FORCES WHICH MOULD THEM. 123 
 
 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. 
 
 You may have noticed when I made the 
 drops of oil in the mixture of alcohol and 
 water, that when they were brought together 
 they did not at once unite ; they pressed against 
 one another and pushed each other away if 
 allowed, just as the water-drops did in the 
 fountain of which I showed you a photograph. 
 You also may have noticed that the drops of 
 water in the paraffin mixture bounced against 
 one another, or if filled with the paraffin, formed 
 bubbles in which often other small drops, both 
 of water and paraffin, remained floating. 
 
 In all these cases there was a thin film of 
 something between the drops which they were 
 unable to squeeze out, namely, water, paraffin, 
 or air, as the case might be. Will two soap- 
 bubbles also when knocked together be unable 
 to squeeze out the air between them ? This 
 
124 SOAP-BUBBLES, AND 
 
 you can try at home just as well as I can here, 
 but I will perform the experiment at once. I 
 have blown a pair of bubbles, and now when 
 I hit them together they remain distinct and 
 separate (Fig. 54). 
 
 I shall next place a bubble on a ring, which 
 it is just too large to get through. In my 
 hand I hold a ring, on which I have a flat 
 
 Fig. 54- 
 
 film, made by placing a bubble upon it and 
 breaking it on one side. If I gently press 
 the bubble with the flat film, I can push it 
 through the ring to the other side (Fig. 55), 
 and yet the two have not really touched one 
 another at all. The bubble can be pushed 
 backwards and forwards in this way many 
 times. 
 
 I have now blown a bubble and hung it 
 below a ring. To this bubble I can hang 
 
THE FORCES WHICH MOULD THEM. 
 
 another ring of thin wire, which pulls it a little 
 out of shape. Since the pressure inside is less 
 than that corresponding to a complete sphere, 
 and since it is greater than that outside, and this 
 we can tell by looking at the caps, the curve is 
 
 Fig- 55- 
 
 part of one of those represented by the dotted 
 lines in C or E, Fig. 31., However, without 
 considering the curve any more, I shall push 
 the end of the pipe inside, and blow another 
 bubble there, and let it go. It falls gently 
 
1 26 
 
 SOAP-BUBBLES, AND 
 
 Fig. 56. 
 
 until it rests upon the outer bubble; not at 
 the bottom, because the heavy ring keeps that 
 part out of reach, but along 
 a circular line higher up 
 (Fig. 56). I can now drain 
 away the heavy drops of 
 liquid from below the 
 bubbles with a pipe, and 
 leave them clean and 
 smooth all over. I can 
 now pull the lower ring 
 down, squeezing the inner bubble into a shape 
 like an egg (Fig. 57), or swing it round and 
 round, and then with a little 
 care peel away the ring 
 from off the bubble, and 
 leave them both perfectly 
 round every way (Fig. 58). 
 I can draw out the air from 
 the outer bubble till you 
 can hardly see between 
 them, and then blow in, 
 and the harder I blow, the 
 more is it evident that the 
 two bubbles are not touching at all; the 
 inner one is now spinning round and round 
 
(UNI 
 
 THE FORCES WHICII^MOULD THEM. 127 
 
 in the very centre of the large bubble, and 
 finally, on breaking the outer one the inner 
 floats away, none the worse for its very 
 unusual treatment. 
 
 There is a pretty variation of the last experi- 
 ment, which, however, requires that a little 
 green dye called fluorescine, or better, uranine, 
 should be dissolved in a separate dish of the 
 soap-water. Then you 
 can blow the outer 
 bubble with clean 
 soap-water, and the 
 inner one with the 
 coloured water. Then 
 
 if you look at the 
 
 * . Fl g- 5 8 - 
 
 two bubbles by ordin- 
 ary light, you will hardly notice any difference; 
 but if you allow sunlight, or electric light from 
 an arc lamp, to shine upon them, the inner one 
 will appear a brilliant green, while the outer 
 one will remain clear as before. They will not 
 mix at all, showing that though the inner one 
 is apparently resting against the outer one, 
 there is in reality a thin cushion of air between. 
 Now you know that coal-gas is lighter than 
 air, and so a soap-bubble blown with gas, 
 
128 
 
 when let go, floats up to the ceiling at once. 
 I shall blow a bubble on a ring with coal-gas. 
 It is soon evident that it is pulling upwards. 
 I shall go on feeding it with gas, and I want 
 you to notice the very beautiful shapes that 
 it takes (Fig. 59, but imagine the globe inside 
 removed). These are all exactly the curves 
 that a water-drop assumes when hanging from 
 
 a pipe, except that they 
 are the other way up. 
 The strength of the skin 
 is now barely able to 
 withstand the pull, and 
 now the bubble breaks 
 away just as the drop of 
 water did. 
 
 I shall next place a bubble blown with air 
 upon a ring, and blow inside it a bubble 
 blown with a mixture of air and gas. It of 
 course floats up and rests against the top of 
 the outer bubble (Fig. 60). Now I shall let 
 a little gas into the outer one, until the sur- 
 rounding gas is about as heavy as the inner 
 bubble. It now no longer rests against the 
 top, but floats about in the centre of the large 
 bubble (Fig. 61), just as the drop of oil did 
 
THE FORCES WHICH MOULD THEM. 
 
 129 
 
 Fig. 60. 
 
 in the mixture of alcohol and water. You 
 can see that the inner bubble is really lighter 
 than air, because if I 
 break the outer one, the 
 inner one rises rapidly to 
 the ceiling. 
 
 Instead of blowing the 
 first bubble on a heavy 
 fixed ring, I shall now 
 blow one on a light ring, 
 made of very thin wire. This bubble con- 
 tains only air. If I blow inside this a bubble 
 with coal-gas, then the gas-bubble will try 
 and rise, and will press 
 against the top of the 
 outer one with such force 
 as to make it carry up 
 the wire ring and a yard 
 of cotton, and some 
 paper to which the cotton 
 is tied (Fig. 62) ; and all 
 this time, though it is the inner one only 
 which tends to rise, the two bubbles are not 
 really touching one another at all. 
 
 I have now blown an air-bubble on the 
 fixed ring, and pushed up inside it a wire 
 
 Fig. 61. 
 
13 SOAP-BUBBLES, AND 
 
 with a ring on the end. I shall now blow 
 another air-bubble on this inner ring. The 
 next bubble that I shall blow is 
 one containing gas, and this is in- 
 side the other two, and when let 
 go it rests against the top of the 
 second bubble. I next make the 
 second bubble a little lighter by 
 blowing a little gas into it, and 
 then make the outer one larger 
 with air. I can now peel off the 
 inner ring and take it away, leav- 
 ing the two inner bubbles free, 
 inside the outer one (Fig. 63). 
 And now the multiple reflections 
 of the brilliant colours of the dif- 
 ferent bubbles from one to the 
 other, set off by the beautiful 
 forms which the bubbles them- 
 Fig. 62. selves assume, give to the whole a 
 degree of symmetry and splendour 
 which you may go far to see equalled in any 
 other way. I have only to blow a fourth 
 bubble in real contact with the outer bubble 
 and the ring, to enable it to peel off and float 
 away with the other two inside. 
 
