LE VERS. 



251 



as great, the product ( = the work done) remains the same, for the force 

 applied at g is only one-fifth of that at in. 



Action and reaction.— Eeturning once more to Fig. 136, it will be 

 evident that unless the point r be fixed in space, the weight of the 

 limb acting at g and the force of the contracting triceps will carry 

 the upper arm bodily downwards. This they tend actually to do with 

 a force which acts upon the upturned articular surface of the humerus. 

 This action produces (Newton's third law) an equal reaction in the 

 opposite direction, which reaction, if equilibrium be established, must 

 exactly counterbalance the two forces acting at g and at m. 



In the case of most muscular actions we have to consider three 

 forces — that of gravity, that of muscular force, and that of the reaction 

 at a joint. It is by investigating the movements around a joint that 

 we can solve many problems of movement ; thus, given the force of 

 gravity and its moment, and given the distance of the point of applica- 

 tion of the muscular force from the 

 centre of rotation of the joint, we can 

 calculate the muscular force necessary 

 to counterbalance that of gravity 

 acting upon the limb, or any weight 

 supported by the limb. 



Levers.— Although the term has 

 not yet been used, it is evident that 

 the bones fall under the definition of 

 a lever. This is defined as a rigid 

 bar, with a fixed point around which 

 it can rotate, which is acted upon by 

 two or more forces, and the reaction 

 of the fixed point called a fulcrum. 



The raising of the body by the 

 action of the calf muscles. — In his 

 well - known article in Wagner's 



Fig. 137.— To illustrate Weber's theory 

 of the movements around the ankle- 

 joint, a marks the centre of rota- 

 tion of the ball of the great toe ; 

 b that of the ankle-joint; and c 

 the point of attachment of the calf 

 muscles. 



Handivortcrbuch, Bd. hi. S. 88, 



entitled " Muskelbewegung," Edward Weber describes the foot as a 

 lever of the second order. When we stand upon the ground, and then 

 raise the body on the toes, the fulcrum, according to Weber, is situated 

 at the ball of the foot, the weight of the body falls vertically on the 

 position of the ankle-joint, and the muscular pull is at the point of 

 insertion of the tendo Achillis in the heel. Weber therefore supposed 

 the forces and movements to be related as follows : — If M — the 

 muscular pull and W the weight of the body (see Fig. 137), Mx ac= 

 Wxba, overlooking the fact that the shortening of the calf muscle is 

 the real measure for the movement of the point of insertion, whatever 

 space that point may travel through at the same time from other 

 causes. 



Knorz l and Henke 2 rectified this error and gave the true formula, 

 Mxbc = Wxba, 



Richard Ewald 3 explains the matter in the following way : — If a 

 man were to stand on his head and support on his toes another 



1 "Em Beitrag zur Bestimmung der absoluten Muskelkraft," Marburg, 1865. 



2 Ztschr.f. rat. Med., Leipzig u. Heidelberg, I860, Bd. xxiv. 



3 Arch.f. d. <jcs. Physiol., Bonn, 1894, Bd. lix. S. 251 ; and 1896, Bd. lxiv. S. 53. 



