urally and functionally" that they can seize and let go the fulcra on which they act; particularly is this the case in the water and in the air, the form and movement being such that the greatest results are secured with the least expenditure of force. The muscles cover the bones, in layers or strata, and run longitudinally with them, and with each other, but also at every degree of obliquity. The spiral structure and movement of bones of animals have been carefully analyzed by Dr. Pettigrew, and some of his conclusions are illustrated in Fig. 4.

WING OF BIRD.-Shows how the bones of the arm (a), forearm (b), and hand (c), are twisted, and form a conical screw.

ANTERIOR EXTREMITY OF ELEPHANT.-Shows how the bones of the arm (q), forearm (q'æ), and (0), are twisted to form an osseous screw. Cast or mould of the interior of the left ventricle of the heart of a deer. Shows that the left ventricular cavity is conical and spiral in its nature.

The voluntary muscles of the wing, he finds, are upon the same pattern as are those of the involuntary muscles of the heart. He compared the bones removed from the forelimb of a quadruped or bird, with a cast obtained from the cavity of a hollow muscle, the left ventricle of the heart of a mammal, and found that the bones and the cast are twisted upon themselves, and form elegant screws, the threads of which run in the same direction.

FIG. 5.

Diagram, showing the figure-of-8 or double waved track produced by the alternating of the extremities in man in walking and running.

The movement of the limbs of a quadruped is in curves, which, continued, form a figure-of-8, or a series of them; a fact in progression first pointed out by Dr. Pettigrew. Quadrupeds, says the author, walk; fishes swim; insects, bats, and birds, fly by figure-of-8 move

ments; and, in human locomotion, the same phenomenon is observed. The diagram, Fig. 5, shows the curved track made by man walking. The accuracy of this is easily verified by observation. As the limbs swing forward, they move in the arc of an ellipse; that is, in a slight curve outward, and with the arms form the double curves, as shown in the figure. In the movement of the horse, walking or trotting, the same phenomenon appears, as the figure shows.

HORSE IN THE ACT OF TROTTING.-In this, as in all the other paces, the body of the horse is levered forward by a diagonal twisting of the trunk and extremities, the extremities describing a figure-of-8 track (8, u, r, t).

The wings of birds, bats, and insects, describe similar curves. They are produced by the rotation of the wing, as it rises and falls, so that it twists, screw-like, on its long axis, one-half of the figure being formed in the ascent, the other in the descent of the wing.

FIG. 7.

IMITATION OF WING MOVEMENT BY A REED WITH FLEXIBLE SAIL MOVING ON A BALL-ANDSOCKET JOINT, SHOWING THE DOUBLE CURVES.

The double curves or figure-of-8 lines which thus occur are not mere coincidences, nor in any sense accidental, but the expression of a

law of movement of vertebrated animals, and, from a most extended series of observations, Dr. Pettigrew concludes:

"That quadrupeds walk, and fishes swim, and insects, bats, and birds fly, by figure-of-8 movements.

"That the flipper of the sea-bear, the swimming wing of the penguin, and the wing of the insect, bat, and bird, are screws structurally, and resemble the blade of an ordinary screw-propeller.

"That those organs are screws functionally, from their twisting and untwisting, and from their rotating in the direction of their length, when they are made to oscillate.

"That they have a reciprocating action, and reverse their planes more or less completely at every stroke.

"That the wing describes a figure-of-8 track in space when the flying animal is artificially fixed.

"That the wing, when the flying animal is progressing at a high rate of speed in an horizontal direction, describes a looped and then a wave track, from the fact that the figure-of-8 is gradually opened out and unraveled as the animal advances."

He constructed artificial fish-tails, fins, flippers, and wings-flexible and elastic-slightly twisted upon themselves, and applied them respectively to the water and air by a sculling or figure-of-8 motion. The curved surfaces and movements peculiar to the living organs were reproduced. The purely mechanical movement shown in this application of traveling structures to their environment scarcely admits of doubt.

Man is enabled to travel in two of the three great highways of Nature. He can progress upon the land, swim in the water, but fly he cannot; nor has he yet invented a means by which flying is possible. By his applications of natural laws he has "outraced the quadruped on the land and the fish in the sea," and the conclusion from the analogy and nature of things is, that the "tramways of the air will yet be traversed by man's ingenuity."

