114 EARLY DAYS OF DARWINISM 



ever with good reason attempted to set a limit to 

 variation ? Until such limitation, or cause for limita- 

 tion, was shown, I felt I was justified in concluding that 

 variation might go on indefinitely that variation might 

 extend, as indeed there was some positive evidence of 

 its doing, from coloration to minor points of structure, 

 and from minor to major points. Thus it seemed to me 

 that, if mathematicians were right in admitting the truth 

 of Euler's proof of the Binomial Theorem, I could not 

 be very wrong in accepting the truth of Evolution by 

 means of Natural Selection. When afterwards I came 

 to read Mr. Darwin's " Animals and Plants under 

 Domestication," the aptness of my application of the 

 mathematical reasoning seemed to be more and more 

 perfect. In those domesticated animals and plants of 

 which the origin was perfectly certain, we had the definite 

 quantities required for the illustration : in the domesti- 

 cated animals and plants of which the origin was not so 

 certain, we had the indefinite quantities : in the wild 

 animals and plants the unknown quantities. We could 

 prove by experiment that such and such results followed 

 from any next step with regard to our known quantities, 

 and by experiment could prove that similar results 

 followed from the next step with regard to our indefinite 

 quantities. Were we not justified then in concluding 

 that the like results would follow from our unknown 

 quantities ? * 



* " I had often wondered that this obvious illustration had not occurred 

 to Mr. Darwin, in none of whose works have I noticed any allusion to it ; 

 but the cause of the omission I did not suspect until I read his Auto- 

 biography. It was probably due to the fact of his not having made 

 sufficient progress in mathematics to become aware of this simple theorem. 

 He has told us (vol. i. p. 46), ' I attempted mathematics and even went 

 during the summer of 1828 with a private tutor (a very dull man) to 

 Barmouth, but I got on very slowly. The work was repugnant to me, 

 chiefly from my not being able to see any meaning in the early steps in 

 algebra. This impatience was very foolish and in after years I have 

 deeply regretted I did not proceed far enough at least to understand some- 

 thing of the leading principles of mathematics.' He goes on to declare 

 that he did not believe he ' should ever have succeeded beyond a very low 

 grade.' To this belief we may perhaps demur. Under good tuition there 

 seems no reason why he should not have derived as much satisfaction from 



