64 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



asymmetry appeared fairly clearly in the results from each of the 

 individuals taking- part in the experiment. 



On the basis of the mechanism considered, it is essential that the 

 stimuli be presented simultaneously. However, a complication of the 

 mechanism has been considered for which simultaneous presentation 

 is not necessary. Essentially the same results may be obtained if the 

 stimuli are presented in succession (Landahl, 1940a). 



Since the integral of the normal distribution cannot be given in 

 closed form, it is convenient to introduce an approximation by which 

 closed solutions can be obtained. This is especially desirable when 

 one wishes to use the results in other situations. With the distribu- 

 tion (Landahl, 1938a) 



p(C)=-e- fc i<i (7) 



we obtain, if s x > &.., 



log2P w + k( ei -e 2 ) =0 (8) 



to determine the probability of a wrong response when a categorical 

 judgment is required. The applicability of this approximation has 

 been tested by a comparison of theory and experiment made else- 

 where (Landahl, 1938a). 



While our definition of a discriminal sequence rules out the con- 

 currence of the alternative responses and hence requires that the in- 

 hibitory neurons connecting the parallel excitatory chains shall have 

 activity-parameters at least as great as those of the excitatory chains 

 themselves, it is natural to consider also the case where this restric- 

 tion is removed. We noted in chapter iii, in the case of two parallel 

 chains with inhibitory interconnections, what qualitatively different 

 effects might follow the simultaneous stimulation of both chains as 

 different relations are imposed upon the parameters of the constitu- 

 ent neurons. We select for further consideration here only the sym- 

 metric structure consisting of two parallel chains with crossing in- 

 hibition where a > /5 (cf. equations (4) chapter iii), in which case 

 concurrent transmission along the two paths will occur when the two 

 stimuli are sufficiently strong and not too greatly different. 



These chains may lead from neighboring cutaneous receptors, 

 from neighboring retinal elements, or from organs of two disparate 

 sensations. The responses which they occasion may be overt bodily 

 movements or they may be merely awareness of the sensations. The 

 mechanism has a possible application wherever there is interference 

 by a stimulus of one type with evocation of a response by another, 

 and reciprocally. It is at once apparent that the interference by the 



