No. 3.] FACTORS IN THE EVOLUTION OF MAMMALIA. 383 



ical combination " (No. 39, p. 151) ; of course such organic com- 

 bination is not vouched for by a particle of evidence. 



Again, on the theory of heredity propounded by Weismann, 

 such variations are necessarily single, and there is no probability 

 that the same variation will arise twice, even in the same litter. 

 Now it has never been shown that such variations can be per- 

 petuated in spite of the swamping effects of free intercrossing, 

 nor that such minimal differences as a slight shifting of the 

 carpal and tarsal elements, or the presence of a tiny incipient 

 cusp upon a tooth, can be of decisive effect in the struggle for 

 existence. This difficulty has long been felt, and many attempts 

 have been made to meet or to evade it. Weismann has stated 

 the case thus : " Such calculations as those quoted by Darwin 

 from the article in the North British Reveiw of March, 1867, 

 are extremely deceptive, since we have no means of measuring 

 the amount of protection afforded, and we can therefore hardly 

 compute with any certainty, in how great a percentage of individ- 

 uals a change must contemporaneously occur in order to have a 

 chance of becoming transferred to the following generation. . . . 

 Variations which occur singly have but little chance of becoming 

 predominant characters, and this is obviously what Darwin con- 

 cedes; but this is by no means equivalent to the assumption that 

 only those variations which from the first occur in numerous in- 

 dividuals, have a chance of being perpetuated" (No. 58, pp. 65S 

 and 659). But it is difficult to see, on Weismann's principles, 

 how variations can occur other than singly (i.e. excluding those 

 cases of the influence of the environment upon the germ-plasm, 

 by which many individuals are simultaneously affected), except 

 in the direct line in which the change first appeared, for by 

 hypothesis every fertilized ovum is different in important respects 

 from every other, and on the doctrine of chances there is only 

 an infinitesimal probability that it can ever be duplicated. The 

 argument that variations do occur in nature sufficient to give the 

 necessary material for the operation of natural selection, does 

 not touch the real difficulty, which is what causes these varia- 

 tions ? It is taking a great deal for granted to assume that they 

 are solely or even mainly due to sexual reproduction. 



The relatively fixed direction taken by variations, which has 

 been insisted upon by so many observers, — e.g. Askenasy (No. 

 1), Eimer, Geddes and Thompson (No. 21), Osborn (No. 43), — 



