towards which the tail curves. In swimming, the body of the fish describes a waved track, but this can only be done when the head and tail travel in opposite directions, and on opposite sides of a given line, as represented at fig. 32. The anterior and posterior portions of the fish alternately occupy the positions indicated at d c and w v; the fish oscillating on either side of a given line, and gliding along by a sinuous or wave movement.

I have represented the body of the fish as forced into two curves when swimming, as there are never less than two. These I designate the cephalic (d) and caudal (c) curves, from their respective positions. In the long-bodied fishes, such as the eels, the number of the curves is increased, but in every case the curves occur in pairs, and are complementary. The cephalic and caudal curves not only complement each other, but they act as fulcra for each other, the cephalic curve, with the water seized by it, forming the point d'appui for the caudal one, and vice versâ. The fish in swimming lashes its tail from side to side, precisely as an oar is lashed from side to side in sculling. It therefore describes a figure-of-8 track in the water (efghijkl of fig. 32). During each sweep or lateral movement the tail is both extended and flexed. It is extended and its curve reduced when it approaches the line a b of fig. 32, and flexed, and a new curve formed, when it recedes from the line in question. The tail is effective as a propeller both during flexion and extension, so that, strictly speaking, the tail has no back or non-effective stroke. The terms effective and non-effective employed by authors are applicable only in a comparative and restricted sense; the tail always operating, but being a less effective propeller, when in the act of being flexed or curved, than when in the act of being extended or straightened. By always directing the concavity of the tail (s and t) towards the axis of motion (a b) during extension, and its convexity (c and v) away from the axis of motion (a b) during flexion, the fish exerts a maximum of propelling power with a minimum of slip. In extension of the tail the caudal curve (s) is reduced as the tail travels towards the line a b. In flexion a new curve (v) is formed as the tail travels from the line a b. While the tail travels from s in the direction t,

the head travels from d in the direction w.

There is therefore a period, momentary it must be, when both the cephalic and caudal curves are reduced, and the body of the fish is straight, and free to advance without impediment. The different degrees of resistance experienced by the tail in describing its figure-of-8 movements, are represented by the different-sized curves e f, g h, ij, and kl of fig. 32, p. 68. The curves e f indicate the resistance experienced by the tail during flexion, when it is being carried away from and to the right of the line a b. The curves g h indicate the resistance experienced by the tail when it is extended and carried towards the line a b. This constitutes a half vibration or oscillation of the tail. The curves i j indicate the resistance experienced by the tail when it is a second time flexed and carried away from and to the left of the line a b. The curves k l indicate the resistance experienced by the tail when it is a second time extended and carried towards the line a b. This consti

tutes 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 ef and ij 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 gh, kl, 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 wavepressure 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 the tail, the oscillation is greatest in the direction of the latter. The muscular movements travel in spiral waves from before backwards; and the waves of force react upon the water, and cause the fish to glide forwards in a series of curves. Since the head and tail, as has been stated, always travel in opposite directions, and the fish is constantly alternating or changing sides, it in reality describes a waved track. These remarks may be readily verified by a reference to the swimming of the sturgeon, whose movements are unusually deliberate and slow. The number of curves into which the body of the fish is thrown in swimming is increased in the longbodied fishes, as the eels, and decreased in those whose bodies are short or are comparatively devoid of flexibility. In pro

portion as the curves into which the body is thrown in swimming are diminished, the degree of rotation at the tail or in the fins is augmented, some fishes, as the mackerel, using the tail very much after the manner of a screw in a steam-ship. The fish may thus be said to drill the water in two directions, viz. from behind forwards by a twisting or screwing of the body on its long axis, and from side to side by causing its anterior and posterior portions to assume opposite curves. The pectoral and other fins are also thrown into curves when in action, the movement, as in the body itself, travelling in spiral waves; and it is worthy of remark that the wing of the insect, bat, and bird obeys similar impulses, the pinion, as I shall show presently, being essentially a spiral organ.

The twisting of the pectoral fins is well seen in the common perch (Perca fluviatilis), and still better in the 15-spined Stickleback (Gasterosteus spinosus), which latter frequently progresses by their aid alone.1 In the stickleback, the pectoral fins are so delicate, and are plied with such vigour, that the eye is apt to overlook them, particularly when in motion. The action of the fins can be reversed at pleasure, so that it is by no means an unusual thing to see the stickleback progressing tail first. The fins are rotated or twisted, and their free margins lashed about by spiral movements which closely resemble those by which the wings of insects are propelled.2 The rotating of the fish upon its long axis is seen to advantage in the shark and sturgeon, the former of which requires to turn on its side before it can seize its prey, and likewise

1 The Syngnathi, or Pipefishes, swim chiefly by the undulating movement of the dorsal fin.

2 If the pectoral fins are to be regarded as the homologues of the anterior extremities (which they unquestionably are), it is not surprising that in them the spiral rotatory movements which are traceable in the extremities of quadrupeds, and so fully developed in the wings of bats and birds, should be clearly foreshadowed. "The muscles of the pectoral fins," remarks Professor Owen," though, when compared with those of the homologous members in higher vertebrates, they are very small, few, and simple, yet suffice for all the requisite movements of the fins-elevating, depressing, advancing, and again laying them prone and flat, by an oblique stroke, upon the sides of the body. The rays or digits of both pectorals and ventrals (the homologues of the posterior extremities) can be divaricated and approximated, and the intervening webs spread out or folded up."-Op. cit. vol. i. p. 252.

in the pipefish, whose motions are unwontedly sluggish. The twisting of the tail is occasionally well marked in the swimming of the salamander. In those remarkable mammals, the whale,1 porpoise, manatee, and dugong (figs. 33, 34, and 35), the movements are strictly analogous to those of the fish,

FIG. 33.-The Porpoise (Phocæna communis). Here the tail is principally engaged in swimming, the anterior extremities being rudimentary, and resembling the pectoral fins of fishes. Compare with fig. 30, p. 65.-Original.

FIG. 34.-The Manatee (Manatus Americanus). In this the anterior extremities are more developed than in the porpoise, but still the tail is the great organ of natation. Compare with fig. 33, p. 73, and with fig. 30, p. 65. The shape of the manatee and porpoise is essentially that of the fish.-Original.

the only difference being that the tail acts from above downwards or vertically, instead of from side to side or laterally. The anterior extremities, which in those animals are comparatively perfect, are rotated on their long axes, and applied obliquely and non-obliquely to the water, to assist in balancing and turning. Natation is performed almost exclusively by the tail and lower half of the trunk, the tail of the whale exerting prodigious power.

It is otherwise with the Rays, where the hands are princi

1 Vide "Remarks on the Swimming of the Cetaceans," by Dr. Murie, Proc. Zool. Soc., 1865, pp. 209, 210.