If you contrast the results that I have given above with those given on pages 181 to 183 of Wallace's book, you will see the enormous difference. His calculations can only apply to the animal kingdom in those cases in which there is only a union between one individual of each sex; and before you can deal with the question of such animals, you will have to take into consideration many elements besides that of mere fertility, if you wish to get any tolerably accurate result[66]. [66] Here follows the Appendix presenting the calculations on which the above results are founded; but it seems unnecessary to reproduce it on the present occasion.--G. J. R. The above analysis leaves nothing to be added by me. But, in conclusion, I may once more repeat that the particular point with which it is concerned is a point of very subordinate importance. For even if Mr. Wallace's computation of chances had been found by Mr. Moulton to have been an adequate computation--and, therefore, even if it had been thus proved that physiological homogamy must always be associated with some other form of homogamy in order to produce specific divergence--still the importance of selective fertility as a factor of organic evolution would not have been at all diminished. For such a result would merely have shown that, not only "in many cases" (as I originally said), but actually in all cases, the selective fertility which I hold to have been so generally concerned in the differentiation of species has required for this purpose the co-operation of some among the numerous other forms of homogamy. But inasmuch as, by hypothesis, no one of these other or co-operating factors would of itself have been capable of effecting specific divergence in any of the cases where its association with selective fertility is concerned, the mathematical proof that such an association is _always_--and not merely _often_--necessary, would not have materially affected the theory of the origin of species by means of physiological selection. We have now seen, however, that a competent mathematical treatment proves the exact opposite; and, therefore, that Mr. Wallace's criticism fails even as regards the very subordinate point in question. APPENDIX C. SOME EXTRACTS FROM THE AUTHOR'S NOTE-BOOKS.