322 PHYSIOLOGY 



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

 tion in all parts of the cell by diffusion. If we suppose that a neces- 

 sary condition for excitation is that the concentration of the ions in the 

 neighbourhood 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 excita- 

 tion. The rise of the excitatory state would here be determined by 

 the rate at which the ions accumulate, the subsidence of the excitatory 



\B 



FIG. 132. 



state by the rate of dispersal of the ions by diffusion. The formula 

 arrived at b these observers has this form : 



where 



i is the smallest current which will excite, 



t is duration of the current. 

 while X, /UL, 9 are constants which depend on : 



(1) The distance between the membranes. 



(2) The distance from the membrane at which the concentration 



changes are being considered. 



(3) The diffusion constant of the ion. 



(4) The number of ions by which a given quantity of electricity 



is carried. 



(5) A constant expressing in general terms the ease with which 



a propagated disturbance is set up. 



Investigation on these lines may give us in future sufficient in- 

 formation to form a material conception of the factors involved in 

 excitation, factors which in the above formula have only a symbolic 

 existence. Thus a determination of the distance between the mem- 

 branes would give us some clue to the size of the ultimate excitatory 

 units in the tissue involved.* The constant /z has reference only to the 



* It would be premature at present to give any histological significance to 

 Hill and Lucas's diagrammatic cylinder. As Hardy has pointed out, the nerve 

 cannot consist of a row of such cylinders, otherwise excitation would occur 

 throughout the whole intrapolar region, and not be confined to the cathode at 

 make and the anode at break. It may be that we are dealing here again with 

 the polarisable sheath of the ' Kernleiter,' and that the membrane A corresponds 

 to the surface of the axis cylinder or of its neuro-fibrils. 



