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Mr. K. Lucas. 



[June 6, 



There are four main difficulties in the simple hypothesis that the con- 

 centration of ions has to reach a certain definite value at a membrane which 

 the ions cannot pass. The first of these is that of which I have already- 

 spoken, that the mathematical consequences of the hypothesis in the simple 

 form worked out by Nernst are at variance with the behaviour of currents of 

 long duration. The second is that no account is given of the well-known 

 physiological observation that a current rising to its full value up a gradient 

 of less than a certain steepness will never- excite, no matter what the value it 

 ultimately reaches. The third is that the hypothesis in its simple form does- 

 not forecast one of the most fundamental facts of electric excitation, namely, 

 the occurrence of the excitation at the cathode when the current is made, 

 and at the anode when it is broken. The fourth is that we have to postulate 

 membranes whose location in the tissue we do not know. 



These points I shall deal with singly as far as that is possible, but in 

 several cases they seem to dovetail into one another, being probably 

 expressions of a common property of the tissues. The failure of Nernst's 

 formula in the case of single currents of long duration expresses itself in the 

 fact that, whereas if the product of the current strength and the square root 

 of its duration is to remain constant the current strength should always 

 diminish when the duration is increased, in actual practice it is found that, 

 beyond a certain value of the duration, the current strength remains constant 

 no matter how far its duration is increased. This feature of Nernst's formula, 

 to which many physiologists have devoted criticism, is, as he himself stated 

 with all clearness,* merely the consequence of the assumption, made in the- 

 mathematical reasoning, that the two membranes at which ions of opposite 

 sign are concentrated are at a distance from one another which may be- 

 regarded as infinite. This assumption was a perfectly legitimate simplifica- 

 tion when the exciting currents under consideration were only those of very 

 short duration, because in such short times the effect of the proximity of the 

 two membranes — namely, the steep gradient of concentration of ions in the 

 solution between the membranes, and the consequent tendency to equalise 

 the concentrations by diffusion— would not make itself felt. For longer 

 durations of current, Nernst pointed out that, of course, this factor would 

 come in, and would prevent the strength of the exciting current from 

 falling indefinitely with great increase of its duration. Hillf has* since 

 worked out Nernst's hypothesis with a view to currents of longer duration 

 than those contemplated by Nernst, and has been therefore obliged to take 

 account of the distance between the membranes. His results show that a 



* Nernst, loc. cit, pp. 279, 280. 



t Hill, ' Joura. Physiol.,' 1910, vol. 40, p. 190. 



