varies as the square of the velocity; whence it follows that the energy required to generate that _vis viva_ is measured by the square of the velocity it produces. Consequently, did the fish put itself in motion _instantaneously_, the expenditure of energy in generating its own _vis viva_ and simultaneously overcoming the resistance of the water, would vary as the fourth power of the velocity. But the fish cannot put itself in motion instantaneously--it must do it by increments; and thus it results that the amounts of the forces expended to give itself different velocities must be represented by some series of numbers falling between the squares and the fourth powers of those velocities. Were the increments slowly accumulated, the ratios of increasing effort would but little exceed the ratios of the squares; but whoever observes the sudden, convulsive action with which an alarmed fish darts out of a shallow into deep water, will see that the velocity is rapidly generated, and that therefore the ratios of increasing effort probably exceed the ratios of the squares very considerably. At any rate it will be clear that the efforts made by fishes in rushing upon prey or escaping enemies (and it is these extreme efforts which here concern us) must, as fishes become more active, rapidly exalt the strains to be borne by their motor organs; and that of these strains, those which fall upon the notochord must be exalted in proportion to the rest. Thus the development of locomotive power, which survival of the fittest must tend in most cases to favour, involves such increase of stress on the primitive cartilaginous rod as will tend, other things equal, to cause its modification. [Illustration: Figs. 291–293.]