1902.] Photographic Records of the Response of Nerve. 201 



Problems of this type arise when two portions of the same nerve are 

 kept at different temperatures. They may be worked out graphically, 

 or by writing a separate formula for each portion where a sudden 

 change occurs. 



Proceeding to a closer examination of the problem, it will be con- 

 venient to consider in the first place the variations of P.D. due to the 

 propagation of the wave-front of electrical activity. It may be assumed 

 provisionally that its rate of propagation is constant, and that its 

 passage is marked by a sudden definite rise of potential. As a farther 

 simplification, the linear conductor is assumed to be of indefinite 

 length, the origin of co-ordinates being situated to the left of the 

 portion under consideration, so that the position of each of the leads 

 connecting it with the electrometer may be represented by a positive 

 quantity. 



Let the line ON, fig. 8, represent a linear conductor of indefinite 

 length, and let P be the point at which the electrical change originates. 



_o a B p D j y 



Fig. 8. — 2Jeeds no explanation, sare the text. 



Let the distance OP = p. Let leads connecting ON with an electro- 

 meter be placed at any two of the points A, B, or, D, and let their 

 respective distances from be a, b, d. 



Let T = t + s, be the time that has elapsed since the instant of 

 stimulation, s representing the latent period if any exists, and t being 

 the time that . has elapsed since the response commenced. In most 

 cases s is eliminated, and therefore t will be used in the formulae. The 

 exceptions are dealt with on p. 211. 



Let x represent the distance from of the wave-front of the 

 electrical change at the time /. Then x = p ± vt, where v is the 

 velocity of propagation of the wave-front in centimetres per second. 

 The sign of v is positive for all points to the right of p and negative 

 for all points to the left of it. 



In the simple case under discussion, namely, that of a sudden 

 definite rise of potential at the wave-front, it is manifest that a 

 difference of potential will be established between A and B as soon as 

 the wave-front has passed B, and that it will cease when the wave-front 

 reaches A, both electrodes being then at the higher potential : i.e., the 

 P.D. begins when b = p - vt v and ends when a = p - vt 2 . 



Hence t x = (p-b)/v, U = (p-a)lv; 



and the duration of the difference of potential between A and B is 



t 2 -h = (b - a)jv. 



