474 
the attitude of the annexed design by Flaxman 
(fig. 266), in which it will be seen that the 
whole mass of the body lies posterior to the 
vertical line a c’ b, ing through the base of 
support, whereas the preceding theory shews 
that in quick walking and running the swinging 
leg never a beyond the vertical dc, which 
cuts the head of the femur. This figure has 
therefore been drawn upon false principles. 
TABLE 12. 
A Table of fifty-six experiments on running 
with various velocities. Space passed through 
43.43 met. = 142°2504 feet. 
MOTION, 
‘381 Mean Dura- 
5 = \Namber| __ tion | Length ; 
2) 0 Time. of in |Velocity. 
g | Steps. Step. | metres. 
zo 
6 | 28°17] 7°56 | 0°268]| 1°542| 5°753 
3 | 38°83| 9°91 | 0:293]| 1°284] 4°382 
6 | 35°92| 10°80 | 0°301| 1°209| 4:016 
7 | 38°17/ 11°99 | 0°314/ 1°138] 3°624 
3 | 42°67| 13°60 | 0319] 1°018| 3°194 
7 | 46°5 | 15°173] 0°326] 0°934] 2°865 
6 | 53° 16°81 | 0°317/ 0°819] 2°583 
8 | 60°5 | 18:35 | 0°303] 0°718] 2°369 
5 | 71:2 | 21°68 | 0°304| 0°640} 2°105 
4 | 83°75) 25°45 | 0°304|] 0°519]| 1°707 
3 }104°33| 31°84 | 0°305]| 0°416| 1°367 
3 |137°7 | 41°49 | 0°301| 0°315]| 1:046 
From this table we see that the length of 
step increases rapidly, whilst the duration va- 
ries but very little; and that the duration is 
always equal to a half oscillation of a pen- 
dulum. 
Duration of spring .. = 0°2618 dif 
Duration of half oscil- 2 __ 0°323 yr beke 
lation of pendulum § — 
Hence we perceive that the duration of the 
spring is less than the oscillation of the leg as a 
ndulum by a very small fraction only, which 
is probably due to muscular action. 
n quick running the length of step rapidly 
increases, whilst the duration slowly dimi- 
nishes ; but in slow running the length dimi- 
nishes rapidly, whilst the time remains nearly 
the same. The time of a step in quick run- 
ning, compared to that in quick walking, is 
nearly as two to three, whilst the lengths of the 
steps are as two to one, consequently a person 
can run in a given time three times as fast as 
he can walk. The velocity in running is usually 
at the rate of about ten miles in an hour, but 
there are many persons who for a limited period 
can exceed this velocity. 
In the human race, however, the velocity in 
running varies considerably, depending on 
a variety of physical conditions, such as age, 
sex, stature, muscular power, the nature of the 
surface on which the progression is performed, 
and the angle of elevation above, or depression 
below the plane of the horizon. Man is ex- 
ceeded in s by many of the lower animals, 
owing to differences in the structure of the 
locomotive organs, and the physical laws 
they obey. « 
j pen be or jumping.—This mode of pro 
gression is adopted by a great number of 
animals; some of which resort to it only 
the accomplishment of a particular object, 
others as a regular means of locomotion, =—=_— 
In most of the orders of the animal king- 
dom there are some species which transfe 
themselves from place to place by a succession 
of impulses, in air, in water, and on solids: it 
is to the latter we shall confine our on, 
having already briefly mentioned the former in 
the sections on flying and swimming. z 
In leaping, the object to be attained is to 
take the greatest length of step without refer 
ence to its duration ; and herein it differs fror 
running, in which the greatest steps are taken 
in the least possible time. 7 
The height to which animals of different 
orders are capable of springing* varies, but 
according to Straus-Durckheim, all those in 
the same order leap to equal elevations. i 
Amongst insects, the Grasshopper and Cricket, 
and in the order Felis, the Cat, the Leopard, 
and the Tiger, all rise to the same elevations 
above the positions of their respective centres of 
gravity at the instant when their feet quit the 
ground. ’ 
This appears at first to be inconsistent 
the computations made on the proportion + 
the force of muscles to the mass of animals of 
different dimensions. 
— 
aALLECDLION, 
If we select four diffe- 
rent animals of the same order, in which the 
dimensions of one kind are as 1, 2, 3, 4, 
their weights will be as the cubes of thes 
numbers, or, as 1, 8, 27, 64; but since the fore 
of a muscle depends on the number of its” 
fibres, and therefore increases in the ratio of ii 
transverse section ; that is, as the square of on 
of these dimensions, the muscular of th 
animals will be as 1, 4,9, 16, and the velocities 
(supposing the muscles to act instantaneously 
will be as the forces divided by the weights,ora 
1, }, 4, 4, and the heights of the leaps be 
as the squares of the velocities would | 
as 1,}, }, %- Now, as they are all found | 
arrive at the same height, this may be @ 
plained by supposing that the muscles do 
act instantaneously, but as constantly accel 
rating forces during the continuance of the spri 
The force on an unit of mass in the Cat i 
that on an unit in the Tiger, as 1 to 4; and si 
the dimensions of the latter are four times the 
of the former, the tiger passes through fo 
times the space the Cat over, reckor 
from the beginning to the end of the time | 
muscles act, until the animal quits the grou 
and therefore is elevated to the same height 
the cat.+ a 
From these principles we see the reason 
* The spring is that portion of the leap w 
takes place before the feet quit the ground, __ 
+ Thus :—Let s = the space passed thro 
during the spring of the cat, f = the muse 
force employed in the time ¢ of a spring, | : 
by equation (3), = 
s= ft. ¥ <7 ‘ 
Now, as the tiger vasses through a space ==" 
