25° 



ANIMAL MECHANICS. 



the moments 

 brium. 



of the two forces are equal, and there is rest or equili- 



gr (5 units of length) x 5 = mr (1 unit of length) x 25. 



Thus the smaller force acting on the longer 



arm balances the greater force 



acting on the shorter one. From its situation near the joint the force of 

 the muscular contraction of the triceps needs to be very great, in comparison 

 with the force of gravity pulling down the limb. This muscle may be taken 

 as typical of those of the body generally, and when we push, or pull, or lift, 

 the force of muscular exertion is often many times as great as the force 

 against which it is opposed. 



If in Fig. 136 the horizontal line grm represent the rigid lower arm, we 

 may represent the forces acting upon it by straight lines, which can repre- 

 sent these forces, not only in the direction in which they act, but, as in 

 the figure, their lengths may be made to correspond with the magnitudes of 

 the forces. The consideration of these balanced forces is one of statics, 

 but when equilibrium is disturbed by the moments on one or the other 

 side being increased or diminished, a movement of rotation around the 

 point r will occur, and we enter the region of kinetics. If we suppose that 



the force at m (the 

 contraction of the 

 triceps) be increased, 

 rotation of the limb 

 will take place, and 

 after a certain interval 

 of time it will have 

 assumed the position 

 g'rm'. In the per- 

 formance of this 

 movement g will have 

 travelled five times 

 the distance that m 

 has travelled, and in 

 an opposite direction, 

 so that if the force of 

 more than five times 

 will be lifted five 

 lost in power is 



Fig. 136. — Represents the rotation of a rod <jm to the position 



rj'm' around a fulcrum at r. 



little 

 point g 

 What ' is 



contraction of the triceps at m has to be just a 



as great as the force of gravity acting at g, the 



times as far as the point m will be lowered. 



therefore gained in amount of movement, so that an extensive motion of the 



hand occurs Avhen the muscles acting at the elbow-joint shorten to but a slight 



extent. 



When we take into account the element of time, we learn that the velocity 

 of the point g will be five times as great as that of the point m. Movements 



of g to g and m to 



m' take place in the same interval of time, and V= — 



The aforesaid muscles may, on account of the distance of the hand from the 

 elbow-joint, cause the hand, as in the act of throwing a ball, to move with 

 considerable velocity. 



Although 



the hand carrying a Aveight may be moved through a great 



space and with a great velocity, there is no more work done by the arm than 

 is put into it by the muscle. A lever or other machine does not make work ; 

 it only performs work in such ways as may be desired and arranged for. 

 This is affirmed in general principles by the law of the conservation of energy, 

 and may readily be shown from Fig. 136. 



The muscular contraction of the triceps lowers the point m to m', with a 

 force of 25 lb. The work is therefore 25 x mm'. Although, as the result 



of this contraction, the point g is raised to g 



through 



a space five times 



