time extended and carried towards the line _a b_. This constitutes a complete vibration. These movements are repeated in rapid succession so long as the fish continues to swim forwards. They are only varied when the fish wishes to turn round, in which case the tail gives single strokes either to the right or left, according as it wishes to go to the right or left side respectively. The resistance experienced by the tail when in the positions indicated by _e f_ and _i j_ is diminished by the tail being slightly compressed, by its being moved more slowly, and by the fish rotating on its long axis so as to present the tail obliquely to the water. The resistance experienced by the tail when in the positions indicated by _g h_, _k l_, is increased by the tail being divaricated, by its being moved with increased energy, and by the fish re-rotating on its long axis, so as to present the flat of the tail to the water. The movements of the tail are slowed when the tail is carried away from the line _a b_, and quickened when the tail is forced towards it. Nor is this all. When the tail is moved slowly away from the line _a b_, it draws a current after it which, being met by the tail when it is urged with increased velocity towards the line _a b_, enormously increases the hold which the tail takes of the water, and consequently its propelling power. The tail may be said to work without slip, and to produce the precise kind of currents which afford it the greatest leverage. In this respect the tail of the fish is infinitely superior as a propelling organ to any form of screw yet devised. The screw at present employed in navigation ceases to be effective when propelled beyond a given speed. The screw formed by the tail of the fish, in virtue of its reciprocating action, and the manner in which it alternately eludes and seizes the water, becomes more effective in proportion to the rapidity with which it is made to vibrate. The remarks now made of the tail and the water are equally _apropos_ of the wing and the air. The tail and the wing act on a common principle. A certain analogy may therefore be traced between the water and air as media, and between the tail and extremities as instruments of locomotion. From this it follows that the water and air are acted upon by curves or wave-pressure emanating in the one instance from the tail of the fish, and in the other from the wing of the bird, the reciprocating and opposite curves into which the tail and wing are thrown in swimming and flying constituting _mobile helices_ or _screws_, which, during their action, produce the precise kind and degree of pressure adapted to fluid media, and to which they respond with the greatest readiness. The whole body of the fish is thrown into action in swimming; but as the tail and lower half of the trunk are more free to move than the head and upper half, which are more rigid, and because the tendons of many of the trunk-muscles are inserted into