460 ACTION OF MUSCLES ON BONES. necessary form of the animal body, Muscles are applied at a great mechanical disadvantage as regards the exercise of their power; that is, a much larger force is employed than would suffice, if differently applied, to overcome the resistance. But we generally find that, in this as in other forms of lever action, what is lost in power is gained in time; and thus a very slight change in the length of a muscle is sufficient to produce a considerable movement. m d bl n a 610. The first source of disadvantage results from the direction in which the muscle is attached to the bone. This is rarely at right angles to it; and consequently a considerable part of the power is lost (see MECHAN. PHILOS., § 299). Thus if the muscle m (fig. 213), whose force we shall suppose equal to 10, be fixed at right angles to the bone l, whose extremity a is movable upon the point of support r, its force of contraction will be most advantageously applied to overcome the resistance, and will draw the bone from the position ab into the direction a c, making it traverse a space which we shall also represent by 10. But if this muscle act obliquely on the bone, in the direction of the line n b for example, it will be quite otherwise; for it will then tend to draw the bone in the direction bn, and will consequently make it approach the articular surface r. But as this bears upon an immovable socket, and as the bone can move in no other way than by turning upon the point r as upon a pivot, the contraction of the muscle to the same amount as before will carry the bone no further than into the direction a d; three-quarters of the force employed will thus be lost, and the resulting effect will be no more than one-fourth of that which the same power applied perpendicularly to the bone would have produced. Fig. 213. 611. We usually find that the muscles are inserted so obliquely, that their power is applied at a great disadvantage; but this disadvantage is rendered much less than it would have otherwise been, by a very simple contrivance,—that very enlargement of the bones at the joints which is necessary to give them the required extent of surface for working over LEVERAGE OF BONES. m 461 m r each other. Thus, let r and o (fig. 214) be two bones connected by a joint; and let the muscle m, which moves the lower bone upon the upper, be attached to the former at i Now as this muscle acts almost precisely in the line of the bones themselves, almost all its power will be expended in drawing the lower bone against the upper. But by the enlargement of the ends of the bones, as seen in fig. 215, the direction of the tendon of the muscle m is so changed, near its insertion i, that the contraction of the muscle will cause the lower bone to turn upon the upper one with comparatively little loss of power. In the knee we find a still greater change of direction effected, by the interposition of a movable bone, the patella or knee-pan, in the substance of the tendon. Fig. 214. Fig. 215. 612. But the advantage or disadvantage with which the muscles act upon the bones, depends in great degree upon the relative distances of their point of attachment from the fulcrum on which the bone moves, and from the point at which the resistance is applied. Every bone acted-on by muscles may be regarded as a lever, having its fulcrum or point of support in the joint, its power where the muscle is attached to it, and its weight where the resistance is to be overcome; and the distances of the fulcrum from the power and the weight respectively are termed the two arms of the lever. Now, on the mechanical principles fully explained elsewhere (MECHAN. PHILOS., § 287), the relative length of these two arms determines the force which is necessary to overcome a given resistance. Thus in the Steelyard (fig. 216), the beam is divided into two arms of unequal length at the point of support or fulcrum a; at the end of the short arm r, hangs the body whose downward pressure we wish to determine; and on the other p there slides a weight, which will balance a greater or less amount of pressure at the opposite extremity r, according as it is made to hang from a point which is more distant from the fulcrum or nearer to it, that is, according as the length Fig. 216. 