§ 257. After these explanations the process of eventual segmentation in the spinal axis itself, will be readily understood. The original cartilaginous rod has to maintain longitudinal rigidity while permitting lateral flexion. As fast as it becomes definitely marked out, it will begin to concentrate within itself a great part of those pressures and tensions caused by transverse strains. As already said, it must be acted upon much in the same manner as a bow, though it is bent by forces acting in a more indirect way; and like a bow, it must, at each bend, have the substance of its convex side extended and the substance of its concave side compressed. So long as the vertebrate animal is small or inert, such a cartilaginous rod may have sufficient strength to withstand the muscular strains; but, other things equal, the evolution of an animal that is large, or active, or both, implies muscular strains which must tend to cause modification in such a cartilaginous rod. The results of greater bulk and of greater vivacity may be best dealt with separately. As the animal increases in size, the rod will grow both longer and thicker. On looking back at the diagrams of forces caused by transverse strains, it will be seen that as the rod grows thicker, its outer parts must be exposed to more severe tensions and pressures if the degree of bend is the same. It is doubtless true that when the fish, advancing by lateral undulations, becomes longer, the curvature assumed by the body at each movement becomes less; and that from this cause the outer parts of the notochord are, other things equal, less strained--the two changes thus partially neutralizing one another. But other things are _not_ equal. For while, supposing the shape of the body to remain constant, the force exerted in moving the body increases as the cubes of its dimensions, the sectional area of the notochord, on which fall the reactions of this exerted force, increases only as the squares of the dimensions: whence results a greater stress upon its substance. This, however, will not be very decided where there is no considerable activity. It is clear that augmenting bulk, taken alone, involves but a moderate residuary increase of strain on each portion of the notochord; and this is probably the reason why it is possible for a large _sluggish_ fish like the Sturgeon, to retain the notochordal structure. But now, passing to the effects of greater activity, a like dynamical inquiry at once shows us how rapidly the violence of the actions and reactions rises as the movements become more vivacious. In the first place, the resistance of a medium such as water increases as the square of the velocity of the body moving through it; so that to _maintain_ double the speed, a fish has to expend four times the energy. But the fish has to do more than this--it has to _initiate_ this speed, or to impress on its mass the force implied by this speed. Now the _vis viva_ of a moving body