1912.] The Process of Excitation in Nerve and Muscle. 515 



concentration. There were available at this time the experimental measure- 

 ments made by many physiologists upon the relation between the minimal 

 effective strength of an exciting current and its duration, rate of rise, and 

 rate of alternation. Nernst* worked out the mathematical consequences 

 of his supposition as far as these relations were concerned, and proceeded 

 to compare the calculated values with those observed in actual experiment. 



We shall miss the whole meaning of Nernst's work, and shall attribute 

 to it errors which it did not contain, if we do not set clearly before 

 us from the beginning the limitations which he consciously made in his 

 mathematical treatment of the question. Speaking of his theory he says,f 

 " It is limited to stimuli whose duration does not exceed a certain value ; 

 probably, however, divergence will presently be found also in cases where 

 the action of the stimulus extends only over an excessively short period of 

 time." In accordance with this Nernst found, as have others who have 

 applied his formulae to experimental observations, that the agreement 

 between calculated and observed values of an exciting current is good only 

 for currents whose duration falls within a limited range. For example, 

 his theory leads to the prediction that single exciting currents of variable 

 duration will just suffice to excite if the product of their strength and the 

 square root of their duration is kept constant; in practice it is observed 

 that for durations above or below a certain range the strength of the 

 current must be considerably greater than the formula would indicate. 

 Some physiologists have seen in this fact a reason for rejecting Nernst's 

 work.}: It must, however, be remembered that Nernst was conscious of 

 the intervention of disturbing factors, particularly where currents of long 

 duration were used, and did actually discuss the nature of those factors, 

 though he did not include them in his mathematical treatment, I hold 

 still to the opinion which I expressed in 1908,§ that the hypothesis is of 

 heuristic value to say the least, and that our first concern should be to gain 

 further knowledge of the disturbing factors. 



Accordingly I shall now lay before you, as far as I am able to see them, 

 the points in which Nernst's hypothesis is incomplete, and shall then 

 consider such amendments or extensions of the hypothesis as have been 

 proposed, and the lines along which future work is suggested. 



* Nernst and Barratt, ' Zeitschr. f. Electrochem.,' 1904, vol. 10, p. 664 ; Nernst, ' Arch, 

 f. d. ges. Physiol.,' 1908, vol. 122, p. 275. 



+ Nernst, ' Arch. f. d. ges. Physiol.,' 1908, vol. 122, p. 310. 



\ Einthoven, ' Arch. f. d. ges. Physiol.,' 1900, vol. 82, p. 101 ; Wertheim-Salamonson, 

 ibid., 1905, vol. 106, p. 120 ; Hoorweg, ibid., 1908, vol. 124, p. 511 ; Hermann, ibid., 

 1909, vol. 127, p. 208. 



§ Keith Lucas, ' Journ. Physiol.,' 1908, vol. 37, p. 477. 



