294 PROTOPLASMIC ACTION AND NERVOUS ACTION 



situated a short distance apart must be considered; 

 these are the surfaces where the current-lines intersect 

 the two opposite faces of the irritable element. If 

 these surfaces are close together, the diffusion-gradient 

 set up by a given current is steep, and hence the back- 

 diffusion opposing the polarization is relatively rapid. 

 The production of the critical polarization change will 

 then require a stronger current than with the membranes 

 far apart. This conception explains also why a current 

 passing crosswise through a nerve or parallel-fibered 

 muscle is so much less effective than one passing length- 

 wise. Hill's calculation leads him to the formula, 



i — _ ^^ , for the conditions of stimulation by a constant 



current, where X is a direct function both of the proximity 

 of the two membrane-surfaces concerned (proximity being 

 the reciprocal of the distance apart) and of the rate of 

 movement of the ions; i represents the intensity of 

 the current, t its duration, and \x and B are constants 

 having reference to the conditions of movement of the 

 ions in the tissue. This formula gives a remarkably 

 close agreement with observation through a wide range 

 of intensities. A further essential feature of Hill's theory 

 is its recognition that the polarization change is in reality 

 merely the determining condition of a chemical change 

 which must proceed at a certain minimal rate in order 

 to cause excitation. From this point of view it is possible 

 to understand why not only the degree of polarization 

 attained, but also the rate at which this critical degree 

 is reached determines whether stimulation shall be 

 initiated or not. The stimulation process is a process 

 sui generis^ distinct from the initiatory physical change; 



