Chapter II: Part 2

The figure-of-8 theory of walking, swimming, and flying, as originally propounded in the lectures, papers, and memoirs referred to, has been confirmed not only by the researches and experiments of Professor Marey, but also by those of M. Senecal, M. de Fastes, M. Ciotti, and others. Its accuracy is no longer a matter of doubt. As the limits of the present volume will not admit of my going into the several arrangements by which locomotion is attained in the animal kingdom as a whole, I will only describe those movements which illustrate in a progressive manner the several kinds of progression on the land, and on and in the water and air.

I propose first to analyse the natural movements of walking, swimming, and flying, after which I hope to be able to show that certain of these movements may be reproduced artificially. The locomotion of animals depends upon mechanical adaptations found in all animals which change locality. These adaptations are very various, but under whatever guise they appear they are substantially those to which we resort when we wish to move bodies artificially. Thus in animal mechanics we have to consider the various orders of levers, the pulley, the centre of gravity, specific gravity, the resistance of solids, semi-solids, fluids, etc. As the laws which regulate the locomotion of animals are essentially those which regulate the motion of bodies in general, it will be necessary to consider briefly at this stage the properties of matter when at rest and when moving. They are well stated by Mr. Bishop in a series of propositions which I take the liberty of transcribing:--

“_Fundamental Axioms._--First, every body continues in a state of rest, or of uniform motion in a right line, until a change is effected by the agency of some mechanical force. Secondly, any change effected in the quiescence or motion of a body is in the direction of the force impressed, and is proportional to it in quantity. Thirdly, reaction is always equal and contrary to action, or the mutual actions of two bodies upon each other are always equal and in opposite directions.

“_Of uniform motion._--If a body moves constantly in the same manner, or if it passes over equal spaces in equal periods of time, its motion is uniform. The velocity of a body moving uniformly is measured by the space through which it passes in a given time.

“The velocities generated or impressed on different masses by the same force are reciprocally as the masses.

“_Motion uniformly varied._--When the motion of a body is uniformly accelerated, the space it passes through during any time whatever is proportional to the square of the time.

“In the leaping, jumping, or springing of animals in any direction (except the vertical), the paths they describe in their transit from one point to another in the plane of motion are parabolic curves.

“_The legs move by the force of gravity as a pendulum._--The Professor, Weber, have ascertained, that when the legs of animals swing forward in progressive motion, they obey the same laws as those which regulate the periodic oscillations of the pendulum.

“_Resistance of fluids._--Animals moving in air and water experience in those media a sensible resistance, which is greater or less in proportion to the density and tenacity of the fluid, and the figure, superficies, and velocity of the animal.

“An inquiry into the amount and nature of the resistance of air and water to the progression of animals will also furnish the data for estimating the proportional values of those fluids acting as fulcra to their locomotive organs, whether they be fins, wings, or other forms of lever.

“The motions of air and water, and their directions, exercise very important influences over velocity resulting from muscular action.

“_Mechanical effects of fluids on animals immersed in them._--When a body is immersed in any fluid whatever, it will lose as much of its weight relatively as is equal to the weight of the fluid it displaces. In order to ascertain whether an animal will sink or swim, or be sustained without the aid of muscular force, or to estimate the amount of force required that the animal may either sink or float in water, or fly in the air, it will be necessary to have recourse to the specific gravities both of the animal and of the fluid in which it is placed.

“The specific gravities or comparative weights of different substances are the respective weights of equal volumes of those substances.

“_Centre of gravity._--The centre of gravity of any body is a point about which, if acted upon only by the force of gravity, it will balance itself in all positions; or, it is a point which, if supported, the body will be supported, however it may be situated in other respects; and hence the effects produced by or upon any body are the same as if its whole mass were collected into its centre of gravity.

“The attitudes and motions of every animal are regulated by the positions of their centres of gravity, which, in a state of rest, and not acted upon by extraneous forces, must lie in vertical lines which pass through their basis of support.

“In most animals moving on solids, the centre is supported by variously adapted organs; during the flight of birds and insects it is suspended; but in fishes, which move in a fluid whose density is nearly equal to their specific gravity, the centre is acted upon equally in all directions.”[10]

[10] Cyc. of Anat. and Phy., Art. “Motion,” by John Bishop, Esq.

As the locomotion of the higher animals, to which my remarks more particularly apply, is in all cases effected by levers which differ in no respect from those employed in the arts, it may be useful to allude to them in a passing way. This done, I will consider the bones and joints of the skeleton which form the levers, and the muscles which move them.

“_The Lever._--Levers are commonly divided into three kinds, according to the relative positions of the prop or fulcrum, the power, and the resistance or weight. The straight lever of each order is equally balanced when the power multiplied by its distance from the fulcrum equals the weight, multiplied by its distance, or P the power, and W the weight, are in equilibrium when they are to each other in the inverse ratio of the arms of the lever, to which they are attached. The pressure on the fulcrum however varies.

“In straight levers of the _first kind_, the fulcrum is between the power and the resistance, as in fig. 1, where F is the fulcrum of the lever AB; P is the power, and W the weight or resistance. We have P : W :: BF : AF, hence P.AF = W.BF, and the pressure on the fulcrum is both the power and resistance, or P + W.

“In the second order of levers (fig. 2), the resistance is between the fulcrum and the power; and, as before, P : W :: BF : AF, but the pressure of the fulcrum is equal to W - P, or the weight less the power.

