Here we have to determine the point at which the tree will curve under its own weight, if it be ever so little displaced from the perpendicular[32]. In such an investigation we have to make {20} some assumptions,—for instance, with regard to the trunk, that it tapers uniformly, and with regard to the branches that their sectional area varies according to some definite law, or (as Ruskin assumed[33]) tends to be constant in any horizontal plane; and the mathematical treatment is apt to be somewhat difficult. But Greenhill has shewn that (on such assumptions as the above), a certain British Columbian pine-tree, which yielded the Kew flagstaff measuring 221 ft. in height with a diameter at the base of 21 inches, could not possibly, by theory, have grown to more than about 300 ft. It is very curious that Galileo suggested precisely the same height (_dugento braccia alta_) as the utmost limit of the growth of a tree. In general, as Greenhill shews, the diameter of a homogeneous body must increase as the power 3/2 of the height, which accounts for the slender proportions of young trees, compared with the stunted appearance of old and large ones[34]. In short, as Goethe says in _Wahrheit und Dichtung_, “Es ist dafür gesorgt dass die Bäume nicht in den Himmel wachsen.” But Eiffel’s great tree of steel (1000 feet high) is built to a very different plan; for here the profile of the tower follows the logarithmic curve, giving _equal strength_ throughout, according to a principle which we shall have occasion to discuss when we come to treat of “form and mechanical efficiency” in connection with the skeletons of animals. Among animals, we may see in a general way, without the help of mathematics or of physics, that exaggerated bulk brings with it a certain clumsiness, a certain inefficiency, a new element of risk and hazard, a vague preponderance of disadvantage. The case was well put by Owen, in a passage which has an interest of its own as a premonition (somewhat like De Candolle’s) of the “struggle for existence.” Owen wrote as follows[35]: “In proportion to the bulk of a species is the difficulty of the contest which, as a living organised whole, the individual of such species {21} has to maintain against the surrounding agencies that are ever tending to dissolve the vital bond, and subjugate the living matter to the ordinary chemical and physical forces. Any changes, therefore, in such external conditions as a species may have been originally adapted to exist in, will militate against that existence in a degree proportionate, perhaps in a geometrical ratio, to the bulk of the species. If a dry season be greatly prolonged, the large mammal will suffer from the drought sooner than the small one; if any alteration of climate affect the quantity of vegetable food, the bulky Herbivore will first feel the effects of stinted nourishment.” But the principle of Galileo carries us much further and along more certain lines.