Fig. 63. 
 
 THE FORCES WHICH MOULD THEM. 131 
 
 We have seen that bubbles and drops be- 
 have in very much the same way. Let us 
 see if electricity will 
 produce the same 
 effect that it did on 
 drops. You re- 
 member that a piece 
 of electrified sealing- 
 wax prevented a 
 fountain of water 
 from scattering, be- 
 cause where two 
 drops met, instead 
 of bouncing, they joined together. Now there 
 are on these two rings bubbles which are just 
 resting against one another, but not really 
 touching (Fig. 64). The 
 instant that I take out the 
 sealing-wax you see they 
 join together and become 
 one (Fig. 65). Two soap- 
 bubbles, therefore, enable 
 us to detect electricity, 
 even when present in minute quantity, just as 
 two water fountains did. 
 
 We can use a pair of bubbles to prove the 
 
 Fig. 64. 
 
132 SOAP-BUBBLES, AND 
 
 truth of one of the well-known actions of 
 electricity. Inside an electrical conductor it is 
 impossible to feel any influence of electricity 
 outside, however much there may be, or how- 
 ever near you go to the surface. Let us, 
 therefore, take the two bubbles shown in Fig. 
 56, and bring an electrified stick of sealing- 
 
 Fig. 65. 
 
 wax near. The outer bubble is a conductor; 
 there is, therefore, no electrical action inside, 
 and this you can see because, though the 
 sealing-wax is so near the bubble that it pulls 
 it all to one side, and though the inner one 
 is so close to the outer one that you cannot 
 see between them, yet the two bubbles remain 
 
THE FORCES WHICH MOULD THEM. 
 
 133 
 
 separate. Had there been the slightest elec- 
 trical influence inside, even to a depth of a 
 hundred-thousandth of an inch, the two 
 bubbles would have instantly come together. 
 There is one more experiment which I 
 must show, arid this will be the last; it is 
 
 Fig. 66. 
 
 a combination of the last two, and it beau- 
 tifully shows the difference between an in- 
 side and an outside bubble. I have now 
 a plain bubble resting against the side of the 
 pair that I have just been using. The instant 
 that I take out the sealing-wax the two outer 
 
134 SOAP-BUBBLES. 
 
 bubbles join, while the inner one unharmed 
 and the heavy ring slide down to the bottom 
 of the now single outer bubble (Fig. 66). 
 
 And now that our time has drawn to a close 
 I must ask you whether that admiration and 
 wonder which we all feel when we play with 
 soap-bubbles has been destroyed by these 
 lectures ; or whether now that you know more 
 about them it is not increased. I hope you 
 will all agree with me that the actions upon 
 which such common and every-day phenomena 
 as drops and bubbles depend, actions which 
 have occupied the attention of the greatest 
 philosophers from the time of Newton to the 
 present day, are not so trivial as to be un- 
 worthy of the attention of ordinary people like 
 ourselves. 
 
PRACTICAL HINTS. 
 
 I HOPE that the following practical hints 
 may be found useful by those who wish them- 
 selves to successfully perform the experiments 
 already described. 
 
 Drop with India-rubber Surface. 
 
 A sheet of thin india-rubber, about the 
 thickness of that used in air- balls, as it appears 
 before they have been blown out, must be 
 stretched over a ring of wood or metal eighteen 
 inches in diameter, and securely wired round 
 the edge. The wire will hold the india-rubber 
 better if the edge is grooved. This does not 
 succeed if tried on a smaller scale. This ex- 
 periment was shown by Sir W. Thomson at 
 the Royal Institution. 
 
 Jumping Frame. 
 
 This is easily made by taking a light glass 
 globe about two inches in diameter, such, for 
 
136 SOAP-BUBBLES, AND 
 
 instance, as a silvered ball used to ornament a 
 Christmas-tree or the bulb of a pipette, which 
 is what I used. Pass through the open necks 
 of the bulb a piece of wire about one-twentieth 
 of an inch in diameter, and fix it permanently 
 and water-tight upon the wire by working into 
 the necks melted sealing-wax. An inch or 
 two above the globe, fasten a flat frame of thin 
 wire by soldering, or if this is too difficult, by 
 tying and sealing-wax. A lump of lead must 
 then be fastened or hung on to the lower end, 
 and gradually scraped away until the wire 
 frame will just be unable to force its way 
 through the surface of the water. None of 
 the dimensions or materials mentioned are of 
 importance. 
 
 Paraffined Sieve. 
 
 Obtain a piece of copper wire gauze with 
 about twenty wires to the inch, and cut out 
 from it a round piece about eight inches in 
 diameter. Lay it on a round block, of such a 
 size that it projects about one inch all round. 
 Then gently go round and round with the 
 hands pressing the edge down and keeping it 
 
THE FORCES WHICH MOULD THEM. 137 
 
 flat above, until the sides are evenly turned down 
 all round. This is quite easy, because the wires 
 can allow of the kind of distortion necessary. 
 Then wind round the turned-up edge a few 
 turns of thick wire to make the sides stiff. 
 This ought to be soldered in position, but pro- 
 bably careful wiring will be good enough. 
 
 Melt some paraffin wax or one or two paraffin 
 candles of the best quality in a clean flat dish, 
 not over the fire, which would be dangerous, 
 but on a hot plate. When melted and clear 
 like water, dip the sieve in, and when all is hot 
 quickly take it out and knock it once or twice 
 on the table to shake the paraffin out of the 
 holes. Leave upside down until cold, and 
 then be careful not to scratch or rub off the 
 paraffin. This had best be done in a place 
 where a mess is of no consequence. 
 
 There is no difficulty in filling it or in setting 
 it to float upon water. 
 
 Narroiv Tubes and Capillarity. 
 
 Get some quill-glass tube from a chemist, 
 that is, tube about the size of a pen. If it is 
 more than, say, a foot long, cut off a piece by 
 
138 SOAP-BUBBLES, AND 
 
 first making a firm scratch in one place with 
 a three-cornered file, when it will break at the 
 place easily. To make very narrow tube from 
 this, hold it near the ends in the two hands 
 very lightly, so that the middle part is high up 
 in the brightest part of an ordinary bright and 
 flat gas flame. Keep it turning until at last 
 it becomes so soft that it is difficult to hold it 
 straight. It can then be bent into any shape, 
 but if it is wanted to be drawn out it must be 
 held still longer until the black smoke upon 
 it begins to crack and peel up. Then quickly 
 take it out of the flame, and pull the two ends 
 apart, when a long narrow tube will be formed 
 .between. This can be made finer or coarser by 
 regulating the heat and the manner in which it 
 is pulled out. No directions will tell any one 
 so much as a very little practice. For drawing 
 out tubes the flame of a Bunsen burner or of 
 a blow-pipe is more convenient ; but for bend- 
 ing tubes nothing is so good as the flat gas 
 flame. Do not clean off smoke till the tubes 
 are cold, and do not hurry their cooling by 
 wetting or blowing upon them. In the country 
 where gas is not to be had, the flame of a 
 large spirit-lamp can be made to do, but it 
 
THE FORCES WHICH MOULD THEM. 139 
 
 is not so good as a gas-flame. The narrower 
 these tubes are, the higher will clean water be 
 observed to rise in them. To colour the 
 water, paints from a cclour-box must not be 
 used. They are not liquid, and will clog the 
 very fine tubes. Some dye that will quite 
 dissolve (as sugar does) must be used. An 
 aniline dye, called soluble blue, does very well. 
 A little vinegar added may make the colour 
 last better. 
 
