476 
motion by a force o m perpendicular to oc ; 
by the extension of the thigh at the same time 
the centre will be also urged by a force on, 
perpendicular to the radius o d; the resultant 
of these two forces is o o’, in the direction of 
which the centre of gravity is raised in the 
first instant of motion, and the body and foot 
will be in the position a, b,c, d, e,' o', J; g’. 
If the action of the muscles ceased after this 
first impulse, the body wouldarrive in the second 
instant at p, where o' p = 0 o’, but at the point o’ 
the centre of gravity receives two new impulses, 
one o' m' from the extensor of the leg, and 
another o’ n’ by the extensor of the trochanter ; 
the first is in a direction perpendicular to o' c’, 
the second perpendicular to o' d’, the former 
being combined with the motion o’ p, which is 
that of the centre of gravity ; in the second 
instant there arises a second resultant o’ q, 
which the body would pass through in the se- 
cond moment, if the action of the thigh did 
not take place, but this new force o' n’ being 
con:bined with o’ g, produces the ultimate re- 
sultant o’ o”, which the centre of gravity really 
"weng through in the second moment, and the 
ody takes the position a, b, c’, d’, €’, 0, f”, g”. 
In the moment which follows, the centre of 
gravity would arrive by the second impulse at 
p’, a distance equal o o”, but the forces of 
the muscles continuing to act, one of them 
o” m” produced by the extensor of the leg, 
and always perpendicular to o” c’, gives with 
the motion o” p'a resultant o” 9‘, which being 
combined in its turn with a force o” n” pro- 
duced by the extensor of the trochanter in a 
direction perpendicular to o” d’, gives a new 
ultimate resultant o” o”, which the centre of 
gravity passes through in the third instant. If 
the distance from the point o” to the point b is 
greater than the length of the leg, it is evident that 
the body of the insect will be elevated during 
the third instant, and the muscles being no 
longer able to produce any new impulses, be- 
cause the foot no longer furnishes them with 
points of support, the centre of gravity will in 
the succeeding intervals of time pass over spaces 
equal to o” o”. 
In this demonstration we have only consi- 
dered two forces as acting to produce the leap, but 
there are others which influence the motion of 
the body as above mentioned, the effect of which 
we must here notice. By the extension of the 
hip on the thigh, the body which we have sup- 
i not moveable on the hip would be flexed 
orwards from its horizontal ition; but this 
is corrected by the motion of the body on the hip 
coi by that of the leg on the tarsus, The extensor 
muscle of the tarsus opens the angle a b c, and 
tends to lower the extremity a of the tarsus ; 
but since that is supported the leg 6 c is moved 
and flexed up » giving to the centre of 
gravity a motion forwards and downwards, per- 
dicularly to the radius b 0. This new force 
ing combined with o o’, produces in the first 
instant a resultant more inclined forwards than 
oo. This oblique direction is afterwards cor- 
rected by the motion of the body on the hip. 
In short, if the body were only subject to the 
forces of the muscles of the tarsus, the leg, and 
MOTION. 
Fig. 268. 
im” 
d: } 
: ' 
_h! 
; a ' 
: Fog: wt y 
ty er 
ir 
og 7 a oO 
the thigh, it would take a direction more — 
oblique than f’ g’; but by the’ motion of the 
body on the hip, the centre of gravity receives — 
a new impulse backwards and downwards per= — 
pendicular to eo, and this new force combined 
with o’ 0” gives a resultant more vertical, and 
as it acts in an oblique direction downy 
it diminishes necessarily the velocity of t 
leap; but the body thereby regains its h 
zontal position. e other legs also contri- 
bute to the elevation of the body in leaping, but 
their action must be very feeble, because these 
limbs seldom present a greater size or 
in leaping insects than in other species. The 
middle pair of legs being always directed 
outwards and backwards, urge the body w 
wards and forwards. The anterior pair, on th 
contrary, being placed greatly in advance of 
the centre of gravity, and directed op posite 
to the others, move it upwards and back- 
wards; these limbs, however, being compara- 
tively very feeble, can produce but little effect 
on the direction which the body would take 
were it only impelled by the two hinder pairs. 
In almost all the perfect insects the legs are 
the instruments of leaping, but the Elater is” 
capable of jumping whilst on its back, in or 
der to recover its normal position, which owing 
to its figure it could not otherwise effect. 
this purpose, a mechanism not generally found 
in eo i insects is provided ; the pro-sternum 1s 
prolonged backwards, and terminates im @ 
strong conical spine, which in a state of r 
is lodged in a grooved cavity situated in the 
meso-sternum. ‘The insect having been tured 
on its back, is observed to curve the body 
forcibly backwards; during this movement thi 
spine of the sternum is drawn out of its 
sheath, and rests upon the edge of it, and th 
bases of the elytra are elevated above the plane 
of position. The flexor muscles, situated — 
the inferior aspect of the body, next contrac 
by which the spine is forcibly pressed | 
the edge of its sheath; the sternum is 
suddenly relaxed, the spine darts into its sh 
with great velocity, the head and thorax fly 
and the base of the elytra descends ups 
supporting surface with such force I 
insect by the reaction is propelled up 
the height of one or two inches, during 
the animal turns over upon its legs.” 
order to understand more clearly how this ak 
lace, let a b (fig. 268) be the axis of 
y; © its centre of gravity; # the 
pameie <.- 
