ances for solution, depuration, absorption, and circulation, to yield to the multiplying somatic cells a rich and pure blood. Then we come to an all-important factor, the cost of securing food. Here large expenditure of energy in locomotion is necessitated, and there but little—here great efforts for small portions of food, and there small efforts for great portions: again resulting in physiological poverty or physiological wealth. Next, beyond the cost of nervo-muscular activities in foraging, there is the cost of maintaining bodily heat. So much heat implies so much consumed nutriment, and the loss by radiation or conduction, which has perpetually to be made good, varies according to many circumstances—climate, medium (as air or water), covering, size of body (small cooling relatively faster than large); and in proportion to the cost of maintaining heat is the abstraction from the supplies for cell-formation. Finally, there are three all important co-operative factors, or rather laws of factors, the effects of which vary with the size of the animal. The first is that, while the mass of the body varies as the cubes of its dimensions (proportions being supposed constant), the absorbing surface varies as the squares of its dimensions; whence it results that, other things equal, increase of size implies relative decrease of nutrition, and therefore increased obstacles to cell-multiplication. The second is a further sequence from these laws—namely, that while the weight of the body increases as the cubes of the dimensions, the sectional areas of its muscles and bones increase as their squares; whence follows a decreasing power of resisting strains, and a relative weakness of structure. This is implied in the ability of a small animal to leap many times its own length, while a great animal, like the elephant, can not leap at all: its bones and muscles being unable to bear the stress which would be required to propel its body through the air. What increasing cost of keeping together the bodily fabric is thus entailed, we can not say; but that there is an increasing cost, which diminishes the available materials for increase of size, in beyond question, And then, in the third place, we have augmented expense of distribution of nutriment. The greater the size becomes, the more force must be exerted to send blood to the periphery; and this once more entails deduction from the cell-forming matters.
- Principles of Biology, § 46 (No. 8, April, 1863).
- Ibid. This must not be understood as implying that while the mass increases as the cubes, the quantity of motion which can be generated increases only as the squares; for this would not be true. The quantity of motion is obviously measured, not by the sectioned areas of the muscles alone, but by these multiplied into their lengths, and therefore increases as the cubes. But this admission leaves untouched the conclusion that the ability to bear stress increases only as the squares, and thus limits the ability to generate motion, by relative incoherence of materials.