 Capillarity between Plates. 
 
 Two plates of flat glass, say three to five 
 inches square, are required. Provided they 
 are quite clean and well wetted there is no 
 difficulty. A little soap and hot water will 
 probably be sufficient to clean them. 
 
 Tears of Wine. 
 
 These are best seen at dessert in a glass 
 about half filled with port. A mixture of 
 from two to three parts of water, and one part 
 of spirits of wine containing a very little rosani- 
 line (a red aniline dye), to give it a nice colour, 
 may be used, if port is not available. A piece 
 
I4O SOAP-BUBBLES, AND 
 
 of the dye about as large as a mustard-seed 
 will be enough for a large wine-glass. The 
 sides of the glass should be wetted with the 
 wine. 
 
 Cat-Boxes. 
 
 Every school-boy knows how to make these. 
 They are not the boxes made by cutting slits 
 in paper. They are simply made by folding, 
 and are then blown out like the " frog," which 
 is also made of folded paper. 
 
 Liquid Beads. 
 
 Instead of melting gold, water rolled on to 
 a table thickly dusted with lycopodium, or 
 other fine dust, or quicksilver rolled or thrown 
 upon a smooth table, will show the difference 
 in the shape of large and small beads perfectly. 
 A magnifying-glass will make the difference 
 more evident. In using quicksilver, be care- 
 ful that none of it falls on gold or silver coins, 
 or jewellery, or plate, or on the ornamental 
 gilding on book-covers. It will do serious 
 damage. 
 
THE FORCES WHICH MOULD THEM. 141 
 
 Plateaus Experiment. 
 
 To perform this with very great perfection 
 requires much care and trouble. It is easy 
 to succeed up to a certain point. Pour into 
 a clean bottle about a table-spoonful of salad- 
 oil, and pour upon it a mixture of nine parts 
 by volume spirits of wine (not methylated 
 spirits), and seven parts of water. Shake up 
 and leave for a day if necessary, when it will 
 be found that the oil has settled together by 
 itself. Fill a tumbler with the same mixture 
 of spirit and water, and then with a fine glass 
 pipe, dipping about half-way down, slowly intro- 
 duce a very little water. This will make the 
 liquid below a little heavier. Dip into the oil a 
 pipe and take out a little by closing the upper 
 end with the finger, and carefully drop this into 
 the tumbler. If it goes to the bottom, a little 
 more water is required in the lower half of 
 the tumbler. If by chance it will not sink 
 at all, a little more spirit is wanted in the 
 upper half. At last the oil will just float in 
 the middle of the mixture. More can then 
 be added, taking care to prevent it from touch- 
 ing the sides. If the liquid below is ever so 
 
IJ.2 SOAP-BUBBLES, AND 
 
 little heavier, and the liquid above ever so 
 little lighter than oil, the drop of oil perhaps 
 as large as a halfpenny will be almost per- 
 fectly round. It will not appear round if seen 
 through the glass, because the glass magnifies 
 it sideways, but not up and down, as may be 
 seen by holding a coin in the liquid just above 
 it. To see the drop in its true shape the vessel 
 must either be a globe, or one side must be 
 made of flat glass. 
 
 Spinning the oil so as to throw off a ring 
 is not material, but if the reader can contrive 
 to fix a disc about the size of a threepenny- 
 piece upon a straight wire, arid spin it round 
 without shaking it, then he will see the ring 
 break off, and either return if the rotation is 
 quickly stopped, or else break up into three or 
 four perfect little balls. The disc should be 
 wetted with oil before being dipped into the 
 mixture of spirit and water. 
 
 A Good Mixture for Soap- Bubbles. 
 
 Common yellow soap is far better than 
 most of the fancy soaps, which generally con- 
 tain a little soap and a lot of rubbish. Castille 
 
THE FORCES WHICH MOULD THEM. 143 
 
 soap is very good, and this may be obtained 
 from any chemist. 
 
 Bubbles blown with soap and water alone 
 do not last long enough for many of the 
 experiments described, though they may some- 
 times be made to succeed. Plateau added 
 glycerine, which greatly improves the lasting 
 quality. The glycerine should be pure ; com- 
 mon glycerine is not good, but Price's answers 
 perfectly. The water should be pure distilled 
 water, but if this is not available, clean rain- 
 water will do. Do not choose the first that runs 
 from a roof after a spell of dry weather, but 
 wait till it has rained for some time, the water 
 that then runs off is very good, especially if 
 the roof is blue slate or glass. If fresh rain- 
 water is not to be had, the softest water should 
 be employed that can be obtained. Instead 
 of Castille soap, Plateau found that a pure 
 soap prepared from olive-oil is still better. 
 This is called oleate of soda. It should be 
 obtained freshly prepared from a manufactur- 
 ing chemist. Old, dry stuff that has been 
 kept a long time is not so good. I have 
 always used a modification of Plateau's for- 
 mula, which Professors Reinold and Riicker 
 
144 
 
 found to answer so well. They used less 
 glycerine than Plateau. It is best made as 
 follows. Fill a clean stoppered bottle three- 
 quarters full of water. Add one-fortieth part of 
 its weight of oleate of soda, which will probably 
 float on the water. Leave it for a day, when 
 the oleate of soda will be dissolved. Nearly 
 fill up the bottle with Price's glycerine and 
 shake well, or pour it into another clean bottle 
 and back again several times. Leave the 
 bottle, stoppered of course, for about a week 
 in a dark place. Then with a syphon, that is, 
 a bent glass tube which will reach to the 
 bottom inside and still further outside, draw off 
 the clear liquid from the scum which will have 
 collected at the top. Add one or two drops 
 of strong liquid ammonia to every pint of the 
 liquid. Then carefully keep it in a stoppered 
 bottle in a dark place. Do not get out this 
 stock bottle every time a bubble is to be blown, 
 but have a small working bottle. Never put 
 any back into the stock. In making the liquid 
 do not warm or filter it. Either will spoil it. 
 Never leave the stoppers out of the bottles or 
 allow the liquid to be exposed to the air more 
 than is necessary. This liquid is still perfectly 
 
THE FORCES WHICH MOULD THEM. 145 
 
 good after two years' keeping. I have given 
 these directions very fully, not because I feel 
 sure that all the details are essential, but 
 because it exactly describes the way I happen 
 to make it, and because I have never found 
 any other solution so good. Castille soap, 
 Price's glycerine, and rain-water will almost 
 certainly answer every purpose, and the same 
 proportions will probably be found to work 
 well. 
 
 Rings for Bubbles. 
 
 These may be made of any kind of wire. 
 I have used tinned iron about one-twentieth 
 of an inch in diameter. The joint should be 
 smoothly soldered without lumps. If solder- 
 ing is a difficulty, then use the thinnest wire 
 that is stiff enough to support the bubbles 
 steadily, and make the joint by twisting the 
 end of the wire round two or three times. 
 Rings two inches in diameter are convenient. 
 I have seen that dipping the rings in melted 
 paraffin is recommended, but I have not found 
 any advantage from this. The nicest material 
 for the light rings is thin aluminium wire, 
 about as thick as a fine pin (No. 26 to 30, 
 
 K 
 
146 SOAP-BUBBLES, AND 
 
 B. W. G.), and as this cannot be soldered, the 
 ends must be twisted. If this is not to be 
 had, very fine wire, nearly as fine as a hair 
 (No. 36, B. W. G.), of copper or of any other 
 metal, will answer. The rings should be wetted 
 with the soap mixture before a bubble is placed 
 upon them, and must always be well washed 
 and dried when done with. 
 
 Threads in Ring. 
 
 There is no difficulty in showing these 
 experiments. The ring with the thread may 
 be dipped in the soap solution, or stroked 
 across with the edge of a piece of paper or 
 india-rubber sheet that has been dipped in the 
 liquid, so as to form a film on both sides of 
 the thread. A needle that has also been 
 wetted with the soap may be used to show 
 that the threads are loose. The same needle 
 held for a moment in a candle-flame supplies 
 a convenient means of breaking the film. 
 
 Blow out Candle with Soap-Bubble. 
 
 For this, the bubble should be blown on 
 the end of a short wide pipe, spread out at 
 one end to give a better hold for the bubble. 
 
THE FORCES WHICH MOULD THEM. 147 
 
 The tin funnel supplied with an ordinary 
 gazogene answers perfectly. This should be 
 washed before it is used again for filling the 
 gazogene. 
 
 Bubbles balanced against one another. 
 
 These experiments are most conveniently 
 made on a small scale. Pieces of trun brass 
 tube, three-eighths or half an inch in diameter, 
 are suitable. It is best to have pieces of 
 apparatus, specially prepared with taps, for 
 easily and quickly stopping the air from leav- 
 ing either bubble, and for putting the two 
 bubbles into communication when required. 
 It should not be difficult to contrive to per- 
 form the experiments, using india-rubber con- 
 necting tubes, pinched with spring clips to 
 take the place of taps. There is one little 
 detail which just makes the difference between 
 success and failure. This is to supply a 
 mouth-piece for blowing the bubble, made of 
 glass tube, which has been drawn out so fine 
 that these little bubbles cannot be blown out 
 suddenly by accident. It is very difficult, 
 otherwise, to adjust the quantity of air in such 
 small bubbles with any accuracy. In balancing 
 
148 SOAP-BUBBLES, AND 
 
 a spherical against a cylindrical bubble, the 
 short piece of tube, into which the air is sup- 
 plied, must be made so that it can be easily 
 moved to or from a fixed piece of the same 
 size closed at the other end. Then the two 
 ends of the short tube must have a film spread 
 over them with a piece of paper, or india- 
 rubber, but there must be no film stretched 
 across the end of the fixed tube. The two 
 tubes must at first be near together, until the 
 spherical bubble has been formed. They may 
 then be separated gradually more and more, 
 and air blown in so as to keep the sides of 
 the cylinder straight, until the cylinder is suf- 
 ficiently long to be nearly unstable. It will 
 then far more evidently show, by its change of 
 form, than it would if it were short, when the 
 pressure due to the spherical bubble exactly 
 balances that due to a cylindrical one. If the 
 shadow of the bubbles, or an image formed 
 by a lens on a screen, is then measured, it will 
 be found that the sphere has a diameter which 
 is very accurately double that of the cylinder. 
 
THE FORCES WHICH MOULD THEM. 149 
 
 Thaumatrope for shoiving the Formation and 
 Oscillations of Drops. 
 
 The experiment showing the formation of 
 water-drops can be very perfectly imitated, 
 and the movements actually made visible, with- 
 out any necessity for using liquids at all, by 
 simply converting Fig. 35 (at end of book) into 
 the old-fashioned instrument called a thauma- 
 trope. What will then be seen is a true repre- 
 sentation, because the forms in the figure are 
 copies of a series of photographs taken from 
 the moving drops at the rate of forty-three 
 photographs in two seconds. 1 
 
 Obtain a piece of good cardboard as large 
 as the figure, and having brushed it all over 
 on one side with thin paste, lay the figure 
 upon it, and press it down evenly. Place it 
 upon a table, and cover it with a few thick- 
 nesses of blotting-paper, and lay over all a flat 
 piece of board large enough to cover it. 
 Weights sufficient to keep it all flat may be 
 added. This must be left all night at least, 
 until the card is quite dry, or else it will curl 
 
 i For particulars see Philosophical Magazine^ Sep- 
 tember 1890. 
 
r 5 
 
 up and be useless. Now with a sharp chisel 
 or knife, but a chisel if possible, cut out the 
 forty-three slits near the edge, accurately 
 following the outline indicated in black and 
 white, and keeping the slits as narrow as 
 possible. Then cut a hole in the middle, so as 
 to fit the projecting part of a sewing-machine 
 cotton-reel, and fasten the cotton-reel on the 
 side away from the figure with glue or small 
 nails. It must be fixed exactly in the middle. 
 The edge should of course be cut down to 
 the outside of the black rim. 
 
 Now having found a pencil or other rod 
 on which the cotton-reel will freely turn, use 
 this as an axle, and holding the disc up in 
 front of a looking-glass, and in a good light, 
 slowly and steadily make it turn round. The 
 image of the disc seen through the slit in the 
 looking-glass will then perfectly represent every 
 feature of the growing and falling drop. As 
 the drop grows it will gradually become too 
 heavy to be supported, a waist will then begin 
 to form which will rapidly get narrower, until 
 the drop at last breaks away. It will be seen 
 to continue its fall until it has disappeared in the 
 liquid below, but it has not mixed with this, 
 
THE FORCES WHICH MOULD THEM. 1^1 
 
 and so it will presently appear again, having 
 bounced out of the liquid. As it falls it will 
 be seen to vibrate as the result of the sudden 
 release from the one-sided pull. The neck 
 which was drawn out will meanwhile have 
 gathered itself in the form of a little drop, which 
 will then be violently hit by the oscillations of 
 the remaining pendant drop above, and driven 
 down. The pendant drop will be seen to 
 vibrate and grow at the same time, until it 
 again breaks away as before, and so the 
 phenomena are repeated. 
 
 In order to perfectly reproduce the experi- 
 ment, the axle should be firmly held upon a 
 stand, and the speed should not exceed one 
 turn in two seconds. 
 
 The effect is still more real if a screen is 
 placed between the disc and the mirror, which 
 will only allow one of the drops to be seen. 
 
 Water-drops in Paraffin and Bisulphide of 
 Carbon. 
 
