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plain that they; too; would make the change of place better if they



had an even number; in fact if none were missing and they had the



limbs which correspond to one another。 In this way they could equalize



their own weight; and not oscillate to one side; if they had



corresponding supports instead of one section of the opposite sides



being unoccupied by a limb。 A walking creature advances from each of



its members alternately; for in this way it recovers the same figure



that it had at first。



                                 9







  The fact that all animals have an even number of feet; and the



reasons for the fact have been set forth。 What follows will explain



that if there were no point at rest flexion and straightening would be



impossible。 Flexion is a change from a right line to an arc or an



angle; straightening a change from either of these to a right line。



Now in all such changes the flexion or the straightening must be



relative to one point。 Moreover; without flexion there could not be



walking or swimming or flying。 For since limbed creatures stand and



take their weight alternately on one or other of the opposite legs; if



one be thrust forward the other of necessity must be bent。 For the



opposite limbs are naturally of equal length; and the one which is



under the weight must be a kind of perpendicular at right angles to



the ground。



  When then one leg is advanced it becomes the hypotenuse of a



right…angled triangle。 Its square then is equal to the square on the



other side together with the square on the base。 As the legs then



are equal; the one at rest must bend either at the knee or; if there



were any kneeless animal which walked; at some other articulation。 The



following experiment exhibits the fact。 If a man were to walk parallel



to a wall in sunshine; the line described (by the shadow of his



head》 would be not straight but zigzag; becoming lower as he bends;



and higher when he stands and lifts himself up。



  It is; indeed; possible to move oneself even if the leg be not bent;



in the way in which children crawl。 This was the old though



erroneous account of the movement of elephants。 But these kinds of



movements involve a flexion in the shoulders or in the hips。 Nothing



at any rate could walk upright continuously and securely without



flexions at the knee; but would have to move like men in the wrestling



schools who crawl forward through the sand on their knees。 For the



upper part of the upright creature is long so that its leg has to be



correspondingly long; in consequence there must be flexion。 For



since a stationary position is perpendicular; if that which moves



cannot bend it will either fall forward as the right angle becomes



acute or will not be able to progress。 For if one leg is at right



angles to the ground and the other is advanced; the latter will be



at once equal and greater。 For it will be equal to the stationary



leg and also equivalent to the hypotenuse of a right…angled



triangle。 That which goes forward therefore must bend; and while



bending one; extend the other leg simultaneously; so as to incline



forward and make a stride and still remain above the perpendicular;



for the legs form an isosceles triangle; and the head sinks lower when



it is perpendicularly above the base on which it stands。



  Of limbless animals; some progress by undulations (and this



happens in two ways; either they undulate on the ground; like



snakes; or up and down; like caterpillars); and undulation is a



flexion; others by a telescopic action; like what are called



earthworms and leeches。 These go forward; first one part leading and



then drawing the whole of the rest of the body up to this; and so they



change from place to place。 It is plain too that if the two curves



were not greater than the one line which subtends them undulating



animals could not move themselves; when the flexure is extended they



would not have moved forward at all if the flexure or arc were equal



to the chord subtended; as it is; it reaches further when it is



straightened out; and then this part stays still and it draws up



what is left behind。



  In all the changes described that which moves now extends itself



in a straight line to progress; and now is hooped; it straightens



itself in its leading part; and is hooped in what follows behind。 Even



jumping animals all make a flexion in the part of the body which is



underneath; and after this fashion make their leaps。 So too flying and



swimming things progress; the one straightening and bending their



wings to fly; the other their fins to swim。 Of the latter some have



four fins; others which are rather long; for example eels; have only



two。 These swim by substituting a flexion of the rest of their body



for the (missing) pair of fins to complete the movement; as we have



said before。 Flat fish use two fins; and the flat of their body as a



substitute for the absent pair of fins。 Quite flat fish; like the Ray;



produce their swimming movement with the actual fins and with the



two extremes or semicircles of their body; bending and straightening



themselves alternately。



                                10







  A difficulty might perhaps be raised about birds。 How; it may be



said; can they; either when they fly or when they walk; be said to



move at four points? Now we did not say that all Sanguinea move at



four points; but merely at not more than four。 Moreover; they cannot



as a fact fly if their legs be removed; nor walk without their



wings。 Even a man does not walk without moving his shoulders。



Everything indeed; as we have said; makes a change of place by flexion



and straightening; for all things progress by pressing upon what being



beneath them up to a point gives way as it were gradually;



accordingly; even if there be no flexion in another member; there must



be at least in the point whence motion begins; is in feathered



(flying) insects at the base of the 'scale…wing'; in birds at the base



of the wing; in others at the base of the corresponding member; the



fins; for instance; in fish。 In others; for example snakes; the



flexion begins in the joints of the body。



  In winged creatures the tail serves; like a ship's rudder; to keep



the flying thing in its course。 The tail then must like other limbs be



able to bend at the point of attachment。 And so flying insects; and



birds (Schizoptera) whose tails are ill…adapted for the use in



question; for example peacocks; and domestic cocks; and generally



birds that hardly fly; cannot steer a straight course。 Flying



insects have absolutely no tail; and so drift along like a



rudderless vessel; and beat against anything they happen upon; and



this applies equally to sharded insects; like the scarab…beetle and



the chafer; and to unsharded; like bees and wasps。 Further; birds that



are not made for flight have a tail that is of no use; for instance



the purple coot and the heron and all water…fowl。 These fly stretching



out their feet as a substitute for a tail; and use their legs



instead of a tail to direct their flight。 The flight of insects is



slow and frail because the character of their feathery wings is not



proportionate to the bulk of their body; this is heavy; their wings



small and frail; and so the flight they use is like a cargo boat



attempting to make its voyage with oars; now the frailty both of the



actual wings and of the outgrowths upon them contributes in a



measure to the flight described。 Among birds; the peacock's tail is at



one time useless because of its size; at another because it is shed。



But birds are in general at the opposite pole to flying insects as



regards their feathers; but especially the swiftest flyers among them。



(These are the birds with curved talons; for swiftness of wing is



useful to their mode of life。) The rest of their bodily structure is



in harmony with their peculiar movement; the small head; the slight



neck; the strong and acute breastbone (acute like the prow of a



clipper…built vessel; so as to be well…girt; and strong by dint of its



mass of flesh); in order to be able to push away the air that beats



against it; and that easily and without exhaustion。 The hind…quarters;



too; are light and taper again; in order to conform to the movement of



the front and not by their breadth to suck the air。



                                11







  So much then for these questions。 But why an animal that is to stand



erect must necessarily be not only a biped; but must also have the



superior parts of the body lighter; and those that lie under these



heavier; is plain。 Only if situated like this could it possibly



carry itself easily。 And so man; the only erect animal; has legs



longer and stouter relatively to the upper parts of his body than



any other animal with legs。 What we observe in children also is



evidence of this。 Children cannot walk erect because they are always



dwarf…like; the upper parts of their bodies being longer and stouter



than the lower。 With advancing years the lower increase



disproportionately; until the children get their appropriate size; and



then and not till then they succeed in walking erect。 Birds are



hunchbacked yet stand on two legs because their weight is set back;



after the principle of horses fashioned in bronze with their



forelegs prancing。 But their being bipeds and able to stand is above



all due to their having the hip…bone shaped like a thigh; and so large



that it looks as if they had two thighs; one in the leg before the



knee…joint; the other joining his part to the fundament。 Really this



is not a thigh but a hip; and if it were not so large the bird could



not be a biped。 As in a man or a quadruped; the thigh and the rest



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