1. The Social Use of Space 13 



mine the probability of this switching, which is synonymous with the 

 probability of terminating a trip. 



Let: tj = the number of trips reaching any jth distance from home. 

 Nj = the number of trips that stop at the jth. distance. 

 Pj = probability of stopping at the jth distance. 



Then: 



tj~i - tj = Vi-itj-i (10) 



Nj = p,tj (11) 



Nj - Nj_i =pjtj - pj-it.j^i (12) 



If Pj = p (a constant independent of j), then: 



Nj - Nj^i = p(ij - ij_i) 



= -p(tj-i - l.j) (13) 



Nj - iVy_i = -piptj^i) (14) 



And by analogy to Eq. (11): 



iVy_i = pti^i (15) 



Substituting Eq. (15) into Eq. (14): 



Nj - Nj^i = -pNj^i (16) 



Therefore 



p = (Nj_r - Nj)/Nj_r (17) 



This p represents a constant probability of terminating trips which 

 arrive at a point regardless of the distance from home. Rigorous proof that 

 this p actually is a constant is difficult from present data because of the 

 barrier produced by the relatively short alley. However, the validity of a 

 constant p, independent of distance, may be arrived at intuitively since an 

 equation of the form y = exp (a + hx) best represents the observed data. 

 In other words, log ij plotted against x forms a straight line. Whenever 

 this is so, Eq. (17) must be true. 



Utilizing Eq. (9) stated in the form : 



loge?/ = a - bx (18) 



the expected number of trips terminating at Nj^i and Nj, where j = 2, 

 were found to be as shown in Table lb, along with the p values calculated 

 from Eq. (17). Thus, the probability of 0.182 of terminating trips arriving 

 at any distance in the unstructured alley is increased to 0.24 by structuring. 



