(and, therefore, would have ministered to the work of physiological selection almost as well as the others), the 159 deviations become reduced to 72, or about four per cent. of the whole.--G. J. R. I send you the formula and the calculation on which it is based in an Appendix; but as I know you have a holy horror of algebraical formulae, I give you here a few numerical results. The cases I have worked out are those in which the number of insects visiting each flower is 5, or 10, or 15; and I have also taken 5, 10, and 15, to represent the number of flowers which an insect visits each journey. This makes nine cases in all; and I have applied these to two instances--viz. one in which one-fifth of the whole race have developed cross-infertility, and the other in which one-tenth only have done so. Taking first the instance where one-fifth have developed the peculiarity, I find that if on the average five insects visit a flower, and each insect on the average visits five flowers on a journey, the fertility is diminished by about one-tenth. If, however, the average number of flowers the insect visits is ten, the reduction of fertility is less than one per cent. And it becomes inappreciable if the average number is fifteen. If on the average ten insects visit each flower, then, if each insect visits on the average five flowers on a journey, the reduction of fertility is a little over one per cent.; but if it visits ten or fifteen the reduction is inappreciable. If fifteen insects visit the flower on an average, then, if these insects on the average visit five or more flowers on a journey, the reduction of fertility is inappreciable. By the term inappreciable I mean that it is not substantially greater than one-tenth of one per cent.--i.e. not more than one-thousandth.