220 MORPHOLOGICAL DEVELOPMENT. 



ly the violence of the actions and reactions rises as the move 

 ments become more vivacious. In the first place, the resist 

 ance of a medium such as water increases as the square of 

 the velocity of the body moving through it ; so that to main 

 tain 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 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 noto- 

 chord 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 in 

 crease of stress on the primitive cartilaginous rod as will 

 tend, other things equal, to cause its modification. 



