Double-Layer of Solid and Liquid Bodies. 311 



The mean electric intensity in the double-layer of a 

 /c-valent metal at distance x from the surface is given by the 

 equation 



K £ =--!L Ke "ir-\.vy\ |«l<r, . . . (11) 



which is derived from the multiplication of (4), § 2, by k,. 

 From this W ma}' be calculated by means of the relation 



which gives 



1 f*+r _ 1 f*r 



b7rj_, 4ttJ 



W=|j(«»)V, (12) 



or, by (7) and (8), W= ~ Ve (it will be noticed that Ye is 



the energy of the "equivalent" double-layer). Putting 



3 V 



€=— we may replace (12) by the following formula : 



9 V 2 



W=^r- -, (13) 



which is very convenient for the calculation of W when the 

 intrinsic potential V and the atomic radius r are known. 

 We have seen that for mercury r=R = l , 4 x 10~ 8 cm. and 



V =4-2 volts, or ^C.G.S.E. units (Table I.). Consequently 



W - 9 i 4 ^ =4 72^ 



~ 80tt(300) 2 1-4x10- 8 cm. 2 ' 



which corresponds to a surface-tension of 472 — — -. As a 



cm. , 



matter of fact, the surface-tension o£ mercury is 436 — — - 



J cm. 



(according to some other measurements even 460). We see 



that W is slightly larger than a. This is simply explained 



by the fact that r is not equal to, but slightly less than, R. 



The surface-tension of mercury may be thus wholly accounted 



for by the electrostatic energy of its surface double-layer. 



There remains, apparently, no room for the hypothetical 



cohesive forces upon which the classical theories of Laplace 



and Gauss were based. We shall assume that in the case 



of all liquid bodies these forces have no direct influence upon 



the surface-tension, and that the latter depends exclusively 



upon the energy of their electric double-layers ; expressing 



this mathematically, we get 



<r = W * . . (14) 