A balloon floats, it does not fly. It floats because it is lighter than the air; a bird is enabled to fly because it is heavier than the air, and weight is an important element in all, but especially in aërial and land locomotion. It is that by which the extremities of animals seize and hold their position in the media in which they move. If a man were no heavier than the air, the movement of his limbs would avail him nothing. The earth is his fulcrum, as the air is that of the bird, and water that of the fish. Progression, therefore, implies gravity and the power of resistance, which gravity affords. A body which floats is carried along with the media in which it is; having lost its weight, it has lost its power of self-control. A man who cannot swim is at the mercy of the slightest current or wave, if in depth at which the lifting power of the water makes his foothold insecure.

A man standing still commences to progress by throwing his body

slightly forward. Some momentum is thus obtained, the limb being simultaneously advanced. "The throwing forward of the body may be said to inaugurate the movement of walking." The same occurs with a horse, but, if attached to a load, great impetus is attained by the body before either of the limbs is lifted. Momentum thus relieves muscular strain in the limbs and economizes force. How completely this principle is applied in swimming and flying will be presently noticed.

In ordinary walking of man or quadruped, the limbs swing forward without muscular effort. According to Prof. Weber, they swing by the force of gravity as a pendulum, and obey the same laws. If suspended they oscillate freely, and gravity brings them to a position of rest. How much the muscles are saved from exhaustion in ordinary locomotion, by gravity, becomes obvious when we attempt to overcome it by climbing or leaping. The foot being upon the ground, the limb rotates upon it as an axis, carrying the body forward and slightly elevating it, but the elevation is in the arc of a circle, and when the other foot reaches the ground the body is slightly lowered. Thus in progression the trunk continually rises and falls; it really undulates along a given line.

But other motions than those referred to are developed in the act of walking. The movements of the arms and feet are complementary; the right foot and left arm advance together, and vice versa. This begets a diagonal movement which produces oscillation or twisting of the trunk, which is excessive in awkward walkers. To repress this oscillatory swing is indispensable, if great velocity is to be attained. Trained runners flex their arms and hold them steadily at their greatest speed, and every school-boy does the same instinctively, without considering why the act is important. The swiftest-running birds have small wings; those of the ostrich are scarcely more than rudimental.

FIG. 8.

h

SWIMMING OF THE FISU-(After Borelli.)

The diagonal twist or movement referred to is expressed in a spiral wave of motion which traverses the trunk in the direction of its length. This motion is obvious in fishes in the act of swimming. It is a resultant of motions, which are in all vertebrates essentially the In the walking of a cat or panther, this wave of curvature is continuous along the spine. It is really a lateral undulation. We will

same.

follow this curved motion in the swimming of aquatic animals. The illustration of Borelli (Fig. 8), shows only a single curve of the body.

Prof. Owen, commenting on this figure, says the tail of the animal moving from a to i causes the centre of gravity to move forward, and turns the head of the fish in the direction c to h. This implies but a single curve of the body, whereas there are two, the one complementary of the other, as is shown to be the case by Dr. Pettigrew. He says: "Observation and experiment have convinced me that when a fish swims it never throws its body into a single curve, as represented in Borelli's figure, but always in a double or figure-of-8 curve, as shown in Fig. 9.

FIG. 9.

SWIMMING OF THE STURGEON.

In swimming, the body of the fish describes a waved track along a medial line. The two curves of the body act as fulcra for each other, as occurs in the movement of a snake, by its usual lateral undulations when swimming. In fishes and swimming reptiles of great length, there may occur more than two curves, as four, but never three, each curve having its complementary one. "The fish lashes its tail from side to side, and a figure-of-8 track is formed by the movement," both strokes propelling, but with unequal power during the course of the stroke. There is a feature in this movement which is equally obvious in the movement of the wings of birds in the air, that is, a current is formed, as the tail is carried to one side, against which the return-stroke is given; thus, as the author observes, "the tail may be said to work without slip, and to produce the precise kind of currents which afford it the greatest leverage."

And this is true, whether the swing of the tail in swimming is sideways, as with the salmon, or vertically, as occurs with the whale or the porpoise. The fins act as balancers of the body, but the equipoise is impaired if they are injured; and the removal of the tail, as Owen observes, destroys the power of locomotion.

The specific gravity of aquatic animals is nearly that of the water they inhabit, or is made so in many cases by the gaseous contents of their air-bladders. Nevertheless, momentum is an important element in swimming. It originates in the movement of the fins and tail, and not from throwing the body forward, as occurs in the initial movement of walking. The momentum and velocity attained by some