248 BIOLOGY OF DEATH 



that not so many as 25,000 persons could possibly stand 

 upon an acre of ground, let alone live on it. So, similarly, 

 there must be for any area an upper limiting number of 

 persons who can possibly live upon it. In mathematical 

 terms this means that the population curve must have 

 an upper limiting asymptote. 



2. At some time in the more or less remote past the 

 population of human beings upon any given land area 

 must have been nearly or quite zero. So the curve must 

 have somewhere a lower limiting asymptote. 



3. Between these two levels we assume that the rate 

 of growth of the population, that is, the increase in 

 numbers in any given time unit, is proportional to two 

 things, namely: 



a. The absolute amount of growth (or size of population) already 



attained ; 



b. The amount of as yet unutilized, or reserve, means or sources of 



subsistence still available in the area to support further 

 population. 



These hypotheses lead directly to a curve of the form 

 shown in Figure 60, in which the position of the asymp- 

 totes and of the point of inflection, when the population 

 is growing at the most rapid rate, are shown in terms 

 of the constants. It is seen that the whole history of a 

 population, as pictured by this curve, is something like 

 this: In the early years following the settlement of a 

 country 1 the population growth is slow. Presently it 

 begins to grow faster. After it passes the point where 

 half the available resources of subsistence have been 

 drawn upon and utilized, the rate of growth becomes 

 slower, until finally the maximum population which the 

 area will support is reached. 



