on Milllerian Mimicry and Biaposeonatism. 563 



observation macrnified into grrave and substantial error." * 

 Or, as Huxley more tersely puts it, " mathematics will not 

 give a true result when applied to erroneous data." As a 

 single but sufficient instance, I would point to the history 

 of a recent controversy. 



Physicists, on what seemed to be very good a priori 

 grounds, came to the conclusion that geologists and biolo- 

 gists had miscalculated the age of the earth. The biologists 

 and geologists did not dispute the mathematical reasoning 

 of the physicists, but they had confidence in their own 

 facts, and they felt sure that there must be something 

 wrong somewhere about the physicists' data. Their firm- 

 ness has been justified ; and the critics have now practi- 

 cally retired from the position that the geological clock 

 wants altering.f Far be it from me to question Mr. Mar- 

 shall's arithmetic. On arithmetical grounds which seem 

 equally unassailable, it can be proved, as in the old logical 

 puzzle, that if the tortoise once gets a start, Achilles will 

 never catch him. What is the answer ? Solvitur amhiolando. 

 We know that Achilles loill catch the tortoise, arithmetic 

 notwithstanding ; and I venture to say that those who 

 have fairly looked into the evidence know that Miillerian 

 mynicry has taken place on a large scale, however difficult 

 it may be to represent arithmetically the exact steps of 

 its development. 



Is there a flaw in Mr. Marshall's data ? There are 

 several flaws ; as I shall show. 



I shall begin by admitting that if in addition to his 

 original assumption (pp. 97-98) we also allow him to 

 suppose that the two hypothetical species are equally con- 

 spicuous, that they occur at exactly the same time, each 

 form distributed at equal intervals throughout the same 

 area, in which also their enemies are to be found with a 

 similar evenness of distribution, and with a perpetually 

 identical keenness of appetite, there is no doubt that the 

 figures will work out nearly as he says ; though even then 

 it can be shown that there is a theoretical possibility of 

 approach between two forms originally equal in numbers.J 



* "Britisli Medical Journal," 1908, v. 1, p. 508. 



t See Poulton, " Essays on Evolution," 1908 : Essay on " The 

 Age of the Earth." 



X Because if the original number of each, species, A and B, is x ; 

 the number of losses incurred by each species is y ; and the number 

 of A that assimilate themselves to B is ?i ; the original chance of 



TRANS. ENT. SOC. LOND, 1908. — PART IV. (JAN. 1909) 37 



