pages 368

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 contraction.
m’ =	direction of muscle fiber after contraction.
v =	amount of contraction.
m =	tension of the muscle.
φ =	angle of insertion of muscle fiber.
t =	tendon component = m x cos φ = the weight carried by the tendon to balance the muscle tension.
d =	distance tendon is drawn up.
(1) m 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 v = d x cos φ or d = v/cos φ
since t = m x cos φ or m = t/cos φ
m x v = t/cos φ x d x cos φ = t x d

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 φ = 60°, m = 10 kg. and v = 5 mm., the work done by the contracting muscle fiber = m v or 10 x 5 kilogrammillimeters.

FIG. 368– No caption. (See enlarged image)

cos &angle; 60° = 1/2; hence t = 1/2 m; and d = v/1/2 = 2 v; 1/2 m = 5 kg.; and 2 v = 10 mm. 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 φ = 41° 20’ then cos φ = 3/4
hence t = 3/4 m and d = 4/3 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 contraction 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

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