POSITIVE D^DOUBLEMENT. 61 



6-merous flowers are exceedingly common as abnor- 

 malities, and this condition is the normal feature in 

 P. polyphylla, in which even 7-merous flowers are not 

 at all uncommon. The 4- to 7-mery of Paris probably 

 represents an older character than that met with in 

 the flowers of other Liliacese. 



But the most interesting cases are those in which an 

 increase of one member occurs, not haphazardly, but 

 with extreme regularity and system, viz., in every alter- 

 nate whorl, the phenomenon being clearly governed by 

 rhythmic law. This is illustrated by flowers with the 

 following formula : K4 C3 A4 + 3 Gr*- In this case it is 



Fig. 82. — Galanthus nivalis (Snowdrop). Diagram of flower showing- 

 increase of members in alternate whorls, beginning with the calyx, 

 s', the four stamens of the outer whorl. (After Celakovsky.) 



the first, third, and fifth whorl which has the increased 

 number; in a Crocas-&ower it was the second and fourth 

 whorl which was so modified : Ko C4 A3 6-4. In some 

 tulips examined there was an increase in all the whorls, 

 but the first, third, and fifth had one more member 

 than the rest : K5 C4 A5 + 4 G^ 



The present writer has seen, and Celakovsky has 

 described, in many flowers of the snowdrop {Galanthus 

 nivalis), the same rhythmic type of whorl-formation, 

 according to the formula K4 C3 A4 + 3 Gr*; in such cases 

 the gynoeceum may be imperfectly 4-merous (fig. 82). 



This phenomenon of polyphylly tends to be accom- 

 panied in many flowers by a change in phyllotaxy 

 from the whorled to the spiral type. An increase in 



