1. The Social Use of Space 167 



of the constellation (Section VIII, C), while (27r(js^) represents that 

 portion of each individual's home range within which it spends 0.394 of 

 its time. Each individual simultaneously "inhabits" two life spaces, his 

 own and that of the group of which it is a member. 



For all members but the alpha member, tiualitative differences in S^'-''' 

 lead to reductions in v, which in turn bring about reductions in A such that 

 the reduced A is proportional to v. This accommodation will result in /x 

 again exceeding 1.0 and will thus expose the individual to stress from an 

 increased frequency of contacts. Further accommodation, again reducing 

 M to the relative value of 1.0, can come only through quantitative reduction 

 of the target diameter, d, since the S'-"^ qualitative aspect has become a 

 stable factor. It will be recalled that the concept of the constellation pre- 

 supposes a capacity for emitting and receiving signals sufficient for any 

 member to gain contact with any other member despite their spatial separa- 

 tion. Such signals amount to an increase in d at the moment of this emis- 

 sion. The easiest strategy for regaining a m = 1-0 will be for each individual 

 to reduce the frequency of signaling as much as it had reduced its velocity. 

 This line of reasoning culminates in the conclusion that v, a", and d (in the 

 sense of freciuency of signaling) will all be reduced to values inversely 

 proportional to S^"K With respect to the unchanged relative values of 1.0 

 for the alpha individual, these values for beta members become respec- 

 tively 0.9167, (0.9167)- and 0.9167, while for gamma members they be- 

 come respectively 0.4167 (0.4167)2, and 0.4167. 



Consistent with my objective of developing formulations adequate for 

 acquiring data in concrete experimental studies, the above theoretical 

 conclusions may be tested for their application to groups more compact 

 than represented by constellations. Given an experimental N = 12 re- 

 stricted to an area A, one can estimate relative velocity be determining 

 the proportions of a series of time samples in which each individual is 

 active and exposed to situations where social interactions do occur. This 

 velocity we can designate by v. Velocity so estimated will reflect true 

 velocity more accurately than the cruder measure of number of contacts, 

 Tie, used in the specific case in the discussion pertaining to Eq. (113). This 

 is because an animal may be active when all others are at rest. 



The more velocity is reduced, as predicted by Eq. (108), the more the 

 individual should restrict his travels to a smaller portion of the area utilized 

 by the group. Of an originally common home range shared by members 

 of a ''compact" group, low velocity members will come to utilize only a 

 portion. Thus, the ideal design of an area within which social organization 

 is being studied must provide for many subareas to which visitations may 

 be recorded. Otherwise, reduction in home range cannot be detected. 



Likewise, the more an individual reduces his velocity, the more he should 



