90 TEST CASES [ch. x 



their general correctness, for the rival theory of natural selection 

 cannot be used to make predictions at all. All the evidence ob- 

 tained seems to point in the same direction, and seems to show 

 that evolution is moving as an ordered whole, upon lines that 

 have an arithmetical or mathematical basis. The general mathe- 

 matical propositions that underlie the theory that is here being 

 put forward have been worked out fully by Mr G. Udny Yule, 

 whose paper (75) contains a very readable and simple general 

 introduction and summarv that should be read bv all who take 

 any interest in the subject under discussion. 



The actual evolution of new genera and new species seems 

 largely determined by a simple following, differing in speed in 

 each individual case, of the law of continual doubling, as was 

 shown by Yule and the author in 1922 (76). Sir James Jeans has 

 said that "All the pictures which Science now draws of nature, 

 and which alone seem capable of according with observational 

 fact, are mathematical pictures." In this he was referring more 

 especially to the physico-chemical sciences, but the work de- 

 scribed here, and in Age and Area, gives the impression that 

 biology will have to be added to them, though not in such a 

 clearlv-cut condition. 



In this and the following chapters, some test cases are de- 

 scribed, all giving evidence which seems not infrequently conclu- 

 sive that the theory of differentiation, or divergent mutation, 

 is a more probable explanation of evolution than is that of 

 natural selection. The number of cases described may seem 

 excessive to some, but the writer, w^ho is now growing old, has 

 tried to make his position as secure as possible, and has therefore 

 chosen a number of tests from various parts of the subject. 



TEST-CASE I. INCREASE IN NUMBER 

 WITH EVOLUTION 



It is admitted that as time has gone on, plants have increased 

 vastly in number. But how did natural selection, working through 

 gradual adaptation, produce such an increase? The very name 

 selection would seem to imply the picking out of some from among 

 many. One would expect the ultimate result to be a few "super- 

 plants ", not a vast and increasing number with no evidence to 

 show that any one was superior to its immediate relatives. 



On the theory of natural selection new variations, to have any 

 chance of persistence, must have been produced so that acci- 

 dentally or otherwise they suited the conditions, or more com- 



