Mathematical Contributions to the Theory of Evolution, 5 



(4.) The individual variation in the twenty-two series was measured 

 and expressed as a percentage of the racial variation ; the results range 

 from 77 to 98 per cent., with a mean value of 87 per cent. If this 

 percentage variation occurs within the individual, it is clearly idle to 

 speak of variation as a result of sexual reproduction. It exists in full 

 intensity when an individual buds or throws off undifferentiated like 

 organs. The blood-corpuscles produced by a single frog are almost as. 

 variable as the blood-corpuscles in the whole race of frogs. Thus,, 

 variation is established as a primary feature of all vital production 

 whatever. 



(5.) No relation whatever could be found between the intensity of 

 homotyposis (and therefore a fortiori of heredity) and the degree of 

 variability of the species. If species are classified in order of variability 

 for our twenty-two series, the mean homotyposis of the first eleven is 

 0*4559 and of the last eleven is 0*4570. No relation whatever, as far as we 

 were able to judge, could be found between the simplicity or complexity 

 of the organisms dealt with and either their variability or their homotyp- 

 osis. The Mushroom was quite comparable with the Poppy or the 

 Spanish Chestnut. We conclude, accordingly, that there is no evidence 

 at present to show that variation has decreased and heredity increased 

 with the progress of evolution. On the contrary, without laying down 

 any dogma, we should consider the}results obtained as consistent with 

 variability and homotyposis being primary factors of the growth of all 

 living forms and not the product of natural selection, but factors upon 

 which its effectiveness ab initio has depended. If we can show that 

 homotypic correlation is as intense in the simplest forms of life as in 

 the most complex, and that inheritance flows naturally from it, it is 

 clear that our view of living forms will be considerably simplified. 

 Homotyposis is unfortunately obscured by other factors due to growth,, 

 environment, unobserved differentiation, or heterogeneity in one or 

 another form. But the results of this our first investigation in this 

 field seem to support the view just expressed, and to indicate that the 

 Principle of Homotyposis (by which we must again say we mean a 

 numerical appreciation of the likeness and diversity among homotypes) 

 is a fundamental law of nature, which will enable us to sum up in a 

 brief formula a great variety of vital phenomena. 



