i66 Darwin, and after Darwin. 



five or more flowers on a journey, the reduction of fertility 

 is Inappreciable. 



By the term inappreciable I mean that it is not substan- 

 tially greater than one-tenth of one per cent. — i.e. not more 

 than one-thousandth. 



Of course, if the proportion of individuals acquiring the 

 peculiarity is less, the effect on the fertility under the above 

 hypothesis will be greater ; and it will not be counteracted so 

 fully unless the number of insect visits is larger, or unless the 

 insects visit more flowers on a journey. Thus if only one-tenth 

 of the race have developed the peculiarity, then, if each flower 

 is visited on the average by five insects who visit five flowers 

 on each trip, the fertility will be reduced about one-third. 

 If, however, the insects visit on the average ten flowers per 

 trip, it will be only diminished about one-tenth ; and if they 

 visit fifteen on each trip, it will be only diminished about 

 one-fortieth. If in the same case we suppose that each 

 flower receives ten insect visits, then, if the insects visit on an 

 average five flowers per trip, the fertility will be diminished 

 about one-eighth. If they visit ten on a trip, it will be dimi- 

 nished about one-hundredth, and the diminution is inappreciable 

 if they visit fifteen on a trip. Similarly, if a flower receives 

 fifteen insect visits, the diminution is about one-twenty-fifth, 

 if insects visit on the average five flowers on a trip ; and is 

 inappreciable if they visit ten or fifteen. 



These figures will show you that it is exceedingly possible 

 that a peculiarity like this, the effect of which at first sight 

 would seem to be so prejudicial to fertility, may in fact have 

 little or no influence upon it ; and if you set against this the 

 overwhelming importance of such a peculiarity in segregating 

 the type so as to give it a chance of becoming a fixed species, 

 you will, I think, feel that your hypothesis has nothing to 

 fear from a numerical examination. 



I have not examined the case of fertilization by other means ; 

 nor have I examined the case of fertilization in animals, where 

 psychological selection can come in. To obtain any useful 

 results, one would have to consider very carefully the circum- 

 stances of each case ; and at present, at all events, I do not 

 think it would be useful to do so. Nor have I attempted to 



