PRELIMINARY NOTE ON THE SHAPES OF LEAVES. 83 



thought of the hexagon as a shape which gives a theoretically 

 perfect packing. Taking sections of a hexagonal prism, I found 

 the following possible explanation. Many Ivy leaves are verv 

 nearly the shape of a hexagon, with a small triangle cut out of 

 one side and attached to the opposite side. There" are, however, 

 but few leaves which are perfect hexagons. A very large 

 number, on the other hand, are extremely close approximations 

 to the sections of a hexagonal prism. 



Not merely palmate, but also many ovate-cordate leaves, fall 

 under one or the other of the followins: sections of a hexagonal 

 prism, which may be classified as follows : — 



1. True regular hexagons (example, many Ivy leaves). 



2. Sections of a hexagonal prism which have four of their sides 

 equal to one another. 



a. Sections which pass through one of the sides of the 

 original hexagon. This may be called the " shadow 

 hexagon." The section passes from a side to a side of a 

 parallel regular hexagon prism. 



h. Sections which have none of their sides parallel to the 

 original hexagon. This may be called the ^'diamond 

 section." It is, of course, due to the section passing 

 from a rib of the hexagon to a rib. 



3. Sections of a hexagon which have not four equal sides. 

 These are not inclined to the prism in such a manner as to contain 

 either a diagonal or a line joining two opposite sides. 



a. These are most simply described as the " skew shadow 

 hexagon." 



h. The " skew diamond." 

 As a good example of the true shadow hexagon, there is Foly- 

 gonum Convolvulus, Linn., which is very nearly the exact shape ; 

 also Lamium sp., Viola canina, Linn., Urtica dioica, Linn., and 

 even such an unlikely case as Cochlearia officinalis, Linn. 

 Amongst other forms of leaf which appear to me to have this 

 leading idea, I may mention, Humulus Lwpulus, Linn., Acer 

 camjoestre, Linn., Lavatera arhorea, Linn., Wahlenhergia hederacea, 

 Reichb.. Viola pumila, Hook. & Arn., Nepeta Glechoma, Benth., 

 &e. Those which are ovate-cordate tend to pass into the nearly 

 circular leaves of such forms as Viola odorata, Linn., and Calys- 

 tegia Soldanella, Linn. 