“In the third order of lever the power acts between the prop and the resistance (fig. 3), where also P : W :: BF : AF, and the pressure on the fulcrum is P - W, or the power less the weight.

“In the preceding computations the weight of the lever itself is neglected for the sake of simplicity, but it obviously forms a part of the elements under consideration, especially with reference to the arms and legs of animals.

“To include the weight of the lever we have the following equations: P.AF + {AF}.1/2AF = W.BF + {BF}.1/2BF; in the first order, where {AF} and {BF} represent the weights of these portions of the lever respectively. Similarly, in the second order P.AF = W.BF + {AF}.(AF)/2, and in the third order P.AF = W.BF + {BF}.(BF)/2.

“In this outline of the theory of the lever, the forces have been considered as acting vertically, or parallel to the direction of the force of gravity.

“_Passive Organs of Locomotion. Bones._--The solid framework or skeleton of animals which supports and protects their more delicate tissues, whether chemically composed of entomoline, carbonate, or phosphate of lime; whether placed internally or externally; or whatever may be its form or dimensions, presents levers and fulcra for the action of the muscular system, in all animals furnished with earthy solids for their support, and possessing locomotive power.”[11] The levers and fulcra are well seen in the extremities of the deer, the skeleton of which is selected for its extreme elegance.

[11] Bishop, _op. cit._

FIG. 4. Skeleton of the Deer (after Pander and D’Alton). The bones
in the extremities of this the fleetest of quadrupeds are inclined
very obliquely towards each other, and towards the scapular and
iliac bones. This arrangement increases the leverage of the muscular
system and confers great rapidity on the moving parts. It augments
elasticity, diminishes shock, and indirectly begets continuity of
movement, _a._ Angle formed by the femur with the ilium, _b._ Angle
formed by the tibia and fibula with the femur, _c._ Angle formed by
the cannon bone with the tibia and fibula, _d._ Angle formed by the
phalanges with the cannon bone. _e._ Angle formed by the humerus
with the scapula. _f._ Angle formed by the radius and ulna with the
humerus.]

While the bones of animals form levers and fulcra for portions of the muscular system, it must never be forgotten that the earth, water, or air form fulcra for the travelling surfaces of animals as a whole. Two sets of fulcra are therefore always to be considered, viz. those represented by the bones, and those represented by the earth, water, or air respectively. The former when acted upon by the muscles produce motion in different parts of the animal (not necessarily progressive motion); the latter when similarly influenced produce locomotion. Locomotion is greatly favoured by the tendency which the body once set in motion has to advance in a straight line. “The form, strength, density, and elasticity of the skeleton varies in relation to the bulk and locomotive power of the animal, and to the media in which it is destined to move.

“The number of moveable articulations in a skeleton determines the degree of its mobility within itself; and the kind and number of the articulations of the locomotive organs determine the number and disposition of the muscles acting upon them.

“The bones of vertebrated animals, especially those which are entirely terrestrial, are much more elastic, hard, and calculated by their chemical elements to bear the shocks and strains incident to terrestrial progression, than those of the aquatic vertebrata; the bones of the latter being more fibrous and spongy in their texture, the skeleton is more soft and yielding.

“The bones of the higher orders of animals are constructed according to the most approved mechanical principles. Thus they are convex externally, concave within, and strengthened by ridges running across their discs, as in the scapular and iliac bones; an arrangement which affords large surfaces for the attachment of the powerful muscles of locomotion. The bones of birds in many cases are not filled with marrow but with air,--a circumstance which insures that they shall be very strong and very light.

“In the thigh bones of most animals an angle is formed by the head and neck of the bone with the axis of the body, which prevents the weight of the superstructure coming vertically upon the shaft, converts the bone into an elastic arch, and renders it capable of supporting the weight of the body in standing, leaping, and in falling from considerable altitudes.

“_Joints._--Where the limbs are designed to move to and fro simply in one plane, the ginglymoid or hinge-joint is applied; and where more extensive motions of the limbs are requisite, the enarthrodial, or ball-and-socket joint, is introduced. These two kinds of joints predominate in the locomotive organs of the animal kingdom.

“The enarthrodial joint has by far the most extensive power of motion, and is therefore selected for uniting the limbs to the trunk. It permits of the several motions of the limbs termed pronation, supination, flexion, extension, abduction, adduction, and revolution upon the axis of the limb or bone about a conical area, whose apex is the axis of the head of the bone, and base circumscribed by the distal extremity of the limb.”[12]

[12] Bishop, _op. cit._

The ginglymoid or hinge-joints are for the most part spiral in their nature. They admit in certain cases of a limited degree of lateral rocking. Much attention has been paid to the subject of joints (particularly human ones) by the brothers Weber, Professor Meyer of Zürich, and likewise by Langer, Henke, Meissner, and Goodsir. Langer, Henke, and Meissner succeeded in demonstrating the “screw configuration” of the articular surfaces of the elbow, ankle, and calcaneo-astragaloid joints, and Goodsir showed that the articular surface of the knee-joint consist of “a double conical screw combination.” The last-named observer also expressed his belief “that articular combinations with opposite windings on opposite sides of the body, similar to those in the knee-joint, exist in the ankle and tarsal, and in the elbow and carpal joints; and that the hip and shoulder joints consist of single threaded couples, but also with opposite windings on opposite sides of the body.” I have succeeded in demonstrating a similar spiral configuration in the several bones and joints of the wing of the bat and bird, and in the extremities of most quadrupeds. The bones of animals, particularly the extremities, are, as a rule, twisted levers, and act after the manner of screws. This arrangement enables the higher animals to apply their travelling surfaces to the media on which they are destined to operate at any degree of obliquity so as to obtain a maximum of support or propulsion with a minimum of slip. If the travelling surfaces of animals did not form screws structurally and functionally, they could neither seize nor let go the fulcra on which they act with the requisite rapidity to secure speed, particularly in water and air.

