286 PHYSIOLOGY 



a nature that the excited spot is negative to adjacent unexcited spots. This 

 electrical change rises rapidly to a maximum and dies away more slowly, 

 the rate of its rise, and still more of its subsidence, varying largely according 

 to the nature of the tissue under investigation. 



(2) The excitatory change is aroused only at the poles of a current 

 passing through the tissue, i.e. at those places where polarisation can oc 



in consequence of the electrical movement of ions. 



(3) Excitation only occurs at the cathode at make of the current, 

 and only occurs if the current attains a sufficient strength within a certain 

 period of time, the relation of strength of current to rate of change varying 

 in different tissues. 



(4) All living tissues are made up of colloids, divided into compartments 

 by membranes of various permeabilities and permeated with salts and other 

 electrolytes in solution. 



Disregarding for the moment all considerations of structure, it is possible 

 to form a hypothesis of the nature of electrical excitation which takes into 

 account the facts just mentioned and enables us to give a quantitative or 

 mathematical expression to the factors involved. An electrical current 

 passing through a tissue containing membranes, impermeable to the dis- 

 solved ions, will set up differences of concentrations at and near the mem- 

 branes. Nernst, on the supposition that these differences of concentrations, 

 when sufficiently large, would cause an excitation, arrived at a formula 

 connecting the lowest current required to excite with its duration, and 

 another formula connecting the lowest amplitude of an electrical current 

 with its frequency. The mathematical investigation of the question has been 

 continued by A. V. Hill in conjunction with Keith Lucas. For this purpose 

 we may suppose that the excitable unit is represented by a cylindrical space 



closed at its two ends by the mem- 

 branes A and B (Fig. 131) and 

 filled with a solution of electro- 

 B lytes. If a current be passed 

 from B to A the positively charged 

 ions will move towards A and 

 FIG. 131. tend to accumulate there. The 



accumulation of the ions near the 



membranes will be limited by the tendency of the ions to equalise their con- 

 centration in all parts of the cell by diffusion. If we suppose that a necessary 

 condition for excitation is that the concentration of the ions in the neigh- 

 bourhood of one of the membranes shall reach a certain definite value, it 

 becomes possible to calculate under what conditions of strength, duration, 

 &c., an electrical current will just produce excitation. The rise of the 

 excitatory state would here be determined by the rate at which the ions 

 accumulate, the subsidence of the excitatory state by the rate of dispersal of 

 the ions by diffusion. The formula arrived at by these observers has this 

 form : ^ 



