SINGLE SYNAPSE : TWO NEURONS 41 



equation (2) , but with t = and t r replaced by t . Thus from a con- 

 sideration of a chain of two neurons one should expect that if all 

 other conditions remain unchanged the same relationship should hold 

 in both cases, except that t would be absent in this case. Since the 

 two cases are experimentally distinct, it may be that the results from 

 the two types of experiments are widely divergent. If so, it may be 

 necessary to assume that there are several neurons in the chain or 

 even circuits in the structure. In any case, the kind of disagreement 

 may suggest the nature of the change to be made in the neural net. 



Let us consider another special case of a chain of two neurons. 

 Let the afferent neuron be of the mixed type with <£ = y> , a > b , and 

 threshold h x . A constant S > h x applied to such a neuron results in 

 a a (= e — j) which is positive, but which vanishes asymptotically. 

 Then, the stimulus being presented at t = when e = j = , if S is 

 large enough, and h not too large, a will first reach the value h at 

 some time t f . From this one can determine a relation t r (S) similar 

 to that of equation (1). If S is maintained at a constant value for a 

 sufficient time, <r reaches a maximum and declines. Let t r + r be the 

 time at which a returns to the value h . Then we can determine the 

 duration T of the reaction as a function of the intensity S when 

 e = j = initially. 



At t = t* > t + t let S be replaced by S + AS, where A S may 

 take on any positive value. Negative values of A S would be of in- 

 terest only if t r < t* < t r + r . Then for t > t* > t r + T we may write 



+ 4>(S + A S) [e- & <<-'*> - «?-«(«-«•>] . 



If A S is large enough, a will again reach h at some time t — t* + t r ' 

 and the response will again be initiated. By setting a = h in equa- 

 tion (3), we obtain t r '(AS, S, t*) from the smaller root, t. For 

 t* > > 1/6 and t r ' < < 1/6 , we may obtain an equation for t r ' which 

 shows the time V to depend only upon A S/S , and not upon h x . 



At some time t = t* + t r ' + t the response will again cease. Using 

 the larger root of a = h in expression (3) we may determine the 

 duration T '(AS ,S ,t*) of the response. For t* > > 1/6 and r > > 1/a, 

 we may write 



T' = -log[/log(l + zlSyS)] -t f ', (4) 



6 



/ being a constant. For fairly large values of A S/S we may neglect 

 t r ' in equation (4). The equation thus makes a definite testable pre- 

 diction as to the nature of the relation between the duration of the 

 response and the relative increase of the stimulus. 