“_Ligaments._--The office of the ligaments with respect to locomotion, is to restrict the degree of flexion, extension, and other motions of the limbs within definite limits.

“_Effect of Atmospheric pressure on Limbs._--The influence of atmospheric pressure in supporting the limbs was first noticed by Dr. Arnott, though it has been erroneously ascribed by Professor Müller to Weber. Subsequent experiments made by Dr. Todd, Mr. Wormald, and others, have fully established the mechanical influence of the air in keeping the mechanism of the joints together. The amount of atmospheric pressure on any joint depends upon the area or surface presented to its influence, and the height of the barometer. According to Weber, the atmospheric pressure on the hip-joint of a man is about 26 lbs. The pressure on the knee-joint is estimated by Dr. Arnott at 60 lbs.”[13]

[13] Bishop, _op. cit._

FIG. 5. Shows the muscular cycle formed by the biceps (_a_) or flexor
muscle, and the triceps (_b_) or extensor muscle of the human arm. At
_i_ the centripetal or shortening action of the biceps is seen, and
at _j_ the centrifugal or elongating action of the triceps (_vide_
arrows). The present figure represents the forearm as flexed upon
the arm. As a consequence, the long axes of the sarcous elements or
ultimate particles of the biceps (_i_) are arranged in a more or less
horizontal direction; the long axes of the sarcous elements of the
triceps (_j_) being arranged in a nearly vertical direction. When
the forearm is extended, the long axes of the sarcous elements of
the biceps and triceps are reversed. The present figure shows how
the bones of the extremities form levers, and how they are moved
by muscular action. If, _e.g._, the biceps (_a_) shortens and the
triceps (_b_) elongates, they cause the forearm and hand (_h_) to
move towards the shoulder (_d_). If, on the other hand, the triceps
(_b_) shortens and the biceps (_a_) elongates, they cause the forearm
and hand (_h_) to move away from the shoulder. In these actions the
biceps (_a_) and triceps (_b_) are the power; the elbow-joint (_g_)
the fulcrum, and the forearm and hand (_h_) the weight to be elevated
or depressed. If the hand represented a travelling surface which
operated on the earth, the water, or the air, it is not difficult to
understand how, when it was made to move by the action of the muscles
of the arm, it would in turn move the body to which it belonged, _d_
Coracoid process of the scapula, from which the internal or short
head of the biceps (_a_) arises, _e_ Insertion of the biceps into
the radius. _f_ Long head of the triceps (_b_). _g_ Insertion of the
triceps into the olecranon process of the ulna.--_Original._]

_Active organs of Locomotion. Muscles, their Properties, Arrangement, Mode of Action, etc._--If time and space had permitted, I would have considered it my duty to describe, more or less fully, the muscular arrangements of all the animals whose movements I propose to analyse. This is the more desirable, as the movements exhibited by animals of the higher types are directly referable to changes occurring in their muscular system. As, however, I could not hope to overtake this task within the limits prescribed for the present work, I shall content myself by merely stating the properties of muscles; the manner in which muscles act; and the manner in which they are grouped, with a view to moving the osseous levers which constitute the bony framework or skeleton of the animals to be considered. Hitherto, and by common consent, it has been believed that whereas a flexor muscle is situated on one aspect of a limb, and its corresponding extensor on the other aspect, these two muscles must be opposed to and antagonize each other. This belief is founded on what I regard as an erroneous assumption, viz., that muscles have only the power of shortening, and that when one muscle, say the flexor, shortens, it must drag out and forcibly elongate the corresponding extensor, and the converse. This would be a mere waste of power. Nature never works against herself. There are good grounds for believing, as I have stated elsewhere,[14] that there is no such thing as antagonism in muscular movements; the several muscles known as flexors and extensors; abductors and adductors; pronators and supinators, being simply correlated. Muscles, when they act, operate upon bones or something extraneous to themselves, and not upon each other. The muscles are folded round the extremities and trunks of animals with a view to operating in masses. For this purpose they are arranged in cycles, there being what are equivalent to extensor and flexor cycles, abductor and adductor cycles, and pronator and supinator cycles. Within these muscular cycles the bones, or extraneous substances to be moved, are placed, and when one side of a cycle shortens, the other side elongates. Muscles are therefore endowed with a centripetal and centrifugal action. These cycles are placed at every degree of obliquity and even at right angles to each other, but they are so disposed in the bodies and limbs of animals that they always operate consentaneously and in harmony. _Vide_ fig. 5, p. 25.

[14] “Lectures on the Physiology of the Circulation in Plants, in the
Lower Animals, and in Man.”--Edinburgh Medical Journal for January
and February 1873.

There are in animals very few simple movements, _i.e._ movements occurring in one plane and produced by the action of two muscles. Locomotion is for the most part produced by the consentaneous action of a great number of muscles; these or their fibres pursuing a variety of directions. This is particularly true of the movements of the extremities in walking, swimming, and flying.

Muscles are divided into the voluntary, the involuntary, and the mixed, according as the will of the animal can wholly, partly, or in no way control their movements. The voluntary muscles are principally concerned in the locomotion of animals. They are the power which moves the several orders of levers into which the skeleton of an animal resolves itself.

