site direction toit, will produce an equilibrium. 
= Fig. 206. 
P 
“hipy 
Let N (fig. 205) be the point acted upon by 
any two forces N F, N F’, which form an angle 
FNF*,, and the line N R their resultant, which 
will draw the point in the direction NR. But 
if a third foree NR’, equal and opposite to NR, 
be applied, it will destroy the motion in 
NR, and the point N will remain at rest by 
the simultaneous action of the three forces 
NR, NF, NF’. 
i Fig. 207. 
RE a 
mak 
= 4 Pee © 
~. 
a oO 
_ Centre of gravity—The centre of gravity 
of any body is a point about which, if acted 
‘upon only by the force of gravity, it will ba- 
ve itself in all positions; or, it is a point 
which, if supported, the body will be sup- 
ported however it may be situated in other 
Tespects; and hence the effects produced by 
or upon any body are the same as if its whole 
_ ‘mass were collected into its centre of gravity. 
. To find the centre 
of gravity of any plane 
body mechanically, 
let the plane a e db 
(fig. 208) be sus- 
penced freely by a 
string from the point 
a, to which a plumb- 
line a6 is also at- 
tached — the latter 
will coincide with 
the vertical line a 6, 
which is to be marked 
with a pencil: then 
i gen the plane 
and plumb-line from 
| a second point e, 
_ Fig. 208. 
! when the plumb-line 
will hang vertically 
+ in the line ed, inter- 
 secting a b in c, the point c will be the centre 
of gravity of the plane. 
a 
i. 
7 
“w 
be 
MOTION. 
409 
To find the distance of the head and feet 
from the centre of gravity of the human body 
in a horizontal position; balance the body 
placed upon a plane a é on a triangular prism 
de,asin fig. 209 ; then draw a line on the plane 
Fig. 209. 
close to the edge of the prism; again balance 
the body in another position and draw a line 
as before, the vertical line passing