172 PHYSIOLOGY 



which is observed in living tissues. Supposing we have (Fig. 31) two solu- 

 tions, A and B, each containing an electrolyte, UV, in different concentrations 

 separated by a membrane m. If u represents the velocity of transmission 

 of U through m, and v the velocity of V, then the electromotive force of the 

 cell is given by the formula 



W ~~Vo577.1og. 10 C2 Volt. 



U + V 



If v is taken as very small, the membrane may be regarded as semipermeable 

 for the corresponding ion V. Supposing we take potassium chloride as the 

 solution, we should have to make the concentration in B eight times that in 

 A, in order to get a current of strength equal to that obtained from the 

 olfactory nerve of the pike, for example. Macdonald has made such an 

 assumption in order to explain the normal nerve current. He suggests that 

 the axis cylinder contains an electrolyte which is equivalent to a 2-6 per 

 cent, solution of potassium chloride. It is unnecessary however to assume 

 such great differences of concentration if we regard the membrane as itself 

 a S9lution of electrolytes, as has been suggested by Cremer, or* if we take 

 different substances on the two sides of the membrane. In the case of two 

 electrolytes, UjYj, U 2 V 2 (U being the cation in each case), separated by a 

 membrane with varying permeability for the different ions, the electro- 

 motive force of the cell is given by the following formula : 



0-0577 lo. 10 % + V * 



where u it DI, u z , v 2 , are the velocities of the corresponding ions. We assume 

 that the concentrations of the two solutions are identical. Now it is evident 



that by making u z and v l very small, the expression log. 10 - 2 may be 



U% "I" ^1 



made to attain any quantity, and in the same way by making u l + v z 

 infinitesimally small, the electromotive force of the combination will also 

 become correspondingly small. The thickness of the membrane does not 

 come into the formula, so that membranes of microscopic or even ultra- 

 microscopic thickness, which we have seen reason to assume as present in 

 and around cells and their parts, could perform all the functions required 

 of the hypothetical membrane in the above example. This is also the case 

 when Y! is the same as V 2 that is to say, there is a common anion or a 

 common cation on the two sides of the membrane. 



It must be remembered that the passage of a current through a membrane 

 impermeable to one or other ion in the surrounding fluid will cause an accu- 

 mulation of the ion at the surface of the membrane, so that this will become 

 polarised. Such an accumulation at any surface will naturally alter the 

 properties of the surface, including its surface tension. The construction of 

 the capillary electrometer depends on this fact. When mercury is in contact 

 with dilute acid or mercuric sulphate solution it takes a positive charge from 

 the fluid, and the state of stress at the surface of contact between the 

 mercury and the negatively charged fluid diminishes the surface tension of 