The movements of the voluntary and involuntary muscles are essentially wave-like in character, _i.e._ they spread from certain centres, according to a fixed order, and in given directions. In the extremities of animals the centripetal or converging muscular wave on one side of the bone to be moved, is accompanied by a corresponding centrifugal or diverging wave on the other side; the bone or bones by this arrangement being perfectly under control and moved to a hair’s-breadth. The centripetal or converging, and the centrifugal or diverging waves of force are, as already indicated, correlated.[15] Similar remarks may be made regarding the different parts of the body of the serpent when creeping, of the body of the fish when swimming, of the wing of the bird when flying, and of our own extremities when walking. In all those cases the moving parts are thrown into curves or waves definitely correlated.

[15] Muscles virtually possess a pulling and pushing power; the
pushing power being feeble and obscured by the flaccidity of the
muscular mass. In order to push effectually, the pushing substance
must be more or less rigid.

It may be broadly stated, that in every case locomotion is the result of the opening and closing of opposite sides of muscular cycles. By the closing or shortening, say of the flexor halves of the cycles, and the opening or elongation of the extensor halves, the angles formed by the osseous levers are diminished; by the closing or shortening of the extensor halves of the cycles, and the opening or elongation of the flexor halves, the angles formed by the osseous levers are increased. This alternate diminution and increase of the angles formed by the osseous levers produce the movements of walking, swimming, and flying. The muscular cycles of the trunk and extremities are so disposed with regard to the bones or osseous levers, that they in every case produce a maximum result with a minimum of power. The origins and insertions of the muscles, the direction of the muscles and the distribution of the muscular fibres insure, that if power is lost in moving a lever, speed is gained, there being an apparent but never a real loss. The variety and extent of movement is secured by the obliquity of the muscular fibres to their tendons; by the obliquity of the tendons to the bones they are to move; and by the proximity of the attachment of the muscles to the several joints. As muscles are capable of shortening and elongating nearly a fourth of their length, they readily produce the precise kind and degree of motion required in any particular case.[16]

[16] The extensor muscles preponderate in mass and weight over the
flexors, but this is readily accounted for by the fact, that the
extensors, when limbs are to be straightened, always work at a
mechanical disadvantage. This is owing to the shape of the bones,
the conformation of the joints, and the position occupied by the
extensors.

FIG. 6.--Wing of bird. Shows how the bones of the arm (_a_), forearm
(_b_), and hand (_c_), are twisted, and form a conical screw. Compare
with Figs. 7 and 8.--_Original._]

FIG. 7.--Anterior extremity of elephant. Shows how the bones
of the arm (_q_), forearm (_q´x_), and foot (_o_), are twisted to
form an osseous screw. Compare with Figs. 6 and 8.--_Original._

FIG. 8.--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. _a_ Portion of right ventricular cavity;
_b_, base of left ventricular cavity; _x_, _y_, spiral grooves
occupied by the spiral _musculi papillares_; _j_, _q_, spiral ridges
projecting between the _musculi papillares_. Compare with Figs. 6 and
7.--_Original._]

The force of muscles, according to the experiments of Schwann, increases with their length, and _vice versa_. It is a curious circumstance, and worthy the attention of those interested in homologies, that the voluntary muscles of the superior and inferior extremities, and more especially of the trunk, are arranged in longitudinal, transverse, and oblique spiral lines, and in layers or strata precisely as in the ventricles of the heart and hollow muscles generally.[17] If, consequently, I eliminate the element of bone from these several regions, I reproduce a typical hollow muscle; and what is still more remarkable, if I compare the bones removed (say the bones of the anterior extremity of a quadruped or bird) with the cast obtained from the cavity of a hollow muscle (say the left ventricle of the heart of the mammal), I find that the bones and the cast are twisted upon themselves, and form elegant screws, the threads or ridges of which run in the same direction. This affords a proof that the involuntary hollow muscles supply the type or pattern on which the voluntary muscles are formed. Fig. 6 represents the bones of the wing of the bird; fig. 7 the bones of the anterior extremity of the elephant; and fig. 8 the cast or mould of the cavity of the left ventricle of the heart of the deer.

[17] “On the Arrangement of the Muscular Fibres in the Ventricles
of the Vertebrate Heart, with Physiological Remarks,” by the
Author.--Philosophical Transactions, 1864.

“On the Muscular Arrangements of the Bladder and Prostate, and
the manner in which the Ureters and Urethra are closed,” by the
Author.--Philosophical Transactions, 1867.

“On the Muscular Tunics in the Stomach of Man and other Mammalia,” by
the Author.--Proceedings Royal Society of London, 1867.

