The inference commonly drawn from such data is that the muscles of small animals possess a force which greatly exceeds that of large quadrupeds or man, allowance being made for size, and that the explanation of this superior force is to be looked for in some peculiarity of composition or texture. Gerstaecker,[90] for example, suggests that the higher muscular force of Arthropoda may be due to the tender and yielding nature of their muscles. An explanation so desperate as this may well lead us to inquire whether we have understood the facts aright. Plateau’s figures give us the ratio of the weight drawn or raised to the weight of the animal. This we may, with him, take as a measure of the _relative muscular force_. In reality, it is a datum of very little physiological value. By general reasoning of a quite simple kind it can be shown that, for muscles possessing the same physical properties, the _relative_ muscular force necessarily increases very rapidly as the size of the animal decreases. For the contractile force of muscles of the same kind depends simply upon the number and thickness of the fibres, _i.e._, upon the sectional area of the muscles. If the size of the animal and of its muscles be increased according to any uniform scale, the sectional area of a given muscle will increase as the square of any linear dimension. But the weight increases in a higher proportion, according to the increase in length, breadth, and depth jointly, or as the cube of any linear dimension.[91] The ratio of contractile force to weight must therefore become rapidly smaller as the size of the animal increases. Plateau’s second table (_see above_) actually gives a value for the relative muscular force of the Bee, in comparison with the Horse, which is only one-fourteenth of what it ought to turn out, supposing that both animals were of similar construction, and that the muscular fibres in both were equal in contractile force per unit of sectional area.[92] [90] Klassen und Ordnungen des Thierreichs, Bd. V., pp. 61–2. [91] This change in the relation of weight to strength, according to the size of the structure, has long been familiar to engineers. (See, for example, “Comparisons of Similar Structures as to Elasticity, Strength, and Stability,” by Prof. James Thomson, Trans. Inst. Engineers, &c., Scotland, 1876.) The application to animal structures has been made by Herbert Spencer (Principles of Biology, Pt. II., ch. i.). The principle can be readily explained by models. Place a cubical block upon a square column. Double all the dimensions in a second model, which may be done by fitting together eight cubes like the first, and four columns, also the same as before except in length. Each column, though no stronger than before, has now to bear twice the weight.