THE GENERAL NEURAL NET 31 



of the linear variation we called the activity-parameter. We found 

 that if a chain of n neurons leads from a synapse s, to a synapse s n , 

 and if fixed stimuli &,•••,£» are applied at each synapse s x , ••• , s n , 

 then the total excitation y n + <r„ + S n present at s n is expressible as 

 a linear function of the total y present at s provided y lies between 

 certain positive fixed limits, and is otherwise constant. In special 

 cases the limits are equal and y n is independent of y , s„. being said to 

 be inaccessible to s . When s n is accessible to s , then the relation 



y,i — S n 4- 3 + Ay' when y < y' , 



Vn = S n + 3 + Ay when y' ^y ^y" , (1) 



y n = S n + 3 + 43/" when */„ > y" , 



obtained in chapter ii for a chain, differs formally from that for a 

 single neuron only by the presence of the term 3 . But if we set 



Z = S n + 3, (2) 



we have more simply 



y n = Z + Ay (3) 



when y lies between the stated limits, and when it does not the near- 

 est limit appears in this equation in place of y, • The similarity to 

 the behavior of a single neuron is now complete, the term Z cor- 

 responding to the stimulus applied at the terminus. However, this 

 term, as well as the limits y and y" , depend here upon the particular 

 stimuli applied at the various synapses of the chain. 



In the discussion of more general types of net, only the occur- 

 rence of circuits can present essential complications and hence we 

 limit ourselves to these, considering first the case of a simple circuit 

 of n neurons. Such a circuit is obtained by closing a chain of n neu- 

 rons, bringing s„ and s into coincidence. But if s n is inaccessible to 

 s before the closure then the closure makes no change in the value 

 of y n . Hence we suppose s n accessible to s c . 



Following Pitts (1942a) in substance, we find it convenient to 

 employ semi-dynamical considerations, taking into account the con- 

 duction-time. Let us introduce as the time-unit the time required for 

 a nervous impulse to traverse the circuit completely. Having defined 

 in chapter ii the 5 and 4 employed in equation (1), we shall have 

 no further occasion to refer to the parameters of the individual fibers, 

 or to the y at any point except s = s n , wherefore it is legitimate to 

 drop all subscripts as designations of neurons and synapses. Fur- 

 ther, it increases somewhat the generality without adding essential 

 complications to allow the stimulus at this point during the interval 

 = t < 1 to be different from the constant value to be assumed there- 



