400 SCIENCE PROGRESS 



hypotheses to suggest that the insects, in their visits to the 

 ancestors of the Bennettitccc for the purpose of eating or col- 

 lecting microspores (pollen), directly exercised a stimulus upon 

 the strobilus, causing a greater flow of nutriment to this region 

 of the plant and inducing an active multiplication or pro- 

 liferation of its parts, which, as already indicated, is the 

 necessary preliminary of variability. At any rate the phloem 

 in the peduncle of the Bennettitean strobilus greatly exceeds the 

 xylem in thickness, and this is a clear indication of the heavy 

 requisition which the very numerous reproductive organs made 

 upon the supply of the necessary nutriment. 



The reduction from an indefinite number of floral leaves 

 to a pentamerous perianth must have occurred at a very early 

 period, since pentamerism is so deep-seated a characteristic 

 of Dicotyledons,^ and the question naturally arises why five 

 should have become the optimum, not a greater or a lesser 

 number. The problem seems to be open to a plausible 

 solution if we turn for a parallel to the early forms of Crinoids. 

 Here the question is quite obviously one of obtaining the 

 greatest economy of material consonant with the maximum 

 area to be exposed by the food-gathering arms, which have 

 also to enclose and protect a central vaulted dome, often pro- 

 longed into a high anal column, e.g. in Poteriocrinus, Botryocrinus. 

 The number five in this case, and still more forcibly in the 

 Blastoids, seems to me to be determined by the geometrical 

 fact that the maximum plane-angle of a polyhedron is that of 

 a pentagon, for the three angles of three adjacent hexagons 

 cannot form a solid angle ; while, on the other hand, four sides 

 based on a square, or three sides on a triangle, would be quite 

 insufficient to ensure the complete protection or space necessary 

 for the full development of the central dome of Crinoids. Now 

 the same reason can be held to apply to the flower of the early 

 Angiosperms, for the greater part of the flower of the Bennettitece, 

 which stand so close to the parent-stock, is occupied (as already 

 described) by a central column composed of innumerable mega- 

 spores or ovules, surrounded by a whorl of fern-like stamens, 

 and by a more external envelope of spiral perianth-leaves. 

 Since in both the flower and the Crinoid the same amount of 



' The fact of the Deniiettitcci; possessing two seed-leaves is one of the strongest 

 of the reasons for considering Dicotyledons to be the parent-stock of the 

 Monocotyledons. 



