Bipedalism

“ In like manner the foot which is off the ground and swinging forward pendulum fashion in space, may be said to roll or rotate upon the trunk, the head of the femur forming the centre of a circle the radius of which is described by the advancing foot. A double rolling movement is thus established, the body rolling on the extremity the one instant, the extremity rolling on the trunk the next. During these movements the body rises and falls. The double rolling movement is necessary not only to the progression of bipeds, but also to that of quadrupeds. ”

“ In impelling a velocipede, the limbs are not constantly in motion; for on level ground, when the impetus is at the average rate, or when the machine is descending an incline, the feet may be removed from the pedals, and the legs be placed on the bar, fixed in front of the machine for that purpose. A slight impulsion to the vehicle from time to time suffices to keep up the speed. When a rider encounters a formidable hill, he can dismount and lead his bicycle by the hand. ”

“ The peculiarity of biped-walking is, that the centre of gravity is shifted from one leg to the other, and the one not employed can shorten itself so as to swing forward, passing by that which supports the body. ”

“ The gyroscope motion in fig. 4 comes to a stop when the rim of the wheel touches the ground; and to realize the motion when the axis is inclined at a greater angle with the upward vertical, the stalk is pivoted in fig. 8 in a lug screwed to the axle of a bicycle hub, fastened vertically in a bracket bolted to a beam. The wheel can now be spun by hand, and projected in any manner so as to produce a desired gyroscopic motion, undulating, looped, or with cusps if the stalk of the wheel is dropped from rest. ”

“ A vibrating pendulum in motion describes a segment of a circle, and returns on the same segment, and at every vibration its described segment decreases.
A revolving pendulum is composed of two or more pendulums, united at their lighter extremities, there revolving on an axis, the heavier extremities being placed at equal distances in the outer circle: this, I believe, is what is termed a fly-wheel when affixed to hand-mills, etc.
The tubular lever is the chief instigator of the whole, and must contain a weight apportioned to the weights of the two pendulums. ”

“ For instance, by being careful to rise upon our instep, we considerably increase the length or amplitude of our stride, and very considerably increase our speed accordingly. On the other hand, in running, we bend and so shorten the leg, in order to accommodate it to a quicker rate of pendulum-swing53. In short, the jointed structure of the leg permits us to use it as the shortest possible pendulum when it is swinging, and as the longest possible lever when it is exerting its propulsive force. ”

“ 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. ”

“ The reason is that these have no power of locomotion, and the superior part is determined relatively to the nutriment, and their nutriment is from the earth. Quadrupeds, polypods, and footless animals again have their superior part corresponding to the intermediate, because they are not erect. Bipeds have theirs corresponding to the superior part of the universe because they are erect, and of bipeds, man par excellence; for man is the most natural of bipeds. ”

“ Its length was the same, but its diameter was reduced to two-thirds, and there were two fingers missing on the hand. The opposable thumb remained, but it now had more the appearance of a claw than a human hand. I tried to scream, but the sound was a glutinous bubble of air that never reached my lips.
"How about the pedal appendages?"
"Well—" there was some hesitation. "Considering the method of locomotion, bisymmetry seems more justified there. However, why bilateral? Why not quadrilateral?"
"Because the organs of sight face only one way." ”

“ A rotary pendulum is kept in motion by the train of the clock ending in a horizontal wheel with a vertical axis, from which pro jects an arm pressing against a spike at the bottom of the pendu lum ; and it has this disadvantage that any inequality in the force of the train, arising from variations of friction or any other cause, is immediately transmitted to the pendulum ; whereas it will be seen that in several kinds of escapements which can be applied to a vibrating pendulum, the variations of force can be rendered nearly or quiteinsensible. ”

“ The means of support afforded by the branches is too precarious, the form of locomotion which practical conditions impose upon the animal too restricted and interrupted to make the development of such a limb as the human leg possible. The need of supplementary support to which an unstable balance must give rise and the facility with which the arms can come to the aid of the legs as the animal makes its way from tree to tree are likewise factors which retard the development of efficient bipedal locomotion. ”

“ Physical laws are constant and invariable; they are subject neither to augmentation or diminution. A stone does not gravitate towards the earth with more force at one time than another; in every case marble has the same elasticity, &c. On the other hand, at every instant, sensibility and contractility are increased, diminished, or altered; they are scarcely ever the same.
It follows, therefore, that the physical phenomena are never variable, that at all periods and under every influence they are the same ”

“ But with the pendulum the control of the weight over it is small, for the bob can be made of considerable weight, because it swings from its suspending spring without friction, and such a heavy weight at the end of a long rod is scarcely altered in its rate by variations of pressure on the pallets.
Galileo and Huyghens who followed him found that the oscillations of a simple pendulum are isochronous at all places where the force of gravity is equal, and that the time of oscillation depends on the length of the pendulum—the shorter the pendulum the shorter time of oscillation, and vice versâ. ”

“ But it may be said that the force of gravity when the 'cycle leans, say to the right, is in fact resolved into two components, one vertical and the other lateral, and it is the latter only that causes the bicyclist to fall. This does not help the matter, for both components are perpendicular to the course of the bicycle, and hence its forward motion can in no way counteract either of them. Unless some other force comes into play, the bicyclist must fall toward whichever side he happens to begin to lean. ”

