284 TRANS. ST. LOUIS ACAD. SCIENCE. 



carry away double the amount that might be carried away from 

 the flower if there were but a single set. This last is a natural 

 provision, since the insect in flying about wastes some of its pol- 

 len load. 



Trimorphism in flowers is a device for their surer and more 

 abundant cross-fertilization. In studying the fertilization of flow- 

 ers, one sees countless examples of marvelously intricate and as 

 it were ingenious mechanical devices for cross-fertilization. In 

 trimorphic species the effectiveness of the device depends more 

 upon mathematical principles — aside from the sterility of illegiti- 

 mate unions, which Darwin and Hildebrand have demonstrated 

 experimentally. 



A small insect reaching for nectar in the long-styled form would 

 not leave any pollen on the stigmas ; and a small insect crawling 

 into the short-styled flower might not carry pollen away. There 

 are three forms of flower, and, speaking roughly, we may divide 

 the insects which seek these flowers into two classes, large and 

 small. Consequently, two insects, one large and cue small, flying 

 from one flower to another, have each a choice, so to speak, of 

 six combinations. In all six combinations, a large insect (a hive- 

 bee, for instance) would probably efiect fertilization, while an 

 insect 5 mm. in length would probably eflect only three fertiliza- 

 tions. If, on the contrary, all the flowers were of one form, it is 

 evident that some insects, even if they went from flower to flower 

 all day long, might fail to fertilize any flower. As it is, the flower 

 is arranged for any insect, within certain limits of course. 



Assuming that the three forms of the trimorphic species occur 

 in the ratio of 4, ^ and 11, and tliat an insect requires a minute to 

 go from flower to flower ; and, given the size of the insect and 

 the number of flowers in the field, a calculation of the probabili- 

 ties as to the number of fertilizations effected could be made. 

 The result of such a calculation would serve only to give one an 

 idea as to the mathematical principle involved. But this calcu- 

 lation neglects altogether the fact that an insect could get a suffl- 

 cient burden of pollen from one flower to fertilize perhaps a dozen 

 others ; and, too, we would have to tike into consideration the 

 fact that an insect, instead of making one of the six combinations, 

 might fly from one flower to another ol the same form, and thus 



