THE MUSCLE AS A MACHINE. 



241 



The sides of this figure will possess a double curvature like a saddle, 

 a curvature of a small circle in vertical, a curvature of a large circle 

 in horizontal, direction. A saddle - shaped surface can glide on its 

 counterpart to a certain extent around either of two axes (in the figure 

 around an axis passing through cc or xx). Thus the surfaces may be 

 brought to a multitude of new positions, by first rotating on one and 

 then on the other axis. In this respect the saddle-joint lies between 

 the hinge and ball-and-socket joint. Its freedom of movement is 

 principally due to the absence of lateral ligaments. The trapezio- 

 metacarpal joint is an example of a saddle-joint. 



We may conceive an ellipsoidal joint as formed in the following 

 manner. Take the arc ab of a circle whose centre is at c, and allow the 

 arc to revolve around an axis xx on the same side of the arc as 

 its centre, and the figure (abb' a') will be formed. At the sides of this 

 figure the surface resembles an ellipsoid, and will, like the saddle-joint, 

 allow of rotation in two axes, namely, an axis passing through c and 

 the axis xx. The first carpal joint is 

 ellipsoidal. 



E. du Bois Reymond, 1 says, " as a matter 

 of practical experience, a certain movement 

 of rotation is possible because the surfaces 

 do not geometrically correspond, the stronger 

 convexity not fitting the weaker concavity. a 

 A saddle-joint or ellipsoidal joint with rigid 

 and perfectly adapted surfaces would not 

 be capable of movement at all." 



F 



FIG. 129. To illustrate the 

 formation of an ellipsoidal 

 joint. 



THE MUSCLE AS A MACHINE. 



The phenomena of muscular contraction 

 are fully discussed in the portion of this 

 work directed to the special physiology of 

 muscle. We may, however, select for 

 discussion a few of the points which have 

 to be borne in mind, when studying the part 

 these structures play in producing the movements of the trunk and 

 limbs. When an unexcited muscle is stretched by a force, such as the 

 weight of a limb, or other load, it elongates until a point is reached 

 at which there is equilibrium. At this point the stress applied is 

 equalled by the stress in the muscle acting in the contrary direction. 

 While with most inorganic matter the elongation or distortion is pro- 

 portional to the distorting force (ut tensio sicut vis), in the case of the 

 muscle it follows the formula y 2 =ax 2 -{-bx, where y is the elongation, 

 x the weight, and a and I are constants. 2 The curve representing the 

 elongation of a muscle when loaded with increasing weights is given 

 in Fig. 130, and it will be seen that the muscle becomes less and less 

 extensible as the weight increases. It is on this account that muscles 

 are able to play an important role in the maintenance of equilibrium, 

 quite apart from their action in shortening. They play the part of 

 ligaments and prevent too free a movement of the body in undesirable 

 directions. Thus, over-extension of the knee is in part prevented by 



l Arch.f. PhysioL, Leipzig, 1895. 



2 Werthehn, Ann. de chim,, Paris, tomes xii. and xxi. 



VOL. II. 16 



