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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 very 
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 following 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. . 
6. 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.” 
b. The “ skew diamond.” 
As a good example of the true shadow hexagon, there is Poly- 
gonum Convolvulus, Linn., whieh is very nearly the exact shape ; 
also Lamium sp., Viola canina, Linn., Urtica dioica, Linn., and 
even such an unlikely case as Oochlearia officinalis, Linn. 
Amongst other forms of leaf which appear to me to have this 
leading idea, I may mention, Hwmulus Lupulus, Linn., Acer 
campestre, Linn., Lavatera arborea, Linn., Wahlenbergia 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, 
