154 BOTANY OF THE LIVING PLANT 



in Fig. 112. At its base it is about .V of an inch in diameter, but it is there 

 supported in some degree by its sheathing leaves. It may grow in favourable 

 cases to a length of 30 inches before bearing its inflorescence. Thus the 

 length of the stem is to its diameter as about 500 to i, and still it can uphold 

 the inflorescence at its distal end, together with the weight of the fruit when 

 ripe. This extreme proportion of length to diameter suffices for a small 

 Grass ; but it cannot be maintained indefinitely for larger structures. For 

 the weight of a structure varies as the cube of its dimensions, while the strength 

 varies only as the square. There must be then a limit of size beyond which 

 it becomes impossible for a certain type of structure to maintain its form. 

 For instance, according to the proportion of the Moltnia stem, a ten-foot 

 fishing rod should only be J inch in diameter at the butt ; but it is 

 thicker than that. A striking case is seen in the Giant Bamboos. Ewart 

 quotes one 60 metres high, and 40 cms. in diameter at the base. That 

 is a proportion of only about 150 to i. For a plant of that size these dimensions 

 have been calculated as about the limit possible, though the proportions are 

 less striking than those of the smaller Moltnia. There is in point of fact 

 a size-limit for any plan of construction based upon a certain qualit\' 

 and use of material, beyond which the plant cannot maintain its form. 

 If this limit be overstepped the stem will either bend or break. In the 

 Bamboo, which approaches the limit, the extreme top does bend in a graceful 

 curve ; as it does also in the haulms of most Grasses, which like Molima 

 approach the limit of mechanical resistance resulting from their actual 

 dimensions and structure. 



[b) Stiffening and Protection of Flattened Surfaces. 



The mechanical problems affecting the dorsiventral leaf differ from 

 those of the radially constructed stem. The end to be gained is the 

 largest possible expanse of blade, with the least possible risk from 

 winds, and the employment of the least possible material. The elastic 

 petiole allows the blade as a whole to yield before the wind. In the 

 extreme case of the Aspen, where the least breath causes a shiver of 

 the leaves, the petiole is laterally compressed so as to be very flexible. 

 But in most leaves it is stiffen, and semilunar in section, with the convex 

 side downwards, an arrangement which secures efficient support for the 

 blade, while still permitting some freedom of movement. (Fig. 42, p. 59) 

 .\nother feature of mechanical importance is the cutting of the larger 

 leaves into segments, so that while the aggregate area may still be con- 

 siderable, no unduly large surface is exposed to the wind. The risks of a 

 large leaf-area are two ; first, that of folding into so sharp a curve as 

 to crush the soft mesophyll between the firmer layers of epidermis ; 

 and second, that of tearing from the margin inwards. The former 

 is met by the vascular venation, whicli is often accompanied by 

 sclerotic strands, and by enlargement of the surrounding tissues so 



