_Swimming of the Fish, Whale, Porpoise, etc._--According to Borelli,[42] and all who have written since his time, the fish in swimming causes its tail to vibrate on either side of a given line, very much as a rudder may be made to oscillate by moving its tiller. The line referred to corresponds to the axis of the fish when it is at rest and when its body is straight, and to the path pursued by the fish when it is swimming. It consequently represents the axis of the fish and the axis of motion. According to this theory the tail, when flexed or curved to make what is termed the back or non-effective stroke, is forced away from the imaginary line, its curved, concave, or biting surface being directed outwards. When, on the other hand, the tail is extended to make what is termed the effective or forward stroke, it is urged towards the imaginary line, its convex or non-biting surface being directed inwards (fig. 31). [42] Borelli, “De motu Animalium,” plate 4, fig. 5, sm. 4to, 2 vols. Romæ, 1680. [Illustration: FIG. 31.--Swimming of the Fish.--(After Borelli.)] When the tail strikes in the direction _a i_, the head of the fish is said to travel in the direction _c h_. When the tail strikes in the direction _g e_, the head is said to travel in the direction _c b_; these movements, when the tail is urged with sufficient velocity, causing the body of the fish to move in the line _d c f_. The explanation is apparently a satisfactory one; but a careful analysis of the swimming of the living fish induces me to believe it is incorrect. According to this, the commonly received view, the tail would experience a greater degree of resistance during the back stroke, _i.e._ when it is flexed and carried away from the axis of motion (_d c f_) than it would during the forward stroke, or when it is extended and carried towards the axis of motion. This follows, because the concave surface of the tail is applied to the water during what is termed the back or non-effective stroke, and the convex surface during what is termed the forward or effective stroke. This is just the opposite of what actually happens, and led Sir John Lubbock to declare that there was a period in which the action of the tail dragged the fish backwards, which, of course, is erroneous. There is this further difficulty. When the tail of the fish is urged in the direction _g e_, the head does not move in the direction _c b_ as stated, but in the direction _c h_, the body of the fish describing the arc of a circle, _a c h_. This is a matter of observation. If a fish when resting suddenly forces its tail to one side and curves its body, the fish describes a curve in the water corresponding to that described by the body. If the concavity of the curve formed by the body is directed to the right side, the fish swims in a curve towards that side. To this there is no exception, as any one may readily satisfy himself, by watching the movements of gold fish in a vase. Observation and