214 THE ORIGIN OF SPECIES [pt. ii 



gone onward in a mechanical way, and whose progress can to 

 some extent be predicted from the laws of probability, supple- 

 mented by the principles of Age and Area, Size and Space, etc., 

 provides a still stronger argument. If the "hollow curve" type 

 of distribution of numbers of families in the world, of numbers 

 of genera in families, of nmnbers of species in genera, of dis- 

 tribution of families, genera and species by area, of distribution 

 of genera in a given flora, of the bulk of the phenomena of evo- 

 lution and geographical distribution, etc., held only for grand 

 totals, it might still be possible to say that natural selection had 

 had much to do with the guiding of evolution, and that simply 

 because one was dealing with very large numbers the final result 

 came out more or less in accordance with the laws of probability 

 and of compound interest. But when, as has been shown, this 

 result is exhibited family by family, genus by genus, country 

 by country, and in animals as well as plants, it seems clear that 

 in general evolution and distribution, in some detail, have 

 followed "mechanical" laws, some of which, perhaps, in the 

 shape in which we have described them — as Age and Area, Size 

 and Space, etc. — the work described in this book may have done 

 something to bring into more clear definition. 



One cannot imagine species or genera arising by gradual change, 

 and producing such an arrangement of "wheels within wheels" 

 as that shoAvn in the figure upon p. 156, or such curves as those 

 upon pp. 177 and 187, with the monotypes in a fairly definite 

 relation to the ditypes, these to the tritypes, and so on, the 

 curve practically always turning the corner between 3 and 5. To 

 produce such an arrangement by gradual variation, natural 

 selection is evidently incompetent, and some definite law to guide 

 it, at i^resent inscrutable, is required. In this connection one 

 must not forget that very strong evidence against such a sup- 

 position is provided by the fact that one finds very few con- 

 tinuous really intermediate stages, whether living or fossil, be- 

 tween species or between genera; in the enormous majority of 

 cases they are discontinuous. One may easily find species that 

 have say four characters of one genus and five of another, or 

 varieties behaving in the same way between species, but really 

 intermediate characters are very rare; and indeed, as avc ha^e 

 pointed out above, the\^ are frequently impossible. 



We shall see in Chapter xxii that the hollow curve really 

 represents an approximation to the compound interest rule, and 

 one cannot imagine it to arise by continuous variation, though 



