84 TRANSACTIONS, NATURAL HISTORY SOCIETY OF GLASGOW. 
The fact that such leaves as, e.g., Villarsia have a nearly 
circular shape, is to my mind simply explained by the considera- 
tion that, as they are nearly symmetrically arranged with regard 
to all external agencies such as light and air, &c., there is no 
reason why they should elongate further in one direction than in 
another, and therefore must be circular. These leaves are not 
exposed to interference from their neighbours, which would 
prevent this equal development. As further examples of this 
circular type, Nuphar, Nymphea, Hydrocotyle vulgaris, Linn., 
Ranunculus peltatus, Schrank, and Viola palustris, Linn., may 
be mentioned. 
Turning now to the diamond type of leaf, there are many oval, 
elliptic, and even linear leaves which can be placed here. The 
leaves of Veronica hederefolia, Linn,, Polygonum Roberti, Loisel, 
Dentaria bulbifera, Linn., Parietaria officinalis, Linn., Zpilobium 
roseum, Schreb., can be fitted together in a nearly perfect manner. 
Amongst others may be mentioned Arenaria trinervia, Linn., 
Epilobium alpinum, Linn., Galeobdolon lutewm, Huds., Polygala 
vulgaris, Linn., Polycarpon, and Hieraciwm mwrorum, Linn, 
Some of these leaves give, to my mind, patterns of great beauty, 
probably in consequence of the perfect manner in which they fit 
one another. 
So far the ovate type of leaf, except when it is broadly ovate, 
and cordate at base, has not been alluded to, I shall just men- 
tion a curious point with regard to the leaves of Saponaria offici- 
nalis, Linn, and Mentha sativa, Linn. These plants have their 
leaves opposite and in four rows. The angle of the wedge- 
shaped base is in both a right angle, whilst the angle at the apex 
is 60°. The bases of the four leaves thus fit exactly, but the 
exact geometrical idea of this shape is not very clear. 
The point which I wished to discover was whether the question 
could be simplified by the finding of a geometrical idea or plan, 
which a leaf will, of course, vary to suit its own individual needs. 
These variations in individuals are sometimes distinctly connected 
with variations in the environment (as I tried to show in a paper 
read before the Linnean Society, December 18th, 1890; see 
Journal of the Linnean Society, vol. xxviii.) ; but without some 
clear plan or geometrical idea, it is obvious that the fitting 
could not be as perfect as it now is, 

