MOTION. 



475 



Fig. 267. 



a 



many of the small insects leap a greater dis- 

 tance in proportion to their masses than the 

 larger animals; for example, if the Flea, which 

 can leap two hundred times its own height, 

 were as large as the Cricket, it could only leap 

 as far as it does at present ; but the latter can 

 leap much higher than the former, and there- 

 fore, of these two insects, the Cricket is the 

 best organized for leaping. We shall now pro- 

 ceed to investigate the effect of the extension of 

 the legs of insects in leaping. 



and the muscular force equals \ /, during the 

 time t' of its spiing, 



..4s=^t' 3 . (36) 



and, 



The velocity of the cat will be, 



r = JWs 

 hence, that of the tiger is, 



(37) 



r' ^1 4s t/2/s 

 4 



that is, the tiger and cat have the same velocity, 

 and therefore the same height of spring, reckoned 

 from the positions of their centres of gravity at the 

 instant of their quitting the ground. 



Let / g (Jig. 267) be the axis of the body, 

 passing through the centre of gravity o; a b, 

 the tarsus ; b c, the leg ; c d, the thigh, with 

 the troehanter ; and d e, the hip. All these 

 articulations being flexed, the tarsal extremity 

 b of the leg is advanced forwards under the 

 centre of gravity o, which is a little above it. 

 In this state, if the tarsus a b, which is di- 

 rected backwards, become flexed, the angle 

 a b c opens, and as the tarsus rests against the 

 ground, the leg b c begins to move, and 

 raising its crural extremity, draws with it the 

 whole body. Now, as the centre of gravity is 

 placed before the point b, instead of being 

 elevated, it is, on the contrary, urged forwards 

 and downwards, describing an arc of a circle, 

 of which the centre is b, and the action of the 

 flexor muscle of the tarsus continuing during 

 the whole time that the limb is resting against 

 the ground, the direction of the motion which 

 it impresses on the centre of gravity changes 

 at each point of the arc which the latter de- 

 scribes in being always a tangent to this arc. 

 \V'e might thus determine its action for each of 

 these points, but for greater simplicity we 

 shall select only three ; namely, the commence- 

 ment, middle, and the end of the motion. 



During the flexion of the tarsus, the leg 

 expands itself, and tends to open the angle 

 bed; but since it rests with its tarsal extre- 

 mity upon the plane of 

 position, the thigh c d be- 

 comes moveable, and is 

 raised forwards, turning 

 as a radius round itscruro- 

 tibial articulation c, and 

 carrying with it the whole 

 body, in the same manner 

 '<' as in the motion of the leg; 

 the direction of the force 

 produced by the extensor 

 muscle changes at each 

 point of the curve which the centre of gra- 

 vity describes ; but this direction is always 

 a tangent to the curve, and consequently per- 

 pendicular to the radius c o, passing through the 

 cruro-tibial articulation and centre of gravity. 

 The motion produced by the extensor muscle 

 of the troehanter on the thigh c d, opens the 

 angle c d e, tending to depress it at its tibial 

 extremity, but as it rests upon the leg, which 

 by its own elevation resists it, the motion is 

 wholly communicated to the hip d e, which is 

 flexed forward, and carries the body with it ; 

 the direction of the force of this muscle is 

 perpendicular to the radius d o, passing through 

 d, the articulation of the hip with the tro- 

 ehanter and the centre of gravity. Lastly, the 

 motion produced by the extension of the hip 

 e d upon the body in a direction opposite to 

 that of the thigh, is perpendicular to e o, and 

 impresses on the centre of gravity an oblique 

 impulse downwards and backwards. The forces 

 resulting from the extension of the tarsus and 

 the hip being very feeble, may be neglected. 



The muscular force expended in these mo- 

 tions may be thus approximatively estimated. 

 By the extension of the leg, the centre of gra- 

 vity o will be acted on at the beginning of 



