14 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



Figure 1 



in a negative a at the origin of N , and a somewhat smaller one will 

 yield a sub-threshold, though positive, a . There will be some range 

 h', h" , therefore, which contains h, , and within which S must lie if 

 transmission is to occur. 



These are not the only possible relations that will limit the range 

 over which transmission may occur. We could have, for example 

 (Figure 2), 



- v 



hi= he 



Figure 2 



hi = h e , <j>' (hi) > y>'(hj), y(oo) > </>(oo). 



Then for an S within a limited range, </> exceeds y> , which is all that 

 is required except that h must be sufficiently small. Suppose, then, 

 one has a number of such sets, Ni , N e and N , all with a common 

 origin, and each possessing a characteristic range. If these ranges do 

 not overlap, and if each set is connected through a chain to a par- 

 ticular effector, then any S will excite only the effector corresponding 

 to the particular range on which S lies. 



As a first step in discussing the interaction of perceptions (strict- 

 ly the interaction of the transmitted impulse), and as a kind of gen- 



