SURFACES OF DISCONTINUITY 697 



This hypothesis, as we have pointed out previously, involves a 

 combination of a Gibbs term and a Lippmann term in the 

 expression for da, which are not equivalent to one another, but 

 complementary. Thermodynamical deductions of this equa- 

 tion will be found in the references mentioned above. The 

 most complete theoretical treatment is given in Butler's papers 

 in the first list of these references. In the writer's opinion it 

 suffers somewhat by an unnecessary complication, the intro- 

 duction of a second "surface tension," denoted by 7 in the paper. 

 The writer will give a statement of the theory without introduc- 

 ing this additional conception, at the same time making a critical 

 reference to one feature of such proofs. 



68. The Reason Why Gibbs' Derivation of His Electrocapillary 



Equation [690] Exhibits It as Equivalent to 



Lippmann's Equation 



In the first place it may be well to point out once more 

 just exactly how Gibbs' deduction of [690] comes to be equiva- 

 lent to Lippmann's result, and not complementary to it like the 

 "Gibbs terms" in more recent formulae for da. It simply arises 

 from the fact that in Lippmann's proof "electricity" is a 

 "component" of the mercury whose "chemical potential" 

 corresponds to V, the electric potential. We can actually make 

 the proof of Lippmann's result correspond in every mathemati- 

 cal detail to the manner in which Gibbs derives his adsorption 

 equation. Calling e* the energy of the mercury surface we 

 write 



S(S = fSjjs 4- 0-55 -{- V8Q 



as the condition of equilibrium of this surface, V corresponding 

 to n^ and Q to m^, the potential and quantity of the component, 

 "electric charge." By the usual reasoning based on the fact 

 that an increase of s requires, for equilibrium conditions at the 

 same t, a, V, proportional increases in e^, s, and Q we see that 



e^ = tri^ -\- as -{- VQ. 

 Hence 



des = t dT]S + T)S dt -\- a ds + s da -{- VdQ + Q dV. 



