walking depends, first, on the length of the leg, which, governed
by the laws of the pendulum, swings from behind forwards; secondly,
on the earlier or later interruption which the leg experiences in
its arc of oscillation by being placed on the ground. The weight of
the swinging leg and the velocity of the trunk serve to give the
impulse by which the foot attains a position vertical to the head
of the thigh-bone; but as the latter, according to the laws of the
pendulum, requires in the quickest walking a given time to attain
that position, or _half_ its entire curve of oscillation, it follows
that every person has a certain measure for his steps, and a certain
number of steps in a given time, which, in his natural gait in
walking, he cannot exceed.”
In traversing a given distance in a given time, a tall man will take
fewer steps than a short man, in the same way that a large wheel will
make fewer revolutions in travelling over a given space than a smaller
one. The relation is a purely mechanical one. The nave of the large
wheel corresponds to the ilio-femoral articulation (hip-joint) of the
tall man, the spokes to his legs, and portions of the rim to his feet.
The nave, spokes, and rim of the small wheel have the same relation to
the ilio-femoral articulation (hip-joint), legs and feet of the small
man. When a tall and short man walk together, if they keep step, and
traverse the same distance in the same time, either the tall man must
shorten and slow his steps, or the short man must lengthen and quicken
his.
The slouching walk of the shepherd is more natural than that of the
trained soldier. It can be kept up longer, and admits of greater speed.
In the natural walk, as seen in rustics, the complementary movements
are all evoked. In the artificial walk of the trained army man, the
complementary movements are to a great extent suppressed. Art is
consequently not an improvement on nature in the matter of walking.
In walking, the centre of gravity is being constantly changed,--a
circumstance due to the different attitudes assumed by the different
portions of the trunk and limbs at different periods of time. All
parts of the trunk and limbs of a biped, and the same may be said of a
quadruped, move when a change of locality is effected. The trunk of the
biped and quadruped when walking are therefore in a similar condition
to that of the body of the fish when swimming.
In running, all the movements described are exaggerated. Thus the steps
are more rapid and the strides greater. In walking, a well-proportioned
six-feet man can nearly cover his own height in two steps. In running,
he can cover without difficulty a third more.
In fig. 28 (p. 62), an athlete is represented as bending forward prior
to running.
The left leg and trunk, it will be observed, are advanced beyond the
vertical line (_x_), and the arms are tucked up like the rudimentary
wings of the ostrich, to correct undue oscillation at the shoulders,
occasioned by the violent oscillation produced at the pelvis in the act
of running.
[Illustration:
FIG. 28.--Preparing to run, from a design by Flaxman. Adapted. In the
original of this figure the right arm is depending and placed on the
right thigh.]
In order to enable the right leg to swing forward, it is evident that
it must be flexed, and that the left leg must be extended, and the
trunk raised. The raising of the trunk causes it to assume a more
vertical position, and this prevents the swinging leg from going too
far forwards; the swinging leg tending to oscillate in a slightly
backward direction as the trunk is elevated. The body is more inclined
forwards in running than in walking, and there is a period when both
legs are off the ground, no such period occurring in walking. “In
quick walking, the propelling leg acts more obliquely on the trunk,
which is more inclined, and forced forwards more rapidly than in slow
walking. The time when both legs are on the ground diminishes as the
velocity increases, and it vanishes altogether when the velocity is
at a maximum. In quick running the length of step rapidly increases,
whilst the duration slowly diminishes; but in slow running the length
diminishes rapidly, whilst the time remains nearly the same. The time
of a step in quick running, compared to that in quick walking, is
nearly as two to three, whilst the length of the steps are as two to
one; consequently a person can run in a given time three times as fast
as he can walk. In running, the object is to acquire a greater velocity
in progression than can be attained in walking. In order to accomplish
this, instead of the body being supported on each leg alternately, the
action is divided into two periods, during one of which the body is
supported on one leg, and during the other it is not supported at all.
“The velocity in running is usually at the rate of about ten miles an
hour, but there are many persons who, for a limited period, can exceed
this velocity.”[40]
[40] Cyc. of Anat. and Phy., article “Motion.”
PROGRESSION ON AND IN THE WATER.
If we direct our attention to the water, we encounter a medium less
dense than the earth, and considerably more dense than the air. As
this element, in virtue of its fluidity, yields readily to external
pressure, it follows that a certain relation exists between it and the
shape, size, and weight of the animal progressing along or through it.
Those animals make the greatest headway which are of the same specific
gravity, or are a little heavier, and furnished _with extensive
surfaces_, which, by a dexterous tilting or twisting (for the one
implies the other), or by a sudden contraction and expansion, they
apply wholly or in part to obtain the maximum of resistance in the one
direction, and the minimum of displacement in the other. The change
of shape, and the peculiar movements of the swimming surfaces, are
rendered necessary by the fact, first pointed out by Sir Isaac Newton,
that bodies or animals moving in water and likewise in air experience
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.