“ It is true indeed, that in fact every pendulum, which we can put in motion, will gradually lessen its swing, and at length stop, unless there be some power constantly applied to it, whereby its motion shall be renewed; but this arises from the resistance, which the body meets with both from the air, and the string by which it is hung: for as the air will give some obstruction to the progress of the body moving through it; so also the string, whereon the body hangs, will be a farther impediment ”

“ Remove one of the wheels of your bicycle, and carry it about the room, holding it by the axle while it is spinning rapidly. You will discover that it requires no more force to carry it when spinning than when at rest, provided you do not attempt to tip it from its plane of rotation, but that if you do attempt so to tip it, the wheel seems positively to resist, exerting a force of which it did not show a trace when at rest. ”

“ Every military engineer who had watched the flight of a projectile was aware that the received notions of mechanics would not explain its motions. No theory of the impact of such projectiles had even been proposed. A whole science was to be created. The doctrine of mechanical equilibrium is statics—and this science was founded by Archimedes. The doctrine of mechanical motion is dynamics—and nothing was done in this science till the time of Galileo. ”

“ Every one acquainted with the mechanism of a clock is aware that the weight communicates motion to a train of wheels, and that the movement is regulated by the vibration of a pendulum, which is acted on by the last wheel of the train. That wheel, called174 the escapement, is so formed, that each tooth catches in succession into a detent fixed on the pendulum near the point of suspension, which allows one tooth to pass at each double vibration. The pendulum, therefore, governs the movement of the train of wheels by checking the escapement, and allowing the teeth to pass one by one ”

“ If it be so placed that it must either remain at rest or ascend, it is clear, from the laws of equilibrium, that no motion derived from gravitation can take place; if it may descend, it must either continue to descend forever with a finite velocity, which is impossible,334 or it must first descend and then ascend with a vibratory motion, and then the case will be reducible to that of a pendulum, where it is obvious that no new motion is generated, and that the friction and resistance of the air must soon destroy the original motion. ”

“ And the same Law is manifested in all the phenomena of Rhythm. The pendulum, with a short swing in one direction, has but a short swing in the other; while the long swing to the right invariably means the long swing to the left. An object hurled upward to a certain height has an equal distance to traverse on its return. The force with which a projectile is sent upward a mile is reproduced when the projectile returns to the earth on its return journey. This Law is constant on the Physical Plane, as reference to the standard authorities will show you. ”

“ We have seen the important assistance it afforded in establishing the laws of motion; and when the theory founded on those laws was extended and improved, the pendulum was again instrumental, by a species of approximate reasoning familiar to all who are acquainted with physical inquiries, in pointing out by its minute irregularities in different parts of the earth, a corresponding change in the weight of all bodies in those different situations, supposed to be the consequence of a greater distance from the axis of the earth's rotation ”

“ Others find in its going so fast the reason why the bicycle does not fall—referring, of course, in a blind way to that principle embodied by Newton in his first law: "A body in motion, if left to itself, will continue to move in a straight line forever." ”

“ In a two-track machine, on the other hand, we are compelled to supply springs with lateral motion as a necessary appliance for the comfort of the rider, which lateral motion results in loss of momentum and kinetic energy, whereas in the bicycle our comfort and energy are all confined to one plane ”

“ Lastly, it may be a body rotating or intended to rotate, like a spindle, a spit, or the rolling cylinder of a machine. In the first supposition, all motion is excluded: in the second, rectilinear motion is implied, but rotatory motion is excluded: in the third, rotatory motion is implied as a certain adjunct. The body which is fastened round another, must share the motion or the rest of that other. If the body B is a revolving cylinder, and if I affirm that A is packed or fastened close round it, I introduce the idea of rotation ”

“ If this could be had, then, by introducing a plate of it underneath a body while it was raised, we could elevate the body without doing work; then, removing the plate, we could allow the body to fall and do work; eccentrics or other imposing device being added to move the gravitation intercepter, behold a perpetual motion complete! The great difficulty is that no one has found the proper material for an intercepter. ”

“ Shepherd's arrangement, the impulse of the pendulum is given by successive blows from a spring, which is drawn back and then liberated at each vibration. The hands of the clock are also moved by electro-magnets, by which means the impelling forces and the resistances encountered by the pendulum are always constant. By making the pendulum thus independent of the works, and employing it merely to make and break contract at regular intervals, any number of clocks in the same establishment may be set in motion, and kept exactly together, by a single pendulum. ”

“ To all appearance, the phenomena exhibited by the pendulum are not to be accounted for by impact: in fact, it is usually assumed that corresponding phenomena would take place if the earth and the pendulum were situated in an absolute vacuum, and at any conceivable distance from, one another. If this be so, it follows that there must be two totally different kinds of causes of motion: the one impact—a vera causa, of which, to all appearance, we have constant experience; the other, attractive or repulsive 'force'—a metaphysical entity which is physically inconceivable. ”

“ It is not plain whether the question discussed was that of a bicycle with or without a man upon it, but I take it to be the latter. Some of the gentlemen had no doubt noticed that to give the machine a shove it would keep upright for a longer time running than when standing unsupported. This is purely a case of the law that whirling things tend to keep their own plane, as illustrated in the gyroscope and the spinning top. In the running bicycle without a man upon it to constantly rectify its position, the principle is simply one of the parallelogram of rotations. ”