462 LEVERAGE OF BONES. of the power-arm of the lever is increased or diminished, that of the weight-arm remaining the same. 613. Now in order that there may be an equilibrium, or balancing between the power and the weight, it is necessary that they should be inversely proportional to the lengths of their respective arms; that is, the power multiplied by the length of its arm, should be always equal to the weight multiplied by the length of its arm. Thus, to balance a с Fig. 217. certain resistance r, equal to 10, and applied at the end of a lever a b (fig. 217), whose length we shall call 20, it is necessary that a force p, applied at the same point, and consequently at the same distance from the fulcrum a, should also be equal to 10; but, if the power be applied at the point c, which is at only half the distance from the fulcrum a, it must be doubled in amount, or equal to 20,— since it must be sufficient, when multiplied by its distance 10 from the fulcrum, to make 200, which is the product of the resistance 10 and its distance from the fulcrum 20; and in like manner, if the power be applied at d, where its distance from the fulcrum is only 2, its amount must be 100, in order that its product with the distance at which it is applied may be equal to 200. Hence, when a muscle is applied near the fulcrum, while the resistance is at a distance from it, so that the bone becomes a lever of the "third order," its force must be proportionably greater. 614. But this arrangement greatly increases the rapidity of the motion which is the consequence of the muscular action. For let us suppose that the muscle p (fig. 218) acts upon the lever a r, in such a manner that its point of insertion c tra LEVERAGE OF BONES. 463 verses a space equal to 5 in one second; the extremity r of the lever will traverse a space equal to 25 in the same time, its distance from the fulcrum a being five times as great as that of the point c from the fulcrum. Hence, although, to raise a given weight at r, a power more than five times its amount must be applied at c, that power will raise the weight through a space five times as great as that through which itself passes in the same time. Thus, what is lost in power is gained in time; and the shortening of a muscle, small in amount, but effected with sufficient power, causes the raising of a weight through a considerable space. 615. We shall find that this is the case in regard to most of the muscular actions in the animal economy. Thus, the fore-arm (fig. 219, b, c) is bent upon the arm a by a muscle d, с a Fig. 219. which arises from the top of the latter, and which is inserted at e, a short distance from the elbow-joint. Hence its contraction to a very slight extent will raise the hand through a considerable space; but a proportional increase in its power will be required to overcome any resisting force in the hand. -The arm is straightened again by an antagonist muscle, which lies on the back of the arm, and which is attached to a short projection made by one of the bones of the fore-arm behind the elbow: this muscle also operates at a similar disadvantage in regard to power, and advantage in point of time, in consequence of its point of attachment being so near to the fulcrum. In responding to its action, however, the bones of the fore-arm constitute a lever of the "first order;" the elbowjoint, which serves as the fulcrum, being now between the power and the resistance. 464 BONES OF THE SKULL. Motor Apparatus of Man:-Skeleton and Muscles. 616. Before entering upon the examination of the various movements of the lower animals, and of the means by which these are effected, it will be useful to acquire a general knowledge of the structure of the Human Skeleton, and of the uses of its several parts. The skeleton, which is formed by the union of about 200 bones, is divided like the body into head, trunk, and members. The bones of these parts will now be separately described. 617. The Head is skull, and the face. composed of two parts, the cranium or The cranium (fig. 220) is a bony case of oval form, occupying the upper and back part of the head, n na с ma a f b mi j az Fig. 220.-HUMAN SKULL. f, frontal bone; p, parietal; t, temporal; o, occipital; s, sphenoid; n, nasal; ms, superior maxillary; j, malar or cheek bone; mi, in and serving for the protection of the brain, which is lodged in its cavity. Its walls are made-up of eight bones: the frontal ƒ in the region of the forehead; the two parietal bones p, which occupy d the top and sides of the skull; the two temporal bones t, which form the walls of the temporal ta region; the occipital bone o at the back of the head; and the sphenoid s, and the ethmoid, which assist in forming the floor of the cavity. These bones are firmly united to each other by sutures, the character of which varies in different parts of the cranium, so that they are the better able to resist external violence. Thus, a blow upon the top of the arch formed by the parietal bones will tend to separate them from each other and from the frontal bone, and to force asunder their lower borders. Both these effects are resisted by the peculiarity of the suture which unites different parts of the parietal bone to its neighbours; for at the top of the skull the bones are firmly held together by the interlocking of the projections of each, whilst the lower edge of the parietal bone is prevented from being driven outwards by the overlapping edge of the temporal bones, which form, as it were, a buttress to the arch. This same contrivance ferior maxilla; na, anterior opening of the nose; ta, auditory arerture; az,zygomatic arch; a,b,c,d, lines indicating the facial angle. |