MATHEMATICAL TEST OF NATURAL SELECTION. 169 



applied to the case of mimetic butterflies, with the view 

 of showing that they could not have been produced 

 simply according 1 to the laws of variation, inheritance, 

 and natural selection. In the application of this rigid 

 test,, the very first step is a perfectly gratuitous assump- 

 tion, { that it would require, at the very lowest calcula- 

 tion, one thousand steps to enable the normal Leptalis to 

 put on its protective form.' Who is to prove that fifty 

 differences would be insufficient ? An interval of a thou- 

 sand years might be granted for establishing each one of 

 these variations. Suppose even fifty thousand, instead of 

 only fifty steps, to be necessary, it is another gratuitous 

 assumption that ' the smallest change in the direction 

 of the It/iomia, which we can conceive on any hypothesis 

 to be beneficial to the Leptalis, is at the very lowest 

 one-fiftieth of the change required to produce perfect 

 resemblance.' How small a difference must decide the 

 choice made by a donkey placed equidistant between 

 two bundles of hay ! Certainly, then, a bird on the 

 wing, having to choose amidst myriads of butterflies, 

 may be determined by an almost infinitesimal distinction. 

 Further, though the whole change may be produced by 

 an immense number of small changes, it is not necessary 

 to suppose that all the changes will be equally small. 

 It is merely begging the question to assume that the 

 first change could not possibly be large enough to be of 

 any use. And if it may be of use, the whole mathematical 

 calculation, based on its being useless, breaks down from 

 the beginning. Again, since the Leptalis may have 

 spent one million years in arriving at its present likeness 



