VARIOUS KINDS OF LEVERS ACTED ON BY MUSCLES. 



501 



is greatly increased, but force is lost [i.e., what is gained in rapidity is lost in 

 power]. This arrangement has this advantage, that, owing to the slight contraction 

 of the muscle, little energy is evoked, which would be the case had the muscular 

 contraction been more considerable ( 300, I., 3). (6) The muscles act upon the 

 bones as upon a lever with two arms, in which case the power (insertion of the 

 muscle) lies on the other side of the fulcrum opposite to the weight, e.g., the 

 triceps and muscles of the calf. In both cases, the muscular force necessary to 

 overcome the resistance is estimated by the principles of the lever : equilibrium is 

 established when the static moments ( = product of the power in its vertical 

 distance from the fulcrum) are equal ; or when the power and weight are inversely 

 proportional, as their vertical distance from the fulcrum, 



[The Bony Lever. All the three orders of levers are met with in the body. Indeed, in the 

 elbow-joint all the three orders are represented. The annexed scheme shows the relative posi- 

 tions of P, W, and F (tig. 346). The first order represented by such a movement as nodding the 

 head, the second by raising the body on the tiptoes by the muscles 

 of the calf, and the third by the action of the biceps in raising the 

 fore-arm. At the elbow-joint, the first order is illustrated by ex- 

 tending the flexed fore-arm on the upper arm, as in striking a blow 

 on the table, where the triceps attached to the olecranon is the 

 power, the trochlea the fulcrum, and the hand the weight. If the 

 hand rest on the table and the body be raised on it, then the hand 

 is the fulcrum, while the triceps is the power raising the humerus 

 and the parts resting 011 it (W). The third order has already been 

 referred to, e.g., flexing the fore-arm.] 



Direction of Action. It is most important to observe the direc- 

 tion in which the muscular force and weight act upon the lever-arm. 

 Thus, the direction may be vertical to the lever in one position, while after flexion it may act 

 obliquely upon the lever. The static moment of a power acting obliquely on the lever-arm is 

 obtained by multiplying the power with the power acting in a direction vertical to the point 

 of rotation. 



Examples : In fig. 347, I., B x represents the humerus, and x Z the radius; A y, the direc- 

 tion of the traction of the biceps. If the biceps acts at a right angle only, as by lifting 

 horizontally a weight (P) lying on the fore-arm or in the hand, then the power of the biceps 

 (= A) is obtained from the formula, A y x = P x Z, i.e., A = (P x Z) : y x. It is evident 



(1) 



(2) 



(3) 



W A P 



Fig. 346. 

 The three orders of levers 



II. 



II! 



Fig. 347. 

 Scheme of the action of the muscles on bones. 



that, when the radius is depressed to the position x C, the result is different ; then the force of 

 the biceps - A 1 = (P x v x) : x. In fig. 347, II., TF is the tibia, F, the ankle-joint, MC, 

 the foot in a horizontal position. The power of the muscles of the calf ( = a) necessary 

 to equalise a force, p, directed from below against the anterior part of the foot, would be 



