370 ON THE THEORY OF VEGETABLE SPIRALS. 



growth of the stem is the result of a quaquaversal tendency to 

 curvature, so more generally I think it may be asserted, that 

 straight growth in any part of a plant is constrained growth, 

 the result of a tendency to curve in opposite directions. What 

 characterises, therefore, the venation of such a leaf as that of 

 the lily is in this sense the absence of constraint. To this 

 remark an hypothesis is to be added which seems to be justified 

 by the phenomena presented by compound leaves, namely, that 

 the nerves are originally boundary lines, showing where the leaf 

 in its growth paused in its development, just as a range of 

 pebbles marks the old boundary of sea and land after the sea has 

 receded. Thus the lily leaf shows us a single growth in various 

 stages of progress. If we now look at the second division of 

 monocotyledonous leaves, those which have a mid-rib and angular 

 formed nerves, we see the successive stages of a double growth 

 lying on the right hand and left hand respectively of the mid-rib, 

 which is to be regarded as the straight resultant of the opposite 

 curvatures of the boundaries of the two portions; the remaining 

 part of the boundary remaining free and therefore curved. When 

 therefore we say, that with few exceptions, monocotyledonous 

 leaves follow one or other of the types just described, we in 

 effect say that they are either single or double growths, that 

 they belong to the first or second forms of vegetable develop- 

 ment, and rise no higher. Let us now look at the commonest 

 form, namely the penni-nerved of dicotyledonous leaves ; in these 

 not only the mid-rib but the diverging nerves are, at their base 

 at least, straight, exhibiting evidence therefore of constraint, 

 or opposing growth on their two sides. The space between 

 the apex and the first pair of lateral ribs seems to me to be 

 a leaf in itself, that between the first pair and the second to be 

 similarly two independent portions osculating with one another 

 and with the first. By their osculation with one another, they 

 form an additional portion of mid-rib, by their osculations with 

 the central part they form the first pair of lateral ribs, and if 

 we follow the course of either of these ribs we find that it gives 

 out secondary branches, which freed from constraint, or com- 

 paratively so, become curved. In the space they leave, how- 

 ever, we find a secondary central portion, so that the meeting 

 of three elements is exhibited at the sides of the leaf as well 

 as in its central growth: thus the reticulation is throughout 



