MOTION. 
sive; that is, it swings forwards by the force of 
gravity alone, independently of muscular ac- 
tion. The supporting leg is regarded by 
the Messrs. Weber as a substitute for the pro- 
pelling weight of a clock, and the swinging leg 
as the substitute for the pendulum, both ex- 
changing their offices alternately. The distance 
from the point where the ball of the foot of the 
Swinging leg quits to the point where it is again 
placed on the earth, is equal to the length of a 
double step. This outline of the action of the 
legs in walking depends on principles which we 
shall now proceed to investigate more strictly, 
in doing which we shall draw largely from 
the theoretical and experimental researches of 
the Messrs. Weber, whose labours have con- 
tributed so extensively to advance our know- 
ledge in this interesting branch of human phy- 
siology. 
The positions of the body in walking at va- 
rious instants of time have been described both 
by Borelli and Weber; it is thus represented 
by the latter. Let fig. 253 be the vertical, and 
Jig. 254 the ground plan, on planes in a straight 
Fig. 253. 
<A at ke 
a Bigu% “55, 
horizontal path. In fig. 253 the simultaneous 
positions of the two feet are represented at 
the moment when they reach the ground, 
also the position of the centre of gravity of the 
body in the vertical plane. The position of the 
right leg is shown by the continued lines, and 
that of the left leg by the dotted lines. The 
extremity of the right foot is designated by the 
‘letter a, that of the left by the letter b, and the 
centre of gravity by c, the contemporaneous 
positions of these points being denoted by the 
humerals annexed to these letters. In the 
horizontal projection, fig. 254 represents the si- 
multaneous position of both legs and of the cen- 
tre of gravity ; the letters and figures are the same 
as in the preceding diagram. At the instant when 
the hinder leg is raised from the ground at the 
commencement of each step, the extremity of the 
forward leg and the centre of gravity lie in the 
normal plane of the line of progression; for 
example, at the beginning of the first step, 6, 
and ¢,, of the second step a, and c,, and of 
the third step, b, and c,, lie in the normal 
plane of the direction of progression. 
In each step the extremity of one leg must 
VOL. III. 
465 
be advanced as far before the foot of the other 
as in the preceding or following steps the other 
leg was placed before the first, for example :— 
in the first step, the foot, a,,,, must ad- 
vance so far before b,,., as in the second 
step b, ,, ,must advance before a, . 5 ,- 
The time of each step, that is, the space of 
time between the raising of each foot in succes- 
sion, is subdivided by Borelli and the Webers 
into two parts, namely, one part in which 
one leg, and the other when both legs are 
on the ground: for instance, during the first 
step, while the centre of gravity advances 
from c, to c,, one leg, and, while it advances 
from c, to c, both are on the ground.’ In the 
second step, while the centre moves from c, to 
C3, one leg only, but while it advances from 
c, to c, both legs are again on the ground, and 
so on in succession. But there is no instant in 
walking in which the body moves freely through 
the air without either leg touching the ground, 
as in running. 
The sum of the squares of the elevation of the 
centre of the body above the horizontal plane, 
and the length of the step, is equal to the square 
of the length of the extended leg.* This pro- 
position depends on the circumstance that the 
forward leg stands vertical to the ground at the 
instant the hinder leg quits it; and that the 
two legs, with the horizontal distance between 
them, form, at this moment, a right-angled tri- 
angle. According to the Webers, the body, in 
walking, continues to be affected by the exten- 
sor power of one leg only, because the expen- 
diture of the extensor power of the legs to 
support the body is only just sufficient to sus- 
tain it; and this expenditure is at a minimum 
only when the forward leg bears the whole 
burden during that period in which they are 
both on the ground, for as the forward leg acts 
at a less angle than the hinder leg, it is capable 
of supporting the body at a much greater me- 
chanical advantage, which is at a maximum 
when it stands vertically. MM. Weber also 
find that the body is accelerated whilst one 
leg, and is retarded whilst both legs are on 
the ground; for, in slow walking, the forward 
leg being placed on the ground in advance of 
the centre of gravity, it tends for an instant to 
check the horizontal velocity of the body. 
We shall now take a brief view of the velo- 
city in walking, and of the principles on which 
it depends. MM. Weber have shewn that 
the velocity in walking varies with the height 
at which the head of the femur is carried from 
the ground; as this height increuses, the velo- 
city decreases.t The length of each step de- 
creases as the height of the centre of gravity in- 
creases; for the greater the elevation, the less 
will be the distance to which the leg will ex- 
tend ; therefore corpulent persons, and porters 
with heavy burdens on the shoulders, take steps 
of diminished length. The duration of a step, 
* Hence we get eq. 23. 
+ The velocity being uniform =? and 
7 
therefore increases as h decreases. 
2H 
