NATURE 



119 



THURSDAY, JUNE iS, 1874 



PL A TEA U ON SOAP-B UBBLES 



Stalique cxpcrimcntah ct tlicoriquc dcs Liqiiidcs souniis 

 aux scuks Forces moUculaires. Par J. Plateau, Pro- 

 fesseur h. I'Universitd de Gand, cS:c. (Paris, Gauthier- 

 Villars ; London, Triibner & Co. ; Gand et Leipzig, 

 F. Clemm. 1873.) 



ON an Etruscan vase in the Louvre figures ot children 

 are seen blowing bubbles. Those children probably 

 enjoyed their occupation just as modern children 

 do. Our admiration of the beautiful and delicate 

 forms, growing and developing themselves, the feeling 

 that it is cur breath which is turning dirty soap- 

 suds into spheres of splendour, the fear lest by an 

 irreverent touch we may cause the gorgeous vision to 

 vanish with a sputter of soapy w'ater in our eyes, our wist- 

 ful gaze as we watch the perfected bubble when it sails 

 away from the pipe's mouth to join, somewhere in the 

 sky, all the other beautiful things that have vanished be 

 fore it, assure us that, whatever our nominal age may be- 

 we are of the same f imily as those Etruscan children. 



Here, for instance, we have a book, in two volumes, 

 octavo, written by a distinguished man of science, and 

 occupied for the most part with the theory and practice of 

 bubble-blowing. Can the poetry of bubbles survive this ? 

 Will not the lovely visions which have floated before the 

 eyes of untold generations collapse at the rude touch of 

 Science, and " yield their place to cold material laws"? 

 No, we need go no further than this book and its author 

 to learn that the beauty and mystery of natural pheno- 

 mena may make such an impression on a fresh and open 

 mind that no physical obstacle can ever check the course 

 of thought and study which it has once called forth. 



M. Plateau in all his researches seems to have selected 

 for his study those phenomena which exhibit some re- 

 markable beauty of form or colour. In the zeal with 

 which he devoted himself to the investigation of the laws 

 of the subjective impressions of colour, he exposed his 

 eyes to an excess of light, and has ever since been blind. 

 But in spite of this great loss he has continued for many 

 years to carry on experiments such as those described 

 in this book, on the forms of liquid masses and films, 

 which he himself can never either see or handle, but from 

 which he gathers the materials of science as they are 

 furnished to him by the hands, eyes, and minds of de- 

 voted friends. 



So perfect has been the co-operation with which these 

 experiments have been carried out, that there is hardly a 

 single expression in the book to indicate that the measures 

 which he took and the colours with which he was charmed 

 were observed by him, not in the ordinary way, b.'t 

 through the mediation of other persons. 



Which, now, is the more poetical idea — the Etruscan 

 boy blowing bubbles for himself, or the blind man of 

 science teaching his friends how to blow them, and mak- 

 ing out by a tedious process of question and answer the 

 conditions of the forms and tints which he can never 

 see .' 



IJut we must now attempt to follow our author as he 

 passes from phenomena to ideas, from experiment to 

 theory. 



Vol. X. — No. 242 



The surface which forms the boundary between a liquid 

 and its vapour is the seat of phenomena on the careful 

 study of which depends much of our future progress in 

 the knowledge of the constitution of bodies. To take 

 the simplest case, that of a liquid, say water, placed in a 

 vessel which it does not fill, but which contains nothing 

 else. The water lies at the bottom of the vessel, and the 

 upper part, originally empty, becomes rapidly filled with 

 the vapour of water. The temperature and the pressure— 

 the quantities on which the thermal and statical relations 

 of any body to external bodies depend^are the same for 

 the water and its vapour, but the energy of a milligramme 

 of the vapour greatly exceeds that of a milligramme of 

 the water. Hence the energy of a milligramme cf water- 

 substance is much greater when it happens to be in the 

 upper part of the vessel in the state of vapour, than 

 when it happens to be in the lower part of the vessel in 

 the state of water. 



Now we find by experiment that there is no difference 

 between the phenomena in one part of the liquid and 

 those in another part except in a region close to the 

 surface and not more than a thousandth or perhaps a 

 millionth of a millimetre thick. In the vapour also, every- 

 thing is the same, except perhaps in a very thin stratum 

 close to the surface. The change in the value of the 

 energy takes place in the very narrow region between 

 water and vapour. Hence the energy of a milligramme 

 of water is the same all through the mass of the water 

 except in a thin stratum close to the surface, where 

 it is somewhat greater ; and the energy of a milligramme 

 of vapour is the same all through the mass of vapour 

 except close to the surface, where it is probably less. 



The whole energy of the water is therefore, in the 

 first place, that due to so many milligrammes of water ; 

 but besides this, since the water close to the surface has 

 an excess of energy, a correction, depending on this 

 excess, must be added. Thus we have, besides the energy 

 of the water reckoned per milligramme, an additional 

 energy to be reckoned per square millimetre of surface. 



The energy of the vapour may be calculated in the 

 same way at so much per milligramme, with a deduction 

 of so much per square millimetre of surface. The quantity 

 of vapour, however, which lies within the region in which 

 the energy is beginning to change its value is so small 

 that this deduction per square millimetre is always much 

 smaller than the addition which has to be made on 

 account of the liquid. Hence the whole energy of the 

 system may be divided into three parts, one proportional 

 to the mass of liquid, one to the mass of vapour, and the 

 third proportional to the area of the surface which sepa- 

 rates the liquid from the vapour. 



If the system is displaced by an external agent in such 

 a way that the area of the surface of the liquid is increased, 

 the energy of the system is increased, and the only source 

 of this increase of energy is the work done by the external 

 agent. There is therefore a resistance to any motion 

 which causes the extension of the surface of a liquid. 



On the other hand, if the liquid moves in such a way 

 that its surface diminishes, the energy of the system 

 diminishes, and the diminution of energy appears in the 

 form of work done on the external agent which allosvs the 

 surface to diminish. Now a surface which tends to di- 

 minish in area, and which thus tends to draw together 