It has been the almost invariable custom in teaching anatomy, and such parts of physiology as pertain to animal movements, to place much emphasis upon the configuration of the bony skeleton as a whole, and the conformation of its several articular surfaces in particular. This is very natural, as the osseous system stands the wear and tear of time, while all around it is in a great measure perishable. It is the link which binds extinct forms to living ones, and we naturally venerate and love what is enduring. It is no marvel that Oken, Goethe, Owen, and others should have attempted such splendid generalizations with regard to the osseous system--should have proved with such cogency of argument that the head is an expanded vertebra. The bony skeleton is a miracle of design very wonderful and very beautiful in its way. But when all has been said, the fact remains that the skeleton, when it exists, forms only an adjunct of locomotion and motion generally. All the really essential movements of an animal occur in its soft parts. The osseous system is therefore to be regarded as secondary in importance to the muscular, of which it may be considered a differentiation. Instead of regarding the muscles as adapted to the bones, the bones ought to be regarded as adapted to the muscles. Bones have no power either of originating or perpetuating motion. This begins and terminates in the muscles. Nor must it be overlooked, that bone makes its appearance comparatively late in the scale of being; that innumerable creatures exist in which no trace either of an external or internal skeleton is to be found; that these creatures move freely about, digest, circulate their nutritious juices and blood when present, multiply, and perform all the functions incident to life. While the skeleton is to be found in only a certain proportion of the animals existing on our globe, the soft parts are to be met with in all; and this appears to me an all-sufficient reason for attaching great importance to the movements of soft parts, such as protoplasm, jelly masses, involuntary and voluntary muscles, etc.[18] As the muscles of vertebrates are accurately applied to each other, and to the bones, while the bones are rigid, unyielding, and incapable of motion, it follows that the osseous system acts as a break or boundary to the muscular one,--and hence the arbitrary division of muscles into extensors and flexors, pronators and supinators, abductors and adductors. This division although convenient is calculated to mislead. The most highly organized animal is strictly speaking to be regarded as a living mass whose parts (hard, soft, and otherwise) are accurately adapted to each other, every part reciprocating with scrupulous exactitude, and rendering it difficult to determine where motion begins and where it terminates. Fig. 9 shows the more superficial of the muscular masses which move the bones or osseous levers of the horse, as seen in the walk, trot, gallop, etc. A careful examination of these carneous masses or muscles will show that they run longitudinally, transversely, and obliquely, the longitudinal and transverse muscles crossing each other at nearly right angles, the oblique ones tending to cross at various angles, as in the letter X. The crossing is seen to most advantage in the deep muscles.

[18] Lectures “On the Physiology of the Circulation in Plants, in the
Lower Animals, and in Man,” by the Author.--Edinburgh Medical Journal
for September 1872.

In order to understand the twisting which occurs to a greater or less extent in the bodies and extremities (when present) of all vertebrated animals, it is necessary to reduce the bony and muscular systems to their simplest expression. If motion is desired in a dorsal, ventral, or lateral direction only, a dorsal and ventral or a right and left lateral set of longitudinal muscles acting upon straight bones articulated by an ordinary ball-and-socket joint will suffice. In this case the dorsal, ventral, and right and left lateral muscles form _muscular cycles_; contraction or shortening on the one aspect of the cycle being accompanied by relaxation or elongation on the other, the bones and joints forming as it were the diameters of the cycles, and oscillating in a backward, forward, or lateral direction in proportion to the degree and direction of the muscular movements. Here the motion is confined to two planes intersecting each other at right angles. When, however, the muscular system becomes more highly differentiated, both as regards the number of the muscles employed, and the variety of the directions pursued by them, the bones and joints also become more complicated. Under these circumstances, the bones, as a rule, are twisted upon themselves, and their articular surfaces present various degrees of spirality to meet the requirements of the muscular system. Between the straight longitudinal muscles, therefore, arranged in dorsal and ventral, and right and left lateral sets, and those which run in a more or less transverse direction, and between the simple joint whose motion is confined to one plane and the ball-and-socket joints whose movements are universal, every degree of obliquity is found in the direction of the muscles, and every possible modification in the disposition of the articular surfaces. In the fish the muscles are for the most part arranged in dorsal, ventral, and lateral sets, which run longitudinally; and, as a result, the movements of the trunk, particularly towards the tail, are from side to side and sinuous. As, however, oblique fibres are also present, and the tendons of the longitudinal muscles in some instances cross obliquely towards the tail, the fish has also the power of tilting or twisting its trunk (particularly the lower half) as well as the caudal fin. In a mackerel which I examined, the oblique muscles were represented by the four lateral masses occurring between the dorsal, ventral, and lateral longitudinal muscles--two of these being found on either side of the fish, and corresponding to the myocommas or “_grand muscle latéral_” of Cuvier. The muscular system of the fish would therefore seem to be arranged on a fourfold plan,--there being four sets of longitudinal muscles, and a corresponding number of slightly oblique and oblique muscles, the oblique muscles being spiral in their nature and tending to cross or intersect at various angles, an arrest of the intersection, as it appears to me, giving rise to the myocommas and to that concentric arrangement of their constituent parts so evident on transverse section. This tendency of the muscular fibres to cross each other at various degrees of obliquity may also be traced in several parts of the human body, as, for instance, in the deltoid muscle of the arm and the deep muscles of the leg. Numerous other examples of penniform muscles might be adduced. Although the fibres of the myocommas have a more or less longitudinal direction, the myocommas themselves pursue an oblique spiral course from before backwards and from within outwards, _i.e._ from the spine towards the periphery, where they receive slightly oblique fibres from the longitudinal dorsal, ventral, and lateral muscles. As the spiral oblique myocommas and the oblique fibres from the longitudinal muscles act directly and indirectly upon the spines of the vertebræ, and the vertebræ themselves to which they are specially adapted, and as both sets of oblique fibres are geared by interdigitation to the fourfold set of longitudinal muscles, the lateral, sinuous, and rotatory movements of the body and tail of the fish are readily accounted for. The spinal column of the fish facilitates the lateral sinuous twisting movements of the tail and trunk, from the fact that the vertebræ composing it are united to each other by a series of modified universal joints--the vertebræ supplying the cup-shaped depressions or sockets, the intervertebral substance, the prominence or ball.