 All that was said in describing the Plateau 
 experiment applies here. Perfectly spherical 
 and large drops of water can be formed in a 
 
152, SOAP-BUBBLES, AND 
 
 mixture so made that the lower parts are very 
 little heavier, and the upper parts very little 
 lighter, than water. The addition of bisulphide 
 of carbon makes the mixture heavier. This 
 liquid bisulphide of carbon is very danger- 
 ous, and has a most dreadful smell, so that it 
 had better not be brought into the house. The 
 form of a hanging drop, and the way in which 
 it breaks off, can be seen if water is used in 
 paraffin alone, but it is much more evident 
 if a little bisulphide of carbon is mixed with 
 the paraffin, so that water will sink slowly 
 in the mixture. Pieces of glass tube, open 
 at both ends from half an inch to one inch 
 in diameter, show the action best. Having 
 poured some water coloured blue into a glass 
 vessel, and covered it to a depth of several 
 inches with paraffin, or the paraffin mixture, 
 dip the pipe down into the water, having first 
 closed the upper end with the thumb or the 
 palm of the hand. On then removing the 
 hand, the water will rush up inside the tube. 
 Again close the upper end as before, and raise 
 the tube until ths lower end is well above the 
 water, though still immersed in the paraffin. 
 Then allow air to enter the pipe very slowly 
 
THE FORCES WHICH MOULD THEM. 1^3 
 
 by just rolling the thumb the least bit to 
 one side. The water will escape slowly and 
 form a large growing drop, the size of which, 
 before it breaks away, will depend on the 
 density of the mixture and the size of the tube. 
 
 To form a water cylinder in the paraffin the 
 tube must be filled with water as before, but 
 the upper end must now be left open. Then 
 when all is quiet the tube is to be rather 
 rapidly withdrawn in the direction of its own 
 length, when the water which was within it 
 will be left behind in form of a cylinder, 
 surrounded by the paraffin. It will then break 
 up into spheres so slowly, in the case of a 
 large tube, that the operation can be watched. 
 The depth of paraffin should be quite ten times 
 the diameter of the tube. 
 
 To make bubbles of water in the paraffin, 
 the tube must be dipped down into the water 
 with the upper end open all the time, so that 
 the tube is mostly filled with paraffin. It 
 must then be closed for a moment above and 
 raised till the end is completely out of the 
 water. Then if air is allowed to enter slowly, 
 and the tube is gently raised, bubbles of water 
 filled with paraffin will be formed which can 
 
SOAP-BUBBLES, AND 
 
 be made to separate from the pipe, like soap- 
 bubbles from a " churchwarden," by a suitable 
 sudden movement. If a number of water- 
 drops are floating in the paraffin in the pipe, 
 and this can be easily arranged, then the 
 bubbles made will contain possibly a number 
 of other drops, or even other bubbles. A very 
 little bisulphide of carbon poured carefully 
 down a pipe will form a heavy layer above 
 the water, on which these compound bubbles 
 will remain floating. 
 
 Cylindrical bubbles of water in paraffin may 
 be made by dipping the pipe down into the 
 water and withdrawing it quickly without ever 
 closing the top at all. These break up into 
 spherical bubbles in the same way that the 
 cylinder of liquid broke up into spheres of 
 liquid. 
 
 Beaded Spider-webs. 
 
 These are found in the spiral part of the 
 webs of all the geometrical spiders. The 
 beautiful geometrical webs may be found out 
 of doors in abundance in the autumn, or in 
 green-houses at almost any time of the year. 
 To mount these webs so that the beads may 
 
THE FORCES WHICH MOULD THEM. 155 
 
 be seen, take a small flat ring of any material, 
 or a piece of card-board with a hole cut out 
 with a gun-wad cutter, or otherwise. Smear 
 the face of the ring, or the card, with a very 
 little strong gum. Choose a freshly-made 
 web, and then pass the ring, or the card, across 
 the web so that some of the spiral web (not 
 the central part of the web) remains stretched 
 across the hole. This must be done without 
 touching or damaging the pieces that are 
 stretched across, except at their ends. The 
 beads are too small to be seen with the naked 
 eye. A strong magnifying-glass, or a low 
 power microscope, will show the beads and 
 their marvellous regularity. The beads on the 
 webs of very young spiders are not so regular 
 as those on spiders that are fully grown. Those 
 beautiful beads, easily visible to the naked eye, 
 on spider lines in the early morning of an 
 autumn day, are not made by the spider, but 
 are simply dew. They very perfectly show the 
 spherical form of small water-drops. 
 
"56 
 
 Photographs of Water-jets. 
 
 These are easily taken by the method 
 described by Mr. Chichester Bell. The flash 
 of light is produced by a short spark from 
 a few Leyden-jars. The fountain, or jet, should 
 be five or six feet away from the spark, and 
 the photographic plate should be held as close 
 to the stream of water as is possible without 
 touching. The shadow is then so definite that 
 the photograph, when taken, may be examined 
 with a powerful lens, and will still appear sharp. 
 Any rapid dry plate will do. The room, of 
 course, must be quite dark when the plate is 
 placed in position, and the spark then made. 
 The regular breaking up of the jet may be 
 effected by sound produced in almost any way. 
 The straight jet, of which Fig. 41 is a repre- 
 sentation, magnified about three and a quarter 
 times, was regularly broken up by simply 
 whistling to it with a key. The fountains were 
 broken up regularly by fastening the nozzle to 
 one end of a long piece of wood clamped at 
 the end to the stand of a tuning-fork, which 
 was kept sounding by electrical means. An 
 ordinary tuning-fork, made to rest when sound- 
 
THE FORCES WHICH MOULD THEM. 157 
 
 ing against the wooden support of the nozzle, 
 will answer quite as well, but is not quite so 
 convenient. The jet will break up best to 
 certain notes, but it may be tuned to a great 
 extent by altering the size of the orifice or 
 the pressure of the water, or both. 
 
 Fountain and Sealing-wax. 
 
 It is almost impossible to fail over this very 
 striking yet simple experiment. A fountain 
 of almost any size, at any rate between one- 
 fiftieth and a quarter of an inch in the smooth 
 part, and up to eight feet high, will cease to 
 scatter when the sealing-wax is rubbed with 
 flannel and held a few feet away. A suitable 
 size of fountain is one about four feet high, 
 coming from an orifice anywhere near one- 
 sixteenth of an inch in diameter. The nozzle 
 should be inclined so that the water falls 
 slightly on one side. The sealing-wax may be 
 electrified by being rubbed on the coat-sleeve, 
 or on a piece of fur or flannel which is dry. It 
 will then make little pieces of paper or cork 
 dance, but it will still act on the fountain when 
 
158 SOAP-BUBBLES, AND 
 
 it has ceased to produce any visible effect on 
 pieces of paper, or even on a delicate gold-leaf 
 electroscope. 
 
 Bouncing Water-jets. 
 
