MOTION. 
Fig. 267. 
475 
Let f g (fig. 267) be the axis of the body, 
passing through the centre of gravity 0; a 6, 
the tarsus; bc, the leg; c d, the thigh, with 
the trochanter; 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 0, which is a little above it. 
In this state, if the tarsus a 6, which is di- 
rected backwards, become flexed, the angle 
a bc opens, and as the tarsus rests against the 
ground, the leg b ¢ 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 are which the latter de- 
scribes in being always a tangent to this are. 
We 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 
bcd; but since it rests with its tarsal extre- 
mity upon the plane of 
position, the thigh ¢ d be- 
comes moveable, and is 
raised forwards, turning 
as aradius round itscruro- 
tibial articulation c, and 
carrying with it the whole 
body, in the samme manner 
’ asin the motion of the leg; 
the direction of the force 
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 } f, during the 
time ¢’ of its spring, 
ot. Asa 3% 0 Bere aah cast (BR) 
and, 
t = 46. eee eset eee eee eeeeseseenee (37) 
The velocity of the cat will be, 
v— /2fs 
hence, that of the tiger is, 
va VIF wa V 2h 
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. 
’ 
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 0, passing through the 
cruro-tibial articulation and centre of gravity. 
The motion produced by the extensor muscle 
of the trochanter on the thigh c d, opens the 
angle c de, 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 de, which is 
flexed forward, and carries the body with it; 
the direction of the force of this muscle is 
perpendicular to the radius d 0, passing through 
d, the articulation of the hip with the tro- 
chanter 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 0, and 
impresses on the centre of gravity an oblique 
impulse downwardsand 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 
