As I have excluded self-fertilization, it is necessary, if we are to get any trustworthy results, that one should consider the mode in which fertilization will be produced. I have taken the case of fertilization by insects, and have assumed that each flower is visited a certain number of times by insects during the period when fertilization is possible; and, further, that the insects which visit it have on the average visited a certain number of flowers of the same species before they came there. Of course nothing but observation can fix these latter numbers; but I should not be surprised at finding that they are of considerable magnitude[65]. In order to make the results a little 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. [65] In this anticipation Mr. Moulton is right. The well-known botanist, Mr. Bennett, read a most interesting paper on the subject before the British Association in 1881. His results have since been corroborated by other observers. In particular, Mr. R. M. Christy has recorded the movements of 76 insects while visiting at least 2,400 flowers. (_Entomologist_, July 1883, and _Zool. Journal Lin. Soc._, August 1883.) The following is an analysis of his results. In the case of butterflies, in twelve observations on nearly as many species, there are recorded altogether 99 visits to fifteen species of flowers; and of these 99 visits 94 were constant to the same species, leaving only 5 visits to any other, or second species. In the case of the hive-bee, there were 8 individuals observed: these visited altogether 258 flowers, and all the visits paid by the same individual were paid to the same species in each of the eight cases. Lastly, as regards bumble-bees, there were altogether observed 55 individuals belonging to four species. These paid altogether 1751 visits to 94 species of flowers. Of these 1751 visits, 1605 were paid to one species, 131 to two species, 16 to three, 6 to four, and 1 to five. 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 1 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