SINGLE SYNAPSE : TWO NEURONS 43 



Equation (9) makes a definite prediction as to the relationship 

 between the reaction time and the variables S , A S , and t' and is thus 

 subject to experimental test. 



If, for fixed S and t', we now restrict A S to the smallest value 



for which the response can still take place, we obtain a relation of the 



form 



AS S 



log = e- bt 'log — , (10) 



h' K 



where log K = log h x + h/(i . Thus, except for minimal if, the loga- 

 rithm of the testing stimulus A S is an exponentially decreasing func- 

 tion of the time t' of recovery. As the time t' becomes infinite, A S 

 approaches h'. The intensity S determines by how much the ordinate 

 is multiplied in the graph of A S against P. The type of relationship 

 between A S and t' of equation (10) for the case of visual stimuli is 

 found in the work of various investigators (cf. S. Hecht, 1920). 



Suppose next, still assuming that <j> = y> , that any constant stim- 

 ulus has been applied for a long time and that at t = the stimulus 

 is increased at a rate such that cUf>/dt = X . After a time t , we find 

 that 



X X 



<r = — (1- e~ bt ) (1- e~ at ). (11) 



b a 



If X < abh/ (a — b) , where h is the threshold of the second neuron, a 

 will never exceed h and there can be no response. This is analogous 

 to the failure of slowly rising currents to produce excitation in peri- 

 pheral nerves and corresponds to the effect, commonly experienced, 

 that a stimulus which rises slowly in intensity often fails to evoke a 

 response. If X is larger, and response occurs, then from equation (11) 

 we can determine the reaction-time t r '" by solving for t with a = h . 

 It is clear that the reaction-time depends very much upon the manner 

 in which the stimulus is presented. 



Let us consider the effect of a different mode of application of a 

 stimulus to an afferent neuron of the mixed type with <f> = t/' • Let a 

 stimulus S be given for a period of time rT followed by no stimulus 

 for a period of time (l—r)T. Let this be repeated indefinitely. For 

 each successive interval we can determine e and j from the differ- 

 ential equation together with the requirement that £ and j both 

 be continuous. The value of a(t) during the interval < t < rT 

 of stimulation after a large number of repetitions may be obtained 

 as follows. Let e„- t represent the value of e at the beginning of the 

 n-th resting period, and e' n -i the value at the beginning of the n-th 

 period of stimulation, where e — . We use equation (8) of chap- 



