368 



MYOLOGY 



the summation of such contractions and therefore for large contractions. In the 

 first muscle a large load is moved through a short distance and in the second muscle 

 a lighter load is moved through a greater distance. 



The amount of work accomplished by pinnate muscles is not dependent upon 

 the angle of insertion of the muscle fibers into the tendon, as will be seen by the 

 following diagram Fig. 368. 



T' T = direction of the tendon pull. 

 w a = direction of muscle fiber before con- 

 traction. 



TO' = direction of muscle fiber after contrac- 

 tion. 



v = amount of contraction. 

 TO = tension of the muscle. 

 <l> = angle of insertion of muscle fiber. 

 t = tendon component = TO X cos </> = 

 the weight carried by the tendon 

 to balance the muscle tension. 

 d = distance tendon is drawn up. 



(1) TO X v = work done by the muscle fiber. 



(2) t X d = work done by the movement of 



the tendon. 



If we consider the distance v as being very 

 short then the line b c can be dealt with as 

 though it were perpendicular to a c. 



then i) = d X cos </> or d = 



since t = m X cos d> or TO = 



cos </> 



t 

 cos <j> 



TO X V = 



t 



T' 



FIG. 368 



COS 



If this is true for very minute contractions it 

 is likewise true for a series of such contraction 

 and hence for larger contractions. 



If we assume that < = 60, TO = 10 kg. and v 

 = 5 mm., the work done by the contracting 

 muscle fiber = m v or 10 X 5 kilogrammilli- 

 meters. 



cos z 60 = |; hence t = | TO; and d = ^ = 2v;^m = 5 kg.; and 2 v = 10 mm. 



2 



hence t d = 50 kilogrammillimeters or the work done by the movement of the 

 tendon in lifting the load of 5 kg. a distance of 10 mm., and is exactly the same as 

 that done by the muscle fiber. The load on the tendon is but one-half the tension 

 of the muscle, but the distance through which the load is lifted is twice that of the 

 amount of shortening of the muscle. 



If = 41 20' then cos <j> = f 

 hence t = f TO and d = f v and t d = m v 



In pinnate muscles, then, we have the rather unexpected condition in which 

 the same amount of movement of the tendon can be accomplished with less contrac- 

 tion of the muscle than in muscles where the fibers have the same direction as the 

 tendon. 



The Action of Muscles on Joints. If we consider now the action of a single muscle 

 extending over a single joint in which one bone is fixed and the other movable, we 



