648 PRINCIPLES OF GENERAL PHYSIOLOGY 



Cj and c.,, of course, refer to concentrations of the ion concerned, that is, the one 

 to which the membrane is permeable. 



Although there are certain experimental difficulties in the actual investigation 

 of the question, especially when inorganic electrolytes are dealt with, some 

 measurements which I made with Congo-red (1911, 2, pp. 245-247) gave results 

 in satisfactory agreement with the formula. 



If the S3'8tem is not in osmotic equilibrium, so that there is a flow of solvent through the 

 membrane, the electromotive force would not be given by the formula. 



There is an interesting theoretical difficult}', analogous to that involved in electrolytic 

 dissociation already referred to (page 180), which has not yet received satisfactory explanation. 

 We know experimentally that a Helmholtz double layer is formed, owing to the fact that one 

 ion cannot 'move far from the oppositely charged one. But it is not easy to see why this 

 should be so. Suppose the electrolyte completely dissociated. On the kinetic theory, this 

 means that the period during which any oppositely charged ions come within each other's 

 sphere of influence is negligible, so far as electric stresses are concerned. The work required 

 to separate the ions is therefore accomplished, and further separation should not require any 

 more energy. So that, if such a solution be separated from pure solvent by a membrane 

 permeable to one kind of ion only, these ions should be able to diffuse out freely, since they 

 are already out of the range of influence of the opposite ions. Of course, if they did so there 

 would be a large increase in the free energy of the sj-stem, which would infringe the second 

 law of energetics. But if the force uniting the ions is purely electrical, it is difficult to 

 understand why they cannot separate from one another after being dissociated. Larmor (1908) 

 suggested that the energy for dissociation may be drawn from the volume energy of the 

 solvent. 



To return to the question of the electromotive force at a membrane. From 

 the mode of its production, it will be seen to be an illustration of the rationale 

 of metallic electrode potentials, if we regard the metallic ions as being free 

 to escape from the surface of the metal, while the oppositely charged mass of 

 metal cannot. Contrary to the contact potential difference of solutions free 

 to diffuse, it is permanent. We may speak of a membrane of the kind described 

 as being polarised. This form of expression is sometimes convenient. 



In the application of the above theory to the living cell, we see that, if 

 the membrane is permeable to both ions, no electromotive force can be present ; 

 although if one ion be larger than the other, there might be only a small 

 number of pores permeable to the larger ion, so that, for a considerable time, 

 an electromotive force might exist. If, moreover, the membrane were impermeable 

 to both ions, there could be no potential difference, since there would be no 

 possibility of the ions separating to form a double layer. 



In short, a membrane previously impermeable to both ions might give rise 

 to an electromotive force if it became permeable to one only, but not if it 

 became permeable to both. Also a membrane, previously permeable to both 

 ions, might become a source of potential difference if it became permeable to 

 one only. Such changes are, no doubt, taking place in the normal activities 

 of the cell. 



The manner of origin of these potential differences is essentially the same 

 as the "electrical forces at phase boundaries, ' : discussed by Haber and 

 Klemensiewicz (1909); the phenomena described by Beutner (1912 and 1913) 

 are, no doubt, due to the same facts. Suppose that we have a layer of a liquid, 

 immiscible with water, in contact with a solution in water of an electrolyte, 

 of which one ion is soluble in the non-aqueous phase, the other insoluble. 

 It is clear that the former ions will tend to pass into the non-aqueous liquid, 

 but cannot get beyond the boundary, owing to the other ions being unable 

 to do so. We have again a Helmholtz double layer. Thus Beutner finds 

 a potential difference at the contact surface between a watery solution of 

 potassium thiocyanate and a solution of toluidine thiocyanate in toluidine. 

 This is readily accounted for if the potassium ion is insoluble in toluidine, SCN 

 ion being soluble. 



If, in any cell process, ions are newly formed, these will add to the concentra- 

 tion of those of the same sign already present, and increase the potential 

 difference at a membrane of the kind described, as the formula shows. 



We have seen (page 161) that the concentrations expressed in the formula 