The same may be said of the general arrangement of the muscles in the trunk and tail of the Cetacea, the principal muscles in this case being distributed, not on the sides, but on the dorsal and ventral aspects. The lashing of the tail in the whales is consequently from above downwards or vertically, instead of from side to side. The spinal column is jointed as in the fish, with this difference, that the vertebræ (especially towards the tail) form the rounded prominences or ball, the meniscus or cup-shaped intervertebral plates the receptacles or socket.

When limbs are present, the spine may be regarded as being ideally divided, the spiral movements, under these circumstances, being thrown upon the extremities by typical ball-and-socket joints occurring at the shoulders and pelvis. This is peculiarly the case in the seal, where the spirally sinuous movements of the spine are transferred directly to the posterior extremities.[19]

[19] That the movements of the extremities primarily emanate from
the spine is rendered probable by the remarkable powers possessed by
serpents. “It is true,” writes Professor Owen (_op. cit._ p. 261),
“that the serpent has no limbs, yet it can outclimb the monkey,
outswim the fish, outleap the jerboa, and, suddenly loosing the close
coils of its crouching spiral, it can spring into the air and seize
the bird upon the wing.” ... “The serpent has neither hands nor
talons, yet it can outwrestle the athlete, and crush the tiger in the
embrace of its ponderous overlapping folds.” The peculiar endowments,
which accompany the possession of extremities, it appears to me,
present themselves in an undeveloped or latent form in the trunk of
the reptile.

The extremities, when present, are provided with their own muscular cycles of extensor and flexor, abductor and adductor, pronator and supinator muscles,--these running longitudinally and at various degrees of obliquity, and enveloping the hard parts according to their direction--the bones being twisted upon themselves and furnished with articular surfaces which reflect the movements of the muscular cycles, whether these occur in straight lines anteriorly, posteriorly, or laterally, or in oblique lines in intermediate situations. The straight and oblique muscles are principally brought into play in the movements of the extremities of quadrupeds, bipeds, etc. in walking; in the movements of the tails and fins of fishes, whales, etc. in swimming; and in the movements of the wings of insects, bats, and birds in flying. The straight and oblique muscles are usually found together, and co-operate in producing the movements in question; the amount of rotation in a part always increasing as the oblique muscles preponderate. The combination of ball-and-socket and hinge-joints, with their concomitant oblique and longitudinal muscular cycles (the former occurring in their most perfect forms where the extremities are united to the trunk, the latter in the extremities themselves), enable the animal to present, when necessary, an extensive resisting surface the one instant, and a greatly diminished and a comparatively non-resisting one the next. This arrangement secures the subtlety and nicety of motion demanded by the several media at different stages of progression.

FIG. 10.--Extreme form of compressed foot, as seen in the deer, ox,
etc., adapted specially for land transit.--_Original._

FIG. 11.--Extreme form of expanded foot, as seen in the
_Ornithorhynchus_, etc., adapted more particularly for
swimming.--_Original._

FIGS. 12 and 13.--Intermediate form of foot, as seen in the otter
(fig. 12), frog (fig. 13), etc. Here the foot is equally serviceable
in and out of the water.--_Original._

FIG. 14.--Foot of the seal, which opens and closes in the act of
natation, the organ being folded upon itself during the non-effective
or return stroke, and expanded during the effective or forward
stroke. Due advantage is taken of this arrangement by the seal when
swimming, the animal rotating on its long axis, so as to present the
lower portion of the body and the feet obliquely to the water during
the return stroke, and the flat, or the greatest available surface of
both, during the effective or forward stroke.--_Original._]

_The travelling surfaces of Animals modified and adapted to the medium on or in which they move._--In those land animals which take to the water occasionally, the feet, as a rule, are furnished with membranous expansions extending between the toes. Of such the Otter (fig. 12), Ornithorhynchus (fig. 11), Seal (fig. 14), Crocodile, Sea-Bear (fig. 37, p. 76), Walrus, Frog (fig. 13), and Triton, may be cited. The crocodile and triton, in addition to the membranous expansion occurring between the toes, are supplied with a powerful swimming-tail, which adds very materially to the surface engaged in natation. Those animals, one and all, walk awkwardly, it always happening that when the extremities are modified to operate upon two essentially different media (as, for instance, the land and water), the maximum of speed is attained in neither. For this reason those animals which swim the best, walk, as a rule, with the greatest difficulty, and _vice versâ_, as the movements of the auk and seal in and out of the water amply testify.

In addition to those land animals which run and swim, there are some which precipitate themselves, parachute-fashion, from immense heights, and others which even fly. In these the membranous expansions are greatly increased, the ribs affording the necessary support in the Dragon or Flying Lizard (fig. 15), the anterior and posterior extremities and tail, in the Flying Lemur (fig. 16) and Bat (fig. 17, p. 36).

