II 



CHAINS OF NEURONS IN STEADY-STATE ACTIVITY 



From our point of view, a receptor provides only the mediation 

 between certain non-neural events and the occurrence of a stimulus 

 S for one or more neurons, and an effector provides the mediation 

 between the occurrence of an excitation a produced by neurons and 

 certain other non-neural events. We shall not investigate these medi- 

 ations, but shall consider only the problem of relating a to S for any 

 given neural structure. Some of the neural structures actually to be 

 found in the higher forms are of bewildering complexity, so that 

 merely to describe them from observation is the task of a lifetime. 

 We can hope to progress with our problem only if we start with very 

 simple, hypothetical structures. 



The simplest possible connected structure of more than one neu- 

 ron is a chain of neurons. In a chain, every neuron but one has an 

 origin which coincides with the terminus of some other. Call this 

 one neuron N , its origin s and its terminus s t . Let 2V a be the neu- 

 ron whose origin is at Si , let &> be its terminus, and so sequentially, 

 the terminus of the last neuron of a chain of n neurons being s n . If a 

 stimulus S is applied to N at s , it may come from a receptor or from 

 a neuron or neurons not in the chain. If N n - X develops o- at s n , this 

 may act upon an effector or upon a neuron not in the chain. That is 

 immaterial. Suppose that the neurons of our chain are all of the 

 simple excitatory type. Suppose, further, that only a negligible time 

 is required for the o-(= e) produced by any neuron to reach its 

 asymptotic value (/> when a constant stimulus S is applied. In other 

 words, we are now considering the chain only in its asymptotic state 

 after stimulation by a constant stimulus. Then if 



u = S 



is the total stimulus acting at s upon N , it follows that 



o"i — </>o (o"o) 



is the a produced by N. at s x , where fo is the ^-function of N . If 

 no receptor or neuron outside the chain introduces any S or a at s 1 , 

 then 



(T 2 = <£i((Ti) = <£l[<£o(0"o)] 



is the o- produced by N x at s 2 . Thus we can calculate sequentially all 

 the o-i . 



