_ progression. 
~ tension produces an increased velocity in the 
MOTION. 
allowed to accompany the movements of the 
legs without muscular effort. When the body 
is put in motion, the momentum generated re- 
quires an equal furce in the opposite direction 
to stop it, for which purpose the trunk is thrown 
back ; and this, with the resistance of the feet on 
the ground, will commonly suffice. When, 
however, this is not the case, the motion must 
be arrested gradually, or, as it often happens 
when the plane of position is composed of ice, 
the leg goes on without the trunk, and the cen- 
tre of gravity comes to the ground. 
In walking, the trunk is also elevated and 
depressed at each step vertically, as well as 
oscillated in other directions. By the assist- 
ance of a rod graduated into millimetres, which 
was carried at the head of the trochanter major 
by the ambulator, and viewed through a tele- 
scope, Weber was enabled to ascertain the 
amount of the elevation and depression of the 
trunk. He found that when the length of the 
steps treading on the whole sole of the foot 
measured 2.39 feet, the mean elevation and de- 
pression were 1.1 inches. The plane in which 
the rod vibrated, and the magnitude of the 
oscillations, did not appear to vary materially, 
whether the speed was accelerated or retarded. 
In walking on the ball of the great toe the 
mean elevation and depression of the trunk 
was 0.8 inch. 
Estimate of the forces employed in walking. 
The forces which we have to estimate in walk- 
ing are, first, that of the extension of the leg; 
secondly, the gravity of the body ; thirdly, the 
resistance which the body encounters in pro- 
gression. Of these, the first is that force which 
the leg exerts by its extension to bring it into 
a straight line, as if both of its extremities (viz. 
the head of the femur, and that part of the foot 
which is in contact with the ground) endeavoured 
to push each other away. The direction of this 
force depends on the position of the extremi- 
ties of the leg ; but whatever that direction may 
be, it is always resolvable, on the principle of 
the parallelogram of forces, into a vertical and a 
horizontal component. The vertical portion of 
the extension upwards is equal to the second 
force, or the gravity of the body acting vertically 
downwards ; in this case the centre of gravity 
remains at the same height above the plane of 
The horizontal portion of the ex- 
horizontal direction, the magnitude of which 
depends on the position of the supporting leg. 
By means of these forces the body is propelled 
forwards. At the moment the body receives the 
impulse of extension it is accelerated until the 
third force, namely, the resistance,* augmenting 
continually with the velocity, is equal to that 
of the acceleration ; when these two forces neu- 
tralize each other, the body will move forwards 
with an uniform velocity. 
Hitherto the forces which influence walking 
* The principal resistance is occasioned by the 
advanced leg when it reaches the ground. Other 
resistances are the frictions of the joints, of the sole 
of the foot upon the earth, of the air, &c., but these 
are very trifling when compared with the retard- 
ation caused by the advanced leg. 
461 
have been considered as if they were uniformly 
accelerating forces; but though they are not 
strictly such, yet as they recur at the end of 
each step, the mean velocity of the body will 
remain the same as if they actually were so.* 
Let us assume a common point of application 
of the forces, and consider this as the centre of 
the body, or the point of separation between the 
trunk and the legs. The three forces may be re- - 
presented (fig. 250) by three straight lines meet- 
Fig. 250. 
ad 
a 
ing at this point, thus: Let c be the centre of the 
body; draw ca in a vertical direction, c b 
in a horizontal, and c d in the direction of the 
prolongation of the leg on which the body is 
supported. These three lines will represent in 
magnitude and direction the forces which are 
in action during progression, if they be so taken 
that either of them equals the diagonal of the 
parallelogram formed by the other two, and 
will coincide in direction with that diagonal 
produced beyond c. Messrs. Weber do not 
consider those physiologists worth refuting who 
state that the forces which propel the body for- 
wards exceed those that drive it back, for in 
that case, from the continued preponderance of 
force in one direction, there would result, not 
an uniform, but a continually increasing velo- 
city. An uniform motion in a straight line 
can only take place either when no force what- 
ever is exerted on the moving body, or when all 
the forces by which it is affected are in equi- 
librium. 
In order to investigate with greater precision 
the laws which regulate the movement s of the 
body, the Messrs. Weber have considered the 
weight of the trunk to be collected at the point 
of junction of the legs, and the weight of each 
leg, supposed a straight line, to be collected in 
a point at a given distance from that junction. 
The movements of these points are supposed to 
take place in the same vertical plane. They 
have then applied the general equation for the 
motion of a system of material points,t and 
deduced by means of it that the raised leg, in 
walking, swings forward like a pendulum, the 
length of which is the above-mentioned given 
distance, but in consequence of the motion of 
the point of junction, which is supposed to 
* The three forces which influence walking are so 
related to each other, that each of them is equiva- 
lent and opposite to the resultant of the other two. 
+ See Poisson’s Traité de Mechanique, Paris, 
1833, vol. ii. § 531. 
