all dimensions, therefore, the weight will quickly overtake the strength. There is a limit, therefore, beyond which it is impossible to make an arch or suspension-bridge support itself. This fact is so well recognized that it is unnecessary to dwell upon it. I have brought it forward at all only because I wish to apply the principle to other cases where it is not so well recognized.
2. Application to Walking.—Now, this principle applies not only to bridges and arches, but to all kinds of structures, and therefore, also, to locomotive-machines, whether natural or artificial. For example, there is a limit of size beyond which it is impossible to make a successful walking-machine, and beyond which, therefore, a walking animal can not exist. Beyond that limit the supporting bones would crush beneath the weight of the animal. It is in vain to say that we will make the bones and muscles thick and strong in proportion to the increasing size of the animal; for, as the animal increases in size, its weight increases as its volume or as the cube, while the strength of bones and muscles increases only as the cross-section or as the square of the diameter. Therefore, as the animal increases in size, a larger and longer portion of the whole strength is consumed in the support, and less and less is left over for motion, until, finally, the weight overtakes the utmost strength of bones to support or muscles to move. It is probable that the limit of an efficient walking-machine has actually been reached in the largest animals which have walked the earth; such, for example, as the huge dinosaurs of the Jurassic period, recently brought to light by the researches of Marsh and Cope. The whale has probably passed the limit, and therefore was compelled to change its form and take to the water, and become a swimming-machine. Or, to speak more definitely and also more truly, the whale family in times long ago, perhaps in earliest Tertiary times, before it became a true whale family, found it profitable, either for food or for safety, to take to the water; and this not only determined a change of form, but also allowed it to attain a greater size than was compatible with walking.
This principle explains many other things in nature which would otherwise be inexplicable. The marvelous vivacity and energy of insect-motion—the arrowy swiftness of flight of many kinds of flies, the prodigious leaps of fleas, the immense weights dragged by ants—are familiar to all. In text-books on natural history these are given as examples of the almost inconceivable nervous and muscular energy of insects, as compared with vertebrates. It is often said that if our nerve- and muscle-energy were as great as that of a flea, we might easily leap a quarter of a mile. In that case we would have little use for railroads or for seven-league boots, or indeed for flying-machines. Now, this is an entire