394 PRINCIPLES OF GENERAL PHYSIOLOGY 



The factors in question may be discussed briefly here. It may be pointed out that, from 

 the standpoint of general physiology, the vakie of formula- of the kind in question is not so 

 much that of being able to express the relation between the exciting power of an electrical 

 stimulus and its physical properties, but the light that they throw on the nature of the 

 excitatory process itself. 



The first point is that, in Nernst's treatment of the problem, only one membrane 

 is taken account of. But it is clear that there may be another membrane at no 

 great distance from the one under consideration, which will make a considerable 

 difference in the diffusion of the ions, since the ions of opposite sign will be con- 

 centrated there. By the introduction of this conception, Hill deduces a formula 

 which was found by Keith Lucas (1910) to satisfy experimental data when currents _ 

 of long duration are used. The effect of the proximity of the membranes in its 

 tendency to cause the equalisation of concentration by diffusion, owing to the rapid 

 fall of concentration in a short distance, would naturally not come into play in very 

 short periods of closure of the current. 



A second point, which was suggested by Nernst in order to account for the 

 fact that, if a current is allowed to rise in strength at a rate less than a certain 

 critical value, it does not excite at all, is that there is reason to suppose that the 

 separation of ions brought about by the current is accompanied by a slow, 

 independent, automatic process, by which the ions are taken out of the sphere of 

 action in some way before they have attained sufficient concentration to excite. 

 The precise manner in which this happens is not clear, but it is probably a 

 reversible process of the nature of adsorption. 



Hill gives (1910, p. 208) as an illustration a tube of a mixture of oxygen and hydrogen 

 gases. Suppose that this is heated at one end to a temperature at which explosion occurs. 

 This corresponds to an effective stimulus setting up a propagated disturbance. But, if we 

 heat very gradually, not allowing the temperature to rise to the explosion point, the gases 

 combine slowly without explosion, and, if the heating is continued for a sutlicicntly long 

 time, there will be a very small tension of th gases left uncombined, and no explosion will 

 result even when the temperature arrives at the degree usually sufficient. 



According to Hill, the experimental results available at present are not of such a form 

 as to enable his formula to be applied to cases of exciting currents slowly rising in strength. 



Although the complete derivation of the formula is beyond the space that can 

 be given here, it may be of interest to enumerate the factors of which it consists. 

 In its simplest form it is : 



. A. 



\^ffi 



where i and t are the variables, i being the smallest current that will excite when 

 of the duration t. X, p and 6 are constants, whose precise form and significance 

 will be found in the original paper and in that by Keith Lucas (1910, p. 234). It 

 must suffice to say that each of these constants is compounded of other constants 

 to which a definite meaning can be attached. They are : 



a, the distance between the membranes. 



b, the distance from the membrane at which the concentration changes are 



being considered. 



k, the diffusion constant of the ion concerned. 



v, the number of ions, each carrying a given quantity of electricity. 

 C, a constant expressing the rate of " recombination " of the ions in the 

 manner referred to above; or, as Lucas prefers to put it, the ease with 

 which the propagated disturbance is set up in a particular condition. 

 Lucas shows further (1910) how the various constants are affected by certain 

 changes of condition, such as temperature and presence of calcium, and the part 

 played by each in the process of excitation. We note especially the changes in 



C and in k. Now is the diffusion time of the ions concerned in the pi-ore^. and 

 a- 



the constant of the simplified equation is defined by Hill as 



kir- 



log 0= - - 

 a- 



