332 Mathematical Contributions to the Theory of Evolution. 



complex of characters, certain functions of those quantities remain 

 constant, and such constants ought to be discoverable, at any rate in 

 theory, and should serve as the criterion of a common origin, when 

 we deal with local races as having been subjected only to a selection 

 directly differentiating a comparatively few characters. 



In this memoir the analysis is confined to the case of normal fre- 

 quency, but most of the chief results are true for all cases of 

 regression. The effects of selection are illustrated in a very consider- 

 able variety of cases, especially the influence of selection on the coeffi- 

 cients of heredity is fairly fully dealt with. Tables are given for the 

 simpler cases to enable the biologist at once to appreciate the influence 

 of selection, not only on the size and variability of organs, but on 

 their correlations. 



If selection has changed a race from a condition A to a condition B, 

 it becomes of much interest to determine the nature of the selective 

 death-rate by which the process has been carried on, and it is found 

 that this death-rate as represented in the surface of survival-rates 

 enables us to distinguish two kinds of selection, termed in the 

 memoir positive and negative selection. In the first case a race is 

 modified, because the nearer its members are to having their organs 

 with a certain system of values, the better fitted they are to survive ; 

 in the second case the nearer the individuals are to this system 

 the less fitted they are to survive. There will usually be in this 

 second case, not a single system, but an indefinite number of systems 

 which would equally well fit individuals to survive ; in the first case, 

 on the other hand, there are an indefinite number of systems which 

 equally unfit their owners for surviving. This distinction seems of 

 considerable interest. 



For example, to select from the French race a race in femur and 

 humerus like the Aino, we should have to proceed by a positive selec- 

 tion ; but to select from the Aino a race like the French, we should 

 have to proceed by a negative selection. To get 1000 Aino we should 

 have to select for these two organs alone out of some 6,000,000 

 Frenchmen, but to get 1000 Frenchmen from the Aino we must select 

 from about a billion of the latter. Thus we are to some extent able 

 to appreciate the stringency of the selection, which even lasting 

 through long ages, and introducing continuous reproduction, would 

 be needful to enable us to pass in the case of only two organs from 

 one race to the other. Another point brought out by the surface of 

 survival-rates is the fact that the fittest to survive are usually not 

 the most frequent survivors. 



It will be seen that the memoir opens up a novel field of investiga- 

 tion, but one so wide that the theory of it must be limited by close 

 contact with what is needful for the purposes of evolution. We want 

 measurements on the local races of animals to guide us ; at present we 



