NERVOUS CONDUCTION AND EXCITATION 139 



The formulae of Nernst account for the experimental data 

 relating minimal frequency, duration, and current strength 

 necessary to set up an excitation within a restricted range. 

 By taking into consideration the conditions arising when the 

 membranes at which ions of opposite sign collect are close 

 together, A. V. Hill deduced a modified expression relating 

 the duration of an exciting current to its least strength 

 with greater accuracy than the formulae of Nernst. Hill's 

 expression is : 



_ A 



In this equation A, jit, and 6 are constants depending upon the 

 distance apart of the membranes («), and the distance from 

 the membrane excited at which concentration changes are 

 considered (Z>), the number of ions (p) by which a given quantity 

 of electricity is carried, the diffusion constant of the ions 

 involved (k) and an arbitrary factor (C). Thus : 



A= ix—Aa cos — , v—e a* 



2 



whence it is seen that log B is directly proportional to the 

 diffusion constant of the ions concerned. 



Keith Lucas has evaluated the constants of HilFs equation 

 and shown not only a remarkable correspondence between 

 observed and calculated values, but that a number of interesting 

 phenomena are illuminated by the results so obtained. The 

 evaluation is straightforward, if the equation is written ; 



iyiQ^=i — A 



Thus in an experiment of Lapicque the corresponding 

 threshold-values for current strength and duration (in o'ooi 

 sec.) were : 