FIG. 15.--The Red-throated Dragon (_Draco hæmatopogon_, Gray) shows
a large membranous expansion (_b b_) situated between the anterior
(_d d_) and posterior extremities, and supported by the ribs. The
dragon by this arrangement can take extensive leaps with perfect
safety.--_Original._

FIG. 16.--The Flying Lemur _Galeopithecus volans_, Shaw. In the
flying lemur the membranous expansion (_a b_) is more extensive than
in the Flying Dragon (fig. 15). It is supported by the neck, back,
and tail, and by the anterior and posterior extremities. The flying
lemur takes enormous leaps; its membranous tunic all but enabling it
to fly. The Bat, _Phyllorhina gracilis_ (fig. 17), flies with a very
slight increase of surface. The surface exposed by the bat exceeds
that displayed by many insects and birds. The wings of the bat are
deeply concave, and so resemble the wings of beetles and heavy-bodied
short-winged birds. The bones of the arm (_r_), forearm (_d_), and
hand (_n, n, n_) of the bat (fig. 17) support the anterior or thick
margin and the extremity of the wing, and may not inaptly be compared
to the nervures in corresponding positions in the wing of the
beetle.--_Original._]

FIG. 17.--The Bat (_Phyllorhina gracilis_, Peters). Here the
travelling-surfaces (_r d e f_, _a n n n_) are enormously increased
as compared with that of the land and water animals generally.
Compare with figures from 10 to 14, p. 34. _r_ Arm of bat; _d_
forearm of bat; _e f_, _n n n_ hand of bat.--_Original._]

Although no lizard is at present known to fly, there can be little doubt that the extinct Pterodactyles (which, according to Professor Huxley, are intermediate between the lizards and crocodiles) were possessed of this power. The bat is interesting as being the only mammal at present endowed with wings sufficiently large to enable it to fly.[20] It affords an extreme example of modification for a special purpose,--its attenuated body, dwarfed posterior, and greatly elongated anterior extremities, with their enormous fingers and outspreading membranes, completely unfitting it for terrestrial progression. It is instructive as showing that flight may be attained, without the aid of hollow bones and air-sacs, by purely muscular efforts, and by the mere diminution and increase of a continuous membrane.

[20] The Vampire Bat of the Island of Bonin, according to Dr.
Buckland, can also swim; and this authority was of opinion that the
Pterodactyle enjoyed similar advantages.--Eng. Cycl. vol. iv. p. 495.

As the flying lizard, flying lemur, and bat (figs. 15, 16, and 17, pp. 35 and 36), connect terrestrial progression with aërial progression, so the auk, penguin (fig. 46, p. 91), and flying-fish (fig. 51, p. 98), connect progression in the water with progression in the air. The travelling surfaces of these anomalous creatures run the movements peculiar to the three highways of nature into each other, and bridge over, as it were, the gaps which naturally exist between locomotion on the land, in the water, and in the air.

PROGRESSION ON THE LAND.

_Walking of the Quadruped, Biped, etc._--As the earth, because of its solidity, will bear any amount of pressure to which it may be subjected, the size, shape, and weight of animals destined to traverse its surface are matters of little or no consequence. As, moreover, the surface trod upon is rigid or unyielding, the extremities of quadrupeds are, as a rule, terminated by small feet. Fig. 18 (contrast with fig. 17).

FIG. 18.--Chillingham Bull (_Bos Scoticus_). Shows powerful heavy
body, and the small extremities adapted for land transit. Also the
figure-of-8 movements made by the feet and limbs in walking and
running. _u_, _t_ Curves made by right and left anterior extremities.
_r_, _s_ Curves made by right and left posterior extremities. The
right fore and the left hind foot move together to form the waved
line (_s_, _u_); the left fore and the right hind foot move together
to form the waved line (_r_, _t_). The curves formed by the anterior
(_t_, _u_) and posterior (_r_, _s_) extremities form ellipses.
Compare with fig. 19, p. 39.--_Original._]

In this there is a double purpose--the limited area presented to the ground affording the animal sufficient support and leverage, and enabling it to disentangle its feet with the utmost facility, it being a condition in rapid terrestrial progression that the points presented to the earth be few in number and limited in extent, as this approximates the feet of animals most closely to the wheel in mechanics, where the surface in contact with the plane of progression is reduced to a minimum. When the surface presented to a dense resisting medium is increased, speed is diminished, as shown in the tardy movements of the mollusc, caterpillar, and slowworm, and also, though not to the same extent, in the serpents, some of which move with considerable celerity. In the gecko and common house-fly, as is well known, the travelling surfaces are furnished with suctorial discs, which enable those creatures to walk, if need be, in an inverted position; and “the tree-frogs (_Hyla_) have a concave disc at the end of each toe, for climbing and adhering to the bark and leaves of trees. Some toads, on the other hand, are enabled, by peculiar tubercles or projections from the palm or sole, to clamber up old walls.”[21] A similar, but more complicated arrangement, is met with in the arms of the cuttle-fish.

[21] Comp. Anat. and Phys. of Vertebrates, by Professor Owen, vol. i.
pp. 262, 263. Lond. 1866.

The movements of the extremities in land animals vary considerably.

In the kangaroo and jerboa,[22] the posterior extremities only are used, the animals advancing _per saltum_, _i.e._ by a series of leaps.[23]

[22] The jerboa when pursued can leap a distance of nine feet, and
repeat the leaps so rapidly that it cannot be overtaken even by the
aid of a swift horse. The bullfrog, a much smaller animal, can, when
pressed, clear from six to eight feet at each bound, and project
itself over a fence five feet high.

[23] The long, powerful tail of the kangaroo assists in maintaining
the equilibrium of the animal prior to the leaps; the posterior
extremities and tail forming a tripod of support.

The deer also bounds into the air in its slower movements; in its fastest paces it gallops like the horse, as explained at pp. 40–44. The posterior extremities of the kangaroo are enormously developed as compared with the anterior ones; they are also greatly elongated. The posterior extremities are in excess, likewise, in the horse, rabbit,[24] agouti, and guinea pig. As a consequence these animals descend declivities with difficulty. They are best adapted for slightly ascending ground. In the giraffe the anterior extremities are longer and more powerful, comparatively, than the posterior ones, which is just the opposite condition to that found in the kangaroo.

