EVOLUTION 411 



(c) We are able, however, to determine the relative 

 selective death-rate for organs of different sizes ; thus the 

 selective death-rate of an organ of value 5 is to that of 

 one of value 1 1 as ({f/d^ is to /lij/n i. 



(d) In order to determine the proportion of the 

 selective and non-selective death-rates we must ascertain 

 the value of n. This can only be done (i) by follow- 

 ing actually the same individuals during the period of 

 selection ; this is possible in the case of man, and of 

 organisms kept in a state of captivity, but not for those in 

 wild life ; (2) by measuring the total actual reduction of 

 adult life in some limited area during the given epoch on 

 the assumption that there is no migration. The latter 

 process is by no means a certain one, and in the real 

 state of nature is often rendered difficult by the influx of 

 adults due to growth. If, however, we can obtain some 

 measure of the proportions of the selective and non- 

 selective death-rates in the case of man and of organisms 

 in captivity, we shall have at least some ground for 

 appreciation of what are the actual proportions for wild 

 life under natural selection. 



The problem of selection as we have dealt with it here 

 touches only the fringe of a very large subject. As a 

 rule it will not be one organ only, but a group of organs 

 having certain values and certain inter-relationships, which 

 render their bearer fittest for the environment of his race. 

 The mathematician is still competent to deal with the 

 problem and indicate how it is to be quantitatively 

 solved. He proceeds from curves of frequency to surfaces 

 of frequency, and then requiring to go beyond these he 

 finds his problem lands him in space of many dimen- 

 sions (see p. 269), and gives to the study of so-called 

 hyperspace a value it has not hitherto had for natural 

 philosophy, i.e. for the study of the perceptual world. ^ 



^ For example, the study of the "spherical trigonometry" of multiple 

 space is closely allied to the theory of multiple correlation, and further of 

 multiple association. That a quantitative exact study of defective children 

 should need the study first of the geometry of hyperspace may sound para- 

 doxical, but it is none the less true. It is a curious illustration of my 

 statement on p. 13. 



