PLATEAU ON SOAP-BUBBLES. 395 



of the water except in a thin stratum close to the surface, where it is some- 

 what 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 

 separates 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 allows the 

 surface to diminish. Now a surface which tends to diminish in area, and which 

 thus tends to draw together any solid framework which forms its boundary, 

 is said to have surface-tension. Surface-tension is measured by the force acting 

 on one millimetre of the boundary edge. In the case of water at 20C., the 

 tension is, according to M. Quincke, a force of 8*253 milligrammes weight per 

 millimetre. 



M. Plateau hardly enters into the theoretical deduction of the surface- 

 tension from hypotheses respecting the constitution of bodies. We have there- 

 fore thought it desirable to point out how the fact of surface-tension may be 



502 