 This beautiful experiment of Lord Ray- 
 Jeigh's requires a little management to make it 
 work in a satisfactory manner. Take a piece 
 of quill-glass tube and draw it out to a very 
 slight extent (see a former note), so as to 
 make a neck about one-eighth of an inch 
 in diameter at the narrowest part. Break the 
 tube just at this place, after first nicking it 
 there with a file. Connect each of these tubes 
 by means of an india-rubber pipe, or other- 
 wise, with a supply of water in a bottle, and 
 pinch the tubes with a screw-clip until two 
 equal jets of water are formed. So hold the 
 nozzles that these meet in their smooth por- 
 tions at every small angle. They will then 
 for a short time bounce away from one 
 another without mixing. If the air is very 
 dusty, if the water is not clean, or if air- 
 bubbles are carried along in the pipes, the 
 two jets will at once join together. In the 
 
THE FORCES WHICH MOULD THEM. 159 
 
 arrangement that I used in the lantern, the 
 two nozzles were nearly horizontal, one was 
 about half an inch above the other, and they 
 were very slightly converging. They were 
 fastened in their position by melting upon 
 them a little sealing-wax. India-rubber pipes 
 connected them with two bottles about six 
 inches above them, and screw-clips were used 
 to regulate the supply. One of the bottles 
 was made to stand on three pieces of seal- 
 ing-wax to electrically insulate it, and the 
 corresponding nozzle was only held by its 
 sealing-wax fastening. The water in the bottles 
 had been filtered, and one was coloured blue. 
 If these precautions are taken, the jets will 
 remain distinct quite long enough, but are 
 instantly caused to recombine by a piece of 
 electrified sealing-wax six or eight feet away. 
 They may be separated again by touching the 
 water issuing near one nozzle with the finger, 
 which deflects it; on quietly removing the 
 finger the jet takes up its old position and 
 bounces off the other as before. They can 
 thus be separated and made to combine ten 
 or a dozen times in a minute. 
 
i6o 
 
 Fountain and Intermittent Light. 
 
 This can be successfully shown to a large 
 number of people at once only by using an 
 electric arc, but there is no occasion to produce 
 this light if not more than one person at a time 
 wishes to see the evolution of the drops. It is 
 then merely necessary to make the fountain play 
 in front of a bright background such as the 
 sky, to break it up with a tuning-fork or other 
 musical sound as described, and then to look 
 at it through a card disc equally divided near 
 the edge into spaces about two or three inches 
 wide, with a hole about one-eighth of an inch 
 in diameter between each pair of spaces. A 
 disc of card five inches in diameter, with six 
 equidistant holes half an inch from the edge, 
 answers well. The disc must be made to 
 spin by any means very regularly at such 
 a speed that the tuning-fork, or stretched 
 string if this be used, when looked at through 
 the holes, appears quiet, or nearly quiet, when 
 made to vibrate. The separate drops will 
 then be seen, and everything described in the 
 preceding pages, and a great deal more, will 
 be evident. This is one of the most fascin- 
 
THE FORCES WHICH MOULD THEM. l6l 
 
 ating experiments, and it is well worth while 
 to make an effort to succeed. The little 
 motor that I used is one of Cuttriss and Co.'s 
 P. i. motors, which are very convenient for 
 experiments of this kind. It was driven by 
 four Grove's cells. These make it rotate too 
 fast, but the speed can be reduced by moving 
 the brushes slightly towards the position used 
 for reversing the motor, until the speed is 
 almost exactly right. It is best to arrange 
 that it goes only just too fast, then the speed 
 can be perfectly regulated by a very light pres- 
 sure of the finger on the end of the axle. 
 
 Mr. Chichester Bell's Singing Water -jet. 
 
 For these experiments a very fine hole 
 about one seventy-fifth of an inch in diameter 
 is most suitable. To obtain this, Mr. Bell 
 holds the end of a quill-glass tube in a blow- 
 pipe flame, and constantly turns it round and 
 round until the end is almost entirely closed 
 up. He then suddenly and forcibly blows into 
 the pipe. Out of several nozzles made in this 
 way, some are sure to do well. Lord Rayleigh 
 makes nozzles generally by cementing to the 
 
1 62, SOAP-BUBBLES, AND 
 
 end of a glass (or metal) pipe a piece of thin 
 sheet metal in which a hole of the required 
 size has been made. The water pressure should 
 be produced by a head of about fifteen feet. 
 The water must be quite free from dust and 
 from air-bubbles. This may be effected by 
 making it pass through a piece of tube stuffed 
 full of flannel, or cotton-wool, or something of 
 the kind to act as a filter. There should be 
 a yard or so of good black india-rubber tube, 
 about one-eighth of an inch in diameter inside, 
 between the filter and the nozzle. It is best 
 not to take the water direct from the water- 
 main, but from a cistern about fifteen feet 
 above the nozzle. If no cistern is available, 
 a pail of water taken up-stairs, with a pipe 
 coming down, is an excellent substitute, and 
 this has the further advantage that the head 
 of water can be easily changed so as to arrive 
 at the best result. 
 
 The rest of the apparatus is very simple. 
 It is merely necessary to stretch and tie over 
 the end of a tube about half an inch in 
 diameter a piece of thin india-rubber sheet, 
 cut from an air-ball that has not been blown 
 out. The tube, which may be of metal or of 
 
THE FORCES WHICH MOULD THEM. 163 
 
 glass, may either be fastened to a heavy foot, 
 in which case a side tube must be joined to it, 
 as in Fig. 47, or it may be open at both ends 
 and be held in a clamp. It is well to put a 
 cone of card-board on the open end (Fig. 48), 
 if the sound is to be heard by many at a time. 
 If the experimenter alone wishes to hear as 
 well as possible when faint sounds are pro- 
 duced, he should carry a piece of smooth india- 
 rubber tube about half an inch in diameter 
 from the open end to his ear. This, however, 
 would nearly deafen him with such loud noises 
 as the tick of a watch. 
 
 Bubbles and Ether. 
 
 Experiments with ether must be performed 
 with great care, because, like the bisulphide of 
 carbon, it is dangerously inflammable. The 
 bottle of ether must never be brought near 
 a light. If a large quantity is spilled, the 
 heavy vapour is apt to run along the floor and 
 ignite at a fire, even on the other side of a 
 room. Any vessel may be filled with the 
 vapour of ether by merely pouring the liquid 
 upon a piece of blotting-paper reaching up to 
 
164 
 
 the level of the edge. Very little is required, 
 say half a wine-glassful, for a basin that 
 would hold a gallon or more. In a draughty 
 place the vapour will be lost in a short time. 
 Bubbles can be set to float upon the vapour 
 without any difficulty. They may be removed 
 in five or ten seconds by means of one of the 
 small light rings with a handle, provided that 
 the ring is wetted with the soap solution and 
 has no film stretched across it. If taken to 
 a light at a safe distance the bubble will 
 immediately burst into a blaze. If a neigh- 
 bouring light is not close down to the table, 
 but well up above the jar on a stand, it may 
 be near with but little risk. To show the 
 burning vapour, the same wide tube that was 
 used to blow out the candle will answer well. 
 The pear shape of the bubble, owing to its 
 increased weight after being held in the vapour 
 for ten or fifteen seconds, is evident enough 
 on its removal, but the falling stream of heavy 
 vapour, which comes out again afterwards, can 
 only be shown if its shadow is cast upon a 
 screen by means of a bright light. 
 
