V] OF SURFACE ENERGY 207 



pressure is of the magnitude of thousands of atmospheres, — a con- 

 clusion which is supported by other physical considerations. 



The contraction of a liquid surface and other phenomena of 

 surface tension involve the doing of work, and the power to do 

 work is what we call energy. It is obvious, in such a simple case 

 as we have just considered, that the whole energy of the system 

 is diffused throughout its molecules ; but of this whole stock of 

 energy it is only that part which comes into play at or very near 

 to the surface which normally manifests itself in work, and hence 

 we may speak (though the term is open to some objections) of 

 a specific surface energy. The consideration of surface energy, 

 and of the manner in which its amount is increased and multiphed 

 by the multiplication of surfaces due to the subdivision of the 

 organism into cells, is of the highest importance to the physiologist ; 

 and even the morphologist cannot wholly pass it by, if he desires 

 to study the form of the cell in its relation to the phenomena of 

 surface tension or "capillarity." The case has been set forth with 

 the utmost possible lucidity by Tait and by Clerk Maxwell, on 

 whose teaching the following paragraphs are based : they having 

 based their teaching upon that of Gauss, — who rested on Laplace. 



Let E be the whole potential energy of a mass M of liquid; 

 let Cq be the energy per unit mass of the interior liquid (we may 

 call it the internal energy) ; and let e be the energy per unit mass 

 for a layer of the skin, of surface S, of thickness t, and density 

 p {e being what we call the surface energy). It is obvious that the 

 total energy consists of the internal flus the surface energy, and 

 that the former is distributed through the whole mass, minus its 

 surface layers. That is to say, in mathematical language, 



E={M-S . ^tp) e^ + S . lltpe. 



But this is equivalent to writing : 



= Mco + S .i:tp{e - Co) ; 



and this is as much as to say that the total energy of the system 

 may be taken to consist of two portions, one uniform throughout 

 the whole mass, and another, which is proportional on the one hand 

 to the amount of surface, and on the other hand is proportional 

 to the difference between e and e^, that is to say to the difference 

 between the unit values of the internal and the surface energy. 



