48 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



in Figure 5. Notice that the maximum moves to the right with in- 

 creasing r . However, if instead of the 8 used, we had taken the aver- 

 age value over the interval rT , we should have obtained essentially 

 the same results, but with the maximum moving to the left. The 

 equation corresponding to expression (17) is, however, much more 

 complicated. The quantity 6 suggests immediately, in the terms of the 

 visual field, the relative brightness during flicker. Experiments by 

 Bartley (1941) show essentially the same type of variation as ex- 

 pression (17) but there is no significant change in the position of the 

 maximum with r on a range from \ nearly to 1. From what has 

 been stated above, one could probably find a simple average which 

 would give this result. 



If cj) is proportional to S over the range to be considered, then 

 multiplying S by 1/6 would make the responses equal. For the fre- 

 quency / very large, 6 = r , that is, S must be increased to S/r to ap- 

 pear the same as a continuously applied S . This is just a statement 

 of the Talbot law. 



From this brief consideration of the dynamics of two-neuron 

 chains we have been able to derive equations predicting quantitative 

 relations among various experimental variables. These include the 

 relation between reaction-time and intensity of stimulation, for given 

 change in stimulation and period of accommodation. Similarly, the 

 duration of response is determined in terms of these same variables. 

 A Weber ratio is determined as a function of accommodation-time. 

 Furthermore, a relation is determined connecting flicker-frequency, 

 light-dark-ratio and intensity. And finally, relations are determined 

 between relative brightness and the light-dark-ratio and frequency. 

 In some cases, quantitative agreement with experiment is exhibited. 

 In others, general qualitative agreement is obtained. It is well worth 

 noting at this point that while, on the one hand, to the extent that the 

 formulae are verified these manifold relations are all brought within 

 the scope of a single unifying principle, on the other hand the dis- 

 cussion explicitly introduces a great many problems which the experi- 

 ments only vaguely suggest. 



