70 lotka: discontinuous evolution 



arrangement of the individuals in space may be independent of 

 the distribution of the " fluctuations " in the system — at least so 

 far as the critical limits are not exceeded — ; thus, for example, 

 according to the simpler form of the kinetic theory, which regards 

 the molecules as elastic spheres, the probability of finding a 

 molecule at the point x, y, z is independent of the coordinates 

 and velocities of the other molecules, provided only that x, y, z 

 does not fall within the radius of another molecule. If we 

 suppose that chemical action takes place at the time of a col- 

 lision between two molecules, then we see that in this case, the 

 occurrence at a given point, of a fluctuation which would cause 

 a molecule placed at that point to be eliminated from the aggre- 

 gate (namely the presence there of another molecule with certain 

 velocity components), has no influence upon the probability 

 that some molecule or other shall be moving upon the point in 

 question at the moment considered. 



But in an important class of cases the arrangement of the indi- 

 viduals in space is not independent of the distribution of the fluctu- 

 ations in space ; on the contrary, there is a more or less close 

 " correlation " between the occurrence of certain fluctuations in the 

 general conditions of the system and the presence of an individual 

 at the corresponding point of time and space. In fact, it is 

 hardly too much to say, that the dominant tendency in the 

 evolution of the highest types of living organisms, and of modern 

 man in particular, is to make this correlation as close as possible. 



Before we proceed to consider more in detail the manner and 

 means by which this correlation is secured, it will be well to 

 summarise in tabular form the essential points of our analysis. 

 Expressing successive dependencies on the pattern of genea- 

 logical tables, we obtain the following picture : 