THE FORCES WHICH MOULD THEM. 165 
 
 Experiment with Internal Bubbles. 
 
 For these experiments, next to a good solu- 
 tion, the pipe is of the greatest importance. 
 A " churchwarden " is no use. A glass pipe 
 T 5 F inch in diameter at the mouth is best. 
 If this is merely a tube bent near the end 
 through a right angle, moisture condensed in 
 the tube will in time run down and destroy 
 the bubble occasionally, which is very annoy- 
 ing in a difficult experiment. I have made 
 for myself the pipe of which Fig. 67 is a full 
 size representation, and I do not think that 
 it is possible to improve upon this. Those 
 who are not glass-blowers will be able, with 
 the help of cork, to make a pipe with a trap 
 as shown in Fig. 68, which is as good, except 
 in appearance and handiness. 
 
 In knocking bubbles together to show that 
 they do not touch, care must be taken to 
 avoid letting either bubble meet any projection 
 in the other, such as the wire ring, or a heavy 
 drop of liquid. Either will instantly destroy 
 the two bubbles. There is also a limit to the 
 violence which may be used, which experience 
 will soon indicate. 
 
i66 
 
 SOAP-BUBBLES, AND 
 
 In pushing a bubble 
 through a ring smaller than 
 itself, by means of a flat 
 film on another ring, it is 
 important that the bubble 
 should not be too large ; but 
 a larger bubble can be 
 pushed through than would 
 be expected. It is not so 
 easy to push it up as down 
 because of the 'heavy drop of 
 liquid, which it is difficult 
 to completely drain away. 
 
 To blow one bubble inside 
 another, the first, as large as 
 an average orange, should be 
 blown on the lower side of 
 a horizontal ring. A light 
 
 Fig. 67. 
 
 wire ring should then be hung on to this bubble 
 to slightly pull it out of shape. For this pur- 
 pose thin aluminium rings are hardly heavy 
 enough, and so either a heavier metal should 
 
THE FORCES WHICH MOULD THEM. 
 
 ,67 
 
 
 be used, or a small weight 
 should be fastened to the 
 handle of the ring. The 
 ring should be so heavy that 
 the sides of the bubble make 
 an angle of thirty or forty 
 degrees with the vertical, 
 where they meet the ring as 
 indicated in Fig. 56. The 
 wetted end of the pipe is now 
 to be inserted through the 
 top of the bubble, until it 
 has penetrated a clear half 
 inch or so. A new bubble 
 can now be blown any size 
 almost that may be desired. 
 
 Fig. 68. 
 
 To remove the pipe a slow motion will be 
 fatal, because it will raise the inner bubble 
 until it and the outer one both meet the pipe 
 at the same place. This will bring them into 
 true contact. On the other hand, a violent 
 
I 68 SOAP-BUBBLES, AND 
 
 jerk will almost certainly produce too great a 
 disturbance. A rather rapid motion, or a 
 slight jerk, is all that is required. It is advis- 
 able before passing the pipe up through the 
 lower ring, so as to touch the inner bubble, 
 and so drain away the heavy drop, to steady 
 this with the other hand. The superfluous 
 liquid can then be drained from both bubbles 
 simultaneously. Care must be taken after 
 this that the inner bubble is not allowed to 
 come against either wire ring, nor must the 
 pipe be passed through the side where the two 
 bubbles are very close together. To peel off 
 the lower ring it should be pulled down a very 
 little way and then inclined to one side. The 
 peeling will then start more readily, but as 
 soon as it has begun the ring should be raised 
 so as not to make the peeling too rapid, other- 
 wise the final jerk, when it leaves the lower 
 ring, will be too much for the bubbles to 
 withstand. 
 
 Bubbles coloured with fluorescine, or uranine, 
 do not show their brilliant fluorescence unless 
 sunlight or electric light is concentrated upon 
 them with a lens or mirror. The quantity of 
 dye required is so small that it may be difficult 
 
THE FORCES WHICH MOULD THEM. 169 
 
 to take little enough. As much as can be 
 picked up on the last eighth of an inch of 
 a pointed pen-knife will be, roughly speak- 
 ing, enough for a wine-glassful of the soap 
 solution. If the quantity is increased beyond 
 something like the proportion stated, the fluor- 
 escence becomes less and very soon disappears. 
 The best quantity can be found in a few 
 minutes by trial. 
 
 To blow bubbles containing either coal-gas 
 or air, or a mixture of the two, the most 
 convenient plan is to have a small T-shaped 
 glass tube which can be joined by one arm of 
 the T to the blow-pipe by means of a short 
 piece of india-rubber tube, and be connected 
 by its vertical limb with a sufficient length of 
 india-rubber pipe, one-eighth of an inch in 
 diameter inside, to reach to the floor, after 
 which it may be connected by any kind of 
 pipe with the gas supply. The gas can be 
 stopped either by pinching the india-rubber 
 tube with the left hand, if that is at liberty, 
 or by treading on it if both hands are occu- 
 pied. Meanwhile air can be blown in by the 
 other arm of the T, and the end closed by 
 the tongue when gas alone is required. This 
 
170 SOAP-BUBBLES, AND 
 
 end of the tube should be slightly spread out 
 when hot by rapidly pushing into it the cold 
 tang of a file, and twisting it at the same time, 
 so that it may be lightly held by the teeth 
 without fear of slipping. 
 
 If a light T-piece or so great a length of 
 small india-rubber tube cannot be obtained, 
 then the mouth must be removed from the pipe 
 and the india-rubber tube slipped in when air 
 is to be changed for gas. This makes the 
 manipulation more difficult, but all the experi- 
 ments, except the one with three bubbles, can 
 be so carried out. 
 
 The pipe must in every case be made to 
 enter the highest point of a bubble in order 
 to start an internal one. If it is pushed 
 horizontally through the side, the inner bubble 
 is sure to break. If the inner bubble is being 
 blown with gas, it will soon tend to rise. The 
 pipe must then be turned over in such a 
 manner that the inner bubble does not creep 
 along it, and so meet the outer one where 
 penetrated by the pipe. A few trials will show 
 what is meant. The inner bubble may then 
 be allowed to rest against the top of the outer 
 one while being enlarged. When it is desired 
 
THE FORCES WHICH MOULD THEM. 171 
 
 after withdrawing the pipe to blow more air 
 or gas into either the inner or the outer bubble, 
 it is not safe after inserting the pipe again to 
 begin to blow at once ; the film which is now 
 stretched across the mouth of the pipe will 
 probably become a third bubble, and this, under 
 the circumstances, is almost certain to cause a 
 failure, An instantaneous withdrawal of the air 
 destroys this film by drawing it into the pipe. 
 Air or gas may then be blown without danger. 
 If the same experiment is performed upon 
 a light ring with cotton and paper attached, 
 the left hand will be occupied in holding this 
 ring, and then the gas must be controlled by 
 the foot, or by a friend. The light ring- 
 should be quite two inches in diameter. If, 
 when the inner bubble has begun to carry 
 away the ring, &c., the paper is caught hold 
 of, it is possible, by a judicious pull, to cause 
 the two bubbles to leave the ring and so 
 escape into the air one inside the other. For 
 this purpose the smallest ring that will carry 
 the paper should be used. With larger rings 
 the same effect may be produced by inclining 
 the ring, and so allowing the outer bubble to 
 peel off, or by placing the mouth of the pipe 
 
172 
 
 against the ring and blowing a third bubble 
 in real contact with the ring and the outer 
 bubble. This will assist the peeling process. 
 To blow three bubbles, one inside the other 
 two, is more difficult. The following plan I 
 have found to be fairly certain. First blow 
 above the ring a bubble the size of a large 
 orange. Then take a small ring about an inch 
 in diameter, with a straight wire coming down 
 from one side to act as a handle, and after 
 wetting it with the solution, pass it carefully 
 up through the fixed ring so that the small 
 ring is held well inside the bubble. Now 
 pass the pipe, freshly dipped in the solution, 
 into the outer or No. i bubble until it is 
 quite close to the small ring, and begin to 
 blow the No. 2 bubble. This must be started 
 with the pipe almost in contact with the inner 
 ring, as the film on this ring would destroy 
 a bubble that had attained any size. With- 
 draw the pipe, dip it into the liquid, and 
 insert it into the inner bubble, taking care 
 to keep these two bubbles from meeting any- 
 where. Now blow a large gas-bubble, which 
 may rest against the top of No. 2 while it is 
 growing. No. 2 may now rest against the 
 
THE FORCES WHICH MOULD THEM. 173 
 
 top of No. i without danger. Remove pipe 
 from No. 3 by gently lowering it, and let 
 some gas into No. 2 to make it lighter, and 
 at the same time diminish the pressure between 
 Nos. 2 and 3. Presently the small ring can 
 be peeled off No. 2 and removed altogether. 
 But if there is a difficulty in accomplishing 
 this, withdraw the pipe from No. 2 and blow 
 air into No. i to enlarge it, which will make 
 the process easier. Then remove the pipe 
 from No. i. The three bubbles are now 
 resting one inside the other. By blowing a 
 fourth bubble, as described above, against the 
 fixed ring, No. i bubble will peel ofi] and the 
 three will float away. No. i can, while peel- 
 ing, be transferred to a light wire ring from 
 which paper, &c. are suspended. This de- 
 scription sounds complicated, but after a little 
 practice the process can be carried out almost 
 with certainty in far less time than it takes 
 to describe it; in fact, so quickly can it be 
 done, and so simple does it appear, that no one 
 would suppose that so many details had to be 
 attended to. 
 
174 SOAP-BUBBLES, AND 
 
 Bubbles and Electricity. 
 
 These experiments are on the whole the 
 most difficult to perform successfully. The 
 following details should be sufficient to pre- 
 vent failure. Two rings are formed at the 
 end of a pair of wires about six inches long 
 in the straight part. About one inch at the 
 opposite end from the ring is turned down at 
 a right angle. These turned-down ends rest 
 in two holes drilled vertically in a non- 
 conductor such as ebonite, about two or 
 three inches apart. Then if all is right the 
 two rings are horizontal and at the same level, 
 and they may be moved towards or away from 
 one another. Separate them a few inches, and 
 blow a bubble above or below each, making 
 them nearly the same size. Then bring the 
 two rings nearer together until the bubbles 
 just, and only just, rest against one another. 
 Though they may be hammered together 
 without joining, they will not remain long 
 resting in this position, as the convex sur- 
 faces can readily squeeze out the air. The 
 
THE FORCES WHICH 1VTOULD THEM. "1 75 
 
 ebonite should not be perfectly warm and dry, 
 for it is then sure to be electrified, and this 
 will give trouble. It must not be wet, because 
 then it will conduct, and the sealing-wax will 
 produce no result. If it has been used as 
 the support for the rings for some of the pre- 
 vious experiments, it will have been sufficiently 
 splashed by the bursting of bubbles to be in 
 the best condition. It must, however, be well 
 wiped occasionally. 
 
 A stick of sealing-wax should be held in 
 readiness under the arm, in a fold or two of 
 dry flannel or fur. If the wax is very strongly 
 electrified, it is apt to be far too powerful, and 
 to cause the bubbles, when it is presented to 
 them, to destroy each other. A feeble electri- 
 fication is sufficient ; then the instant it is 
 exposed the bubbles coalesce. The wax may 
 be brought so near one bubble in which 
 another one is resting, that it pulls them to 
 one side, but the inner one is screened from 
 electrical action by the outer one. It is im- 
 portant not to bring the wax very near, as in 
 that case the bubble will be pulled so far as 
 to touch it, and so be broken. The wetting 
 
176 SOAP-BUBBLES, AND 
 
 of the wax will make further electrification very 
 uncertain. In showing the difference between 
 an inner and an outer bubble, the same re- 
 marks with regard to undue pressure, electrifi- 
 cation, or loss of time apply. I have generally 
 found that it is advisable in this experiment 
 not to drain the drops from both the bubbles, 
 as their weight seems to steady them ; the 
 external bubble may be drained, and if it is 
 not too large, the process of electrically join- 
 ing the outer bubbles, without injury to the 
 inner one, may be repeated many times. I 
 once caused eight or nine single bubbles to 
 unite with the outer one of a' pair in succes- 
 sion before it became too unwieldy for more 
 accessions to be possible. 
 
 It would _ be going outside my subject 
 to say anything about the management of 
 lanterns. I may, however, state that while 
 the experiments with the small bubbles are 
 best projected with a lens upon the screen, the 
 larger bubbles described in the last lecture can 
 only be projected by their shadows. For this 
 purpose the condensing lens is removed, and 
 
THE FORCES WHICH MOULD THEM. 177 
 
 the bare light alone made use of. An electric 
 arc is far preferable to a lime-light, both 
 because the shadows are sharper, and because 
 the colours are so much more brilliant. No 
 oil lamp would answer, even if the light were 
 sufficient in quantity, because the flame would 
 be far too large to cast a sharp shadow. 
 
 In these hints, which have in themselves 
 required a rather formidable chapter, I have 
 given all the details, so far as I am able, which 
 a considerable experience has shown to be 
 necessary for the successful performance of: 
 the experiments in public. The hints will I 
 hope materially assist those who are not in the 
 habit of carrying out experiments, but who 
 may wish to perform them for their own satis- 
 faction. Though people who are not ex- 
 perimentalists may consider that the hints 
 are overburdened with detail, it is probable 
 that in repeating the experiments they will 
 find here and there, in spite of all my care 
 to provide against unforeseen difficulties, that 
 more detail would have been desirable. 
 
 Though it is unusual to conclude such a 
 book as this with the fullest directions for 
 
 M 
 
178 SOAP-BUBBLES. 
 
 carrying out the experiments described, I 
 believe that the innovation in the present 
 instance is good, more especially because many 
 of the experiments require none of the elabor- 
 ate apparatus which so often is necessary. 
 
 OF THE 
 
 XJHIVERSIT 
 
 THE END. 
 
 Richard Clay &> So/is, Limited, London & Bungny. 
 
LOAN DEPT 
 
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