Appendix B. 165 



more intelligible, I have grouped them under the numbers which 

 represent the average number of flowers that an insect visits 

 in a journey. This is a little more than twice as great as the 

 number which represents the number of flowers he has on the 

 average visited before coming to the individual whose fertility 

 we are considering. 



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 



Adding all these results together, we find that 75 insects (butterflies 

 and bees) visited 117 species of flowers: of these visits, 1957 were 

 constant to one species of flower; 136 were paid also to a second 

 species, 16 also to a third, 6 also to a fourth, and I also to a fifth. Or, 

 otherwise stated, while 1957 were absolutely constant, from such absolute 

 constancy there were only 159 deviations. Moreover, if we eliminate 

 three individual humble-bees, which paid nearly an equal number of visits 

 to two species (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. 



