1. The Social Use of Space 



And using Eq. (41) 



Jap 



107 



2/. 



1 + an% 

 2 



1 + an'fc 



(1 +a/z70- 



• /.(I + an% - 1) 

 1 + an'fc 



f50) 



We can obtain an explicit relation between /„p and N and /aa and N by- 

 substituting Eq. (34) respectively into Eqs. (50) and (46) : 



And 



Jap 



J aa 



2aix'tx-{N 



1 



[1 +aMM'(iV - \)J 



y.{N - 1) 



[1 +a,x,i'{N - \)J 



(51) 



(52) 



The function /«« = when A^ = 1 and also faa approaches as A" tends to 

 infinity. Since faa is continuous and differentiable for all positive values of 

 A", it has a maximum A'^, for some value of fan at which the derivative of 

 faa w'ith respect to A" is zero 



dfa 



dNr 



= = 



and 

 Hence 



m[1 + ann.'{N - !)][! - ann'jN - 1)] 



[1 +«m/(A^- 1)? 



1 - auitx'{N„. - 1) = 



Nm- \ = 



1 



1 



afiix 



or 



ocuii 



Nm - 1 



(53) 



(54) 



(55) 



Thus, the larger a, the smaller Nm. In other words, the position of the 

 maximum shifts to the left as a increases. In order to find the maximal 

 value of faa, faV, we may substitute Eq. (55) into (52) obtaining 



/i:^ = 1/4V (56) 



In other words, the number of responsive-responsive contacts in unit 

 time decreases as the refractory time increases. Since the refractory time. 