[24] The rabbit occasionally takes several short steps with the fore
legs and one long one with the hind legs; so that it walks with the
fore legs, and leaps with the hind ones.

In the giraffe the legs of opposite sides move together and alternate, whereas in most quadrupeds the extremities move diagonally--a remark which holds true also of ourselves in walking and skating, the right leg and left arm advancing together and alternating with the left leg and right arm (fig. 19).

FIG. 19.--Diagram showing the figure-of-8 or double-waved track
produced by the alternating of the extremities in man in walking
and running; the right leg (_r_) and left arm (_s_) advancing
simultaneously to form one step; and alternating with the left
leg (_t_) and right arm (_u_), which likewise advance together to
form a second step. The continuous line (_r_, _t_) gives the waved
track made by the legs; the interrupted line (_s_, _u_) that made
by the arms. The curves made by the right leg and left arm, and by
the left leg and right arm, form ellipses. Compare with fig. 18,
p. 37.--_Original._]

In the hexapod insects, according to Müller, the fore and hind foot of the one side and the middle one of the opposite side move together to make one step, the three corresponding and opposite feet moving together to form the second step. Other and similar combinations are met with in the decapods.

The alternating movements of the extremities are interesting as betokening a certain degree of flexuosity or twisting, either in the trunk or limbs, or partly in the one and partly in the other.

This twisting begets the figure-of-8 movements observed in walking, swimming, and flying. (Compare figs. 6, 7, and 26 _x_, pp. 28 and 55; figs. 18 and 19, pp. 37 and 39; figs. 32 and 50, pp. 68 and 97; figs. 71 and 73, p. 144; and fig. 81, p. 157.)

_Locomotion of the Horse._--As the limits of the present volume forbid my entering upon a consideration of the movements of all the animals with terrestrial habits, I will describe briefly, and by way of illustration, those of the horse, ostrich, and man. In the horse, as in all quadrupeds endowed with great speed, the bones of the extremities are inclined obliquely towards each other to form angles; the angles diminishing as the speed increases. Thus the angles formed by the bones of the extremities with each other and with the scapulæ and iliac bones, are less in the horse than in the elephant. For the same reason they are less in the deer than in the horse. In the elephant, where no great speed is required, the limbs are nearly straight, this being the best arrangement for supporting superincumbent weight. The angles formed by the different bones of the wing of the bird are less than in the fleetest quadruped, the movements of wings being more rapid than those of the extremities of quadrupeds and bipeds. These are so many mechanical adaptations to neutralize shock, to increase elasticity, and secure velocity. The paces of the horse are conveniently divided into the walk, the trot, the amble, and the gallop. If the horse begins his walk by raising his near fore foot, the order in which the feet are lifted is as follows:--first the left fore foot, then the right or diagonal hind foot, then the right fore foot, and lastly the left or diagonal hind foot. There is therefore a twisting of the body and spiral overlapping of the extremities of the horse in the act of walking, in all respects analogous to what occurs in other quadrupeds[25] and in bipeds (figs. 18 and 19, pp. 37 and 39). In the slowest walk Mr. Gamgee observes “that three feet are in constant action on the ground, whereas in the free walk in which the hind foot passes the position from which the parallel fore foot moves, there is a fraction of time when only two feet are upon the ground, but the interval is too short for the eye to measure it. The proportion of time, therefore, during which the feet act upon the ground, to that occupied in their removal to new positions, is as three to one in the slow, and a fraction less in the fast walk. In the fast gallop these proportions are as five to three. In all the paces the power of the horse is being exerted mainly upon a fore and hind limb, with _the feet implanted in diagonal positions_. There is also a constant parallel line of positions kept up by a fore and hind foot, _alternating sides_ in each successive move. These relative positions are renewed and maintained. Thus each fore limb assumes, as it alights, the advanced position parallel with the hind, just released and moving; the hind feet move by turns, in sequence to their diagonal fore, and in priority to their parallel fellows, which following they maintain for nearly half their course, when the fore in its turn is raised and carried to its destined place, the hind alighting midway. All the feet passing over equal distances and keeping the same time, no interference of the one with the other occurs, and each successive hind foot as it is implanted forms a new diagonal with the opposite fore, the latter forming the front of the parallel in one instant, and one of the diagonal positions in the next: while in the case of the hind, they assume the diagonal on alighting and become the terminators of the parallel in the last part of their action.”

[25] If a cat when walking is seen from above, a continuous wave
of movement is observed travelling along its spine from before
backwards. This movement closely resembles the crawling of the
serpent and the swimming of the eel.

FIG. 20.--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 (_s u_, _r t_). The figure-of-8 is produced by the
alternate play of the extremities and feet, two of which are always
on the ground (_a_, _b_). Thus the right fore foot describes the
curve marked _t_, the left hind foot that marked _r_, the left fore
foot that marked _u_, and the right hind foot that marked _s_. The
feet on the ground in the present instance are the left fore and the
right hind. Compare with figs. 18 and 19, pp. 37 and 39.--_Original._]

In the trot, according to Bishop, the legs move in pairs diagonally. The same leg moves rather oftener during the same period in trotting than in walking, or as six to five. The velocity acquired by moving the legs in pairs, instead of consecutively, depends on the circumstance that in the trot each leg rests on the ground during a short interval, and swings during a long one; whilst in walking each leg swings a short, and rests a long period. The undulations arising from the projection of the trunk in the trot are chiefly in the vertical plane; in the walk they are more in the horizontal.