To obtain the degree of resistance and non-resistance necessary
for progression in water, Nature, never at fault, has devised some
highly ingenious expedients,--the Syringograde animals advancing
by alternately sucking up and ejecting the water in which they are
immersed--the Medusæ by a rhythmical contraction and dilatation of
their mushroom-shaped disk--the Rotifera or wheel-animalcules by a
vibratile action of their cilia, which, according to the late Professor
Quekett, twist upon their pedicles so as alternately to increase and
diminish the extent of surface presented to the water, as happens
in the feathering of an oar. A very similar plan is adopted by the
Pteropoda, found in countless multitudes in the northern seas,
which, according to Eschricht, use the wing-like structures situated
near the head after the manner of a double paddle, resembling in
its general features that at present in use among the Greenlanders.
The characteristic movement, however, and that adopted in by far
the greater number of instances, is that commonly seen in the fish
(figs. 29 and 30).
[Illustration:
FIG. 29.--Skeleton of the Perch (_Perca fluviatilis_). Shows the
jointed nature of the vertebral column, and the facilities afforded
for lateral motion, particularly in the tail (_d_), dorsal (_e_,
_f_), ventral (_b_, _c_), and pectoral (_a_), fins, which are
principally engaged in swimming. The extent of the travelling
surfaces required for water greatly exceed those required for land.
Compare the tail and fins of the present figure with the feet of the
ox, fig. 18, p. 37.--(After Dallas.)]
[Illustration:
FIG. 30.--The Salmon (_Salmo salar_) swimming leisurely. The body,
it will be observed, is bent in two curves, one occurring towards
the head, the other towards the tail. The shape of the salmon is
admirably adapted for cleaving the water.--_Original._]
This, my readers are aware, consists of a lashing, curvi-linear, or
flail-like movement of the broadly expanded tail, which oscillates from
side to side of the body, in some instances with immense speed and
power. The muscles in the fish, as has been explained, are for this
purpose arranged along the spinal column, and constitute the bulk of
the animal, it being a law that when the extremities are wanting, as
in the water-snake, or rudimentary, as in the fish, lepidosiren,[41]
proteus, and axolotl, the muscles of the trunk are largely developed.
In such cases the onus of locomotion falls chiefly, if not entirely,
upon the tail and lower portion of the body. The operation of this law
is well seen in the metamorphosis of the tadpole, the muscles of the
trunk and tail becoming modified, and the tail itself disappearing as
the limbs of the perfect frog are developed. The same law prevails in
certain instances where the anterior extremities are comparatively
perfect, but too small for swimming purposes, as in the whale,
porpoise, dugong, and manatee, and where both anterior and posterior
extremities are present but dwarfed, as in the crocodile, triton, and
salamander. The whale, porpoise, dugong, and manatee employ their
anterior extremities in balancing and turning, the great organ of
locomotion being the tail. The same may be said of the crocodile,
triton, and salamander, all of which use their extremities in quite a
subordinate capacity as compared with the tail. The peculiar movements
of the trunk and tail evoked in swimming are seen to most advantage in
the fish, and may now be briefly described.
[41] The _lepidosiren_ is furnished with two tapering flexible
stem-like bodies, which depend from the anterior ventral aspect
of the animal, the _siren_ having in the same region two pairs of
rudimentary limbs furnished with four imperfect toes, while the
_proteus_ has anterior extremities armed with three toes each, and a
very feeble posterior extremity terminating in two toes.
_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
experiment have convinced me that when a fish swims it never throws its
body into a single curve, as represented at fig. 31, p. 67, but always
into a double or figure-of-8 curve, as shown at fig. 32.[43]
[43] It is only when a fish is turning that it forces its body into a
single curve.
[Illustration:
FIG. 32.--Swimming of the Sturgeon. From Nature. Compare with
figs. 18 and 19, pp. 37 and 39; fig. 23, p. 43; and figs. 64 to 73,
pp. 139, 141, and 144.--_Original._]
The double curve is necessary to enable the fish to present a convex
or non-biting surface (_c_) to the water during flexion (the back
stroke of authors), when the tail is being forced away from the axis of
motion (_a b_), and a concave or biting surface (_s_) during extension
(the forward or effective stroke of authors), when the tail is being
forced with increased energy towards the axis of motion (_a b_); the
resistance occasioned by a concave surface, when compared with a convex
one, being in the ratio of two to one. The double or complementary
curve into which the fish forces its body when swimming, is necessary
to correct the tendency which the head of the fish has to move in the
same direction, or to the same side as that 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 (_e_ _f_ _g_ _h_ _i_ _j_ _k_ _l_ 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_, _i j_, and _k l_ 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 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
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 long-bodied fishes, as the eels,
and decreased in those whose bodies are short or are comparatively
devoid of flexibility. In proportion 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.[44] 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.[45] 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 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,[46] porpoise, manatee, and dugong
(figs. 33, 34, and 35), the movements are strictly analogous to those
of the fish, 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.
[44] The _Syngnathi_, or Pipefishes, swim chiefly by the undulating
movement of the dorsal fin.