MOTION. 
they may form the greatest base of support, has 
been mathematically investigated by Parent 
and Barthez. According to the latter, the tra- 
pezium which forms the base of support will 
be a maximum when the prolongations of the 
lines drawn through the central line of each 
foot and passing through the centre of each 
heel form an angle of 38° 56”. 
The calculation of Parent is defective, from 
its being based upon the hypothesis that the 
foot turns as upon a pivot about its articula- 
tion with the leg, instead of around the heel. 
When the body stands erect upon both legs, 
and presses equally on each, the legs will form 
equal angles with the vertical line passing 
through the centre of gravity; but if the two 
legs form different angles with that line, the 
pressure upon the legs will be unequal, and 
will vary with the angles of inclination, 
for example, in fig. 249, a d is perpendicular 
and g 7 parallel to the horizon; if a 
Fig. 249. 
and ag represent the entire force exerted by 
the legs to support the whole body, ad and ai 
will be the corresponding portion of these forces 
necessary to sustain the weight of the body, 
and will also together represent that weight ; 
and if a d and az be found by experiment, the 
absolute forces, a b, ag, will be found.* In 
standing, the limbs serve merely to support the 
body, and to preserve the centre of gravity at a 
certain height above the plane of position, 
within the base of support, which is a necessary 
condition to prevent it from falling. In addi- 
tion to these functions they translate the trunk, 
during progression, from point to point, and 
keep it in equilibrium, in all the varied move- 
ments and under the action of all the extra- 
neous forces incidental to locomotion.+ 
* See Borelli de motu animal. prop. 138, p. 173. 
+ When a man stands with his centre of gravity 
at a vertical height H, above the plane of the hori- 
zon, if his weight be P, then the amount of force 
which he expends in order to stand is, according 
to Poisson, equal to PH.—Traité de Mech. Paris, 
2 - 
459 
Walking.—In walking or running, the body 
may be divided into two portions, namely, the 
trunk, head, neck, and arms, which constitute 
the burden that is to be borne, and the legs 
which support and carry the burden along. 
The former cannot, however, be considered as a 
merely passive or dead weight, as the trunk 
and arms contribute to keep in equilibrio the 
forces acting on the centre of gravity during 
progression. In walking, the trunk is carried 
forwards with its major axis directed nearly 
perpendicularly to the horizon, like a rod poised 
endways on the hand. The power to keep the 
trunk thus poised whilst it is moved forwards 
is attained only after considerable experience 
during the earlier period of man’s career, when 
his unsteady gait, numerous trials, and frequent 
falls afford practical illustrations of the difficulty 
of the process. Every movement of the legs, 
arms, head, or trunk, as well as the bearing of 
burdens in various positions, requires a compen- 
sating movement of some other part, in confor- 
mity to the theory of parallel forces, to preserve 
the whole in equilibrio; therefore, in order to 
keép the supported parts poised on the rounded 
head of either femur, whilst the body is trans- 
ferred from one to the other, and carried forwards 
in the air, either against or in the same direc- 
tion as the wind, there must be a continued in- 
terchange of compensating movements, and 
these actions are placed under the controul of 
the excito-motory division of the nervous sys- 
tem. It is well known that when any portion 
of a rigid body receives motion from a neigh- 
bouring body, all the parts of the rigid body 
will partake of the same motion, only when 
the direction of the force passes from the point 
of contact through the centre of gravity. If this 
is not the case, as, for example, when the upper 
extremity of the propelling leg acts on the 
lower part of the trunk of the human body in 
the erect position, the lower part would be pro- 
pelled forwards and upwards, whilst the centre 
of gravity of the trunk would be left behind, 
and fall backwards; but if this centre be in- 
clined forwards at the beginning of the step, the 
weight of the body and its required momen- 
tum will propel it forwards and downwards ; 
hence the resultant of the several forces will be 
a force which propels the body forwards in a 
direction which, by experience, is found to be 
nearly horizontal: but there is also another 
force which affects the trunk, namely, the re- 
sistance of the air, which tends to turn the 
trunk backwards, and must be counteracted by 
the force of gravity, through the inclination of 
the trunk forwards. The amount of this con- 
stant inclination of the trunk must be estimated 
by the resistanceewhich it encounters from the 
air in walking and running. It must therefore 
be greater in rapid progression, because the 
resistance of the air is then more powerful than 
in more deliberate motion. Without this incli- 
nation it would still be possible to preserve a 
uniform position of the body in walking and 
running, not, however, by the force of its own 
gravity, but by means of the power of the mus- 
cles, which connect it with the limbs ; but this 
