will rise again to its former level. 
MOTION. 
their steps will equal the time of oscillation, and 
the case is nearly the same in a slower pace. 
We observe, therefore, that when children and 
grown persons, or tall and little men, are walk- 
ing together in the pace most easy and natural 
to them, they move in a different time. It is 
true the movements of the legs, like those of 
any other member, may be accelerated by means 
of the muscular force and made to move 
quicker than when they are merely impelled 
by their own gravity in swinging from behind 
forward, but when so continued an exercise of 
muscular power is required, such an unnatural 
pace cannot long be sustained. 
In the estimate already given of the forces 
which have an influence in walking, it will be 
observed that as long as the force of the exten- 
sion of the legs in a vertical direction upwards, 
‘Is equal to that of gravity upon the body acting 
vertically downwards, the centre of gravity will 
“Move in a direction perfectly horizontal; but 
experience shows that as soon as the force of 
the extension of the supporting leg ceases, the 
centre of gravity falls below the horizontal path 
_im which it was previously moving; but the 
instant the other leg stands perpendicularly it 
The mathe- 
matical theory of walking proves that from the 
_ figure of the human machine there must of ne- 
cessity be a sinking of the centre of gravity in 
order that progression may be accomplished. 
By varying the time of the sinking of the body 
at the end of each step, the effect of the resist- 
ance of the air and other extraneous influences 
which would disturb the horizontal velocity of 
the trunk, are compensated. In a favourable 
wind, when it travels at a greater velocity than 
the walker, it is necessary he should increase 
the time of sinking to counteract its effect, and 
preserve a mean uniform motion. 
The application of mechanical principles 
does not accord with slow as it does with that 
of quick walking, for the former is too much 
under the control of the will of the walker, and 
the limbs are not suffered to swing freely by 
their own gravity as in quick walking, in which 
this volition diminishes, according to Weber, 
at least when the slightest exertion is continued 
for any length of time, and it is in this condition 
alone that theory and experiment nearly ap- 
proximate. We must, however, remember that 
‘the control exercised by the muscular system 
over the limbs in slow walking is a new force 
which animals are enabled to interpose in 
order to vary the effects which result from the 
eee! laws in operation during locomotion, 
and by no means refutes the theory of the 
influence of those forces which affect, not only 
the locomotion of animals, but the motion 
of matter universally. 
Running.—The laws which regulate running 
in many of the lower animals, such as qua- 
drupeds and birds, are nearly the same as in 
Man. It will therefore be necessary to enter 
into the details of this movement in reference 
to the latter only. 
The principles upon which walking and 
nning differ.—In running as in walking it 
may be considered as a fundamental law that 
471 
the same motions of the body recur after each 
double step; and that both legs exercise equal 
and alternate actions in these movements. In 
running the object is to acquire a greater velo- 
city in progression than can be attained in 
walking. In order to accomplish this, instead 
of the body being supported on each leg alter- 
nately, the action is divided into two periods, 
during one of which the body is supported 
on one leg, and during the other it is not sup- 
ported at all. The latter condition constitutes 
the principal difference between these two 
modes of progression. When the body is pro- 
jected upwards so as to swing freely in the 
air, the hinder leg must be raised from the 
ground before the advanced swinging leg has 
reached the vertical position; hence, in run- 
ning, the duration of the step is less than the 
half-duration of the oscillation of the leg, be- 
cause, when the advanced leg has reached the 
vertical position and is again placed on the 
ground, the hinder leg has already begun to 
describe a portion of its are of oscillation. By 
these means the duration of the step is di- 
minished, whilst the length is increased, both 
of which tend to augment the velocity. The 
length of the step is consequently greater than 
that side of a right-angled triangle, whose 
hypotheneuse is the extended leg, and the 
other side the elevation of the centre of gravity 
above the ground. In running the step may 
be divided into two periods; the first, the time 
t, during which the body is supported on one 
leg, and the second, the time +r — ¢, during 
which it is not supported at all. 
Forces employed in running. —The forces 
which act in running are the same as in walking; 
first, extension; secondly, gravity; thirdly, 
resistance. In running, a horizontal move- 
ment of the centre of gravity is not practicable 
as in walking, for afthough the extensor power 
might be so regulated that-the centre should 
continue at the same elevation so long as the 
body poised on one leg, it would evidently fall 
during the time it was left unsupported. Now, 
as it is found after the whole time of a step 
to have neither sunk nor risen, and since no 
instantaneous elevation of the centre of gravity 
takes place between the termination of the pre- 
ceding and the commencement of the following 
step; it follows that during the time ¢, it 
must ascend just as much as it sinks during 
the time +— ¢. The effects of gravity and 
resistance have been sufficiently explained in 
the theory of walking.* 
The conditions for regular progression in 
* By an analysis based on data similar to those 
for walking, Messrs. Weber have deduced the 
following equations which express the general 
laws of running. 
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(ks —4h 28)? be? P= I2......00- - (30) 
RE ie By Spr bb nado a's! 9: cole e siee COM) 
: $e LCT te eeerereeeerreeees (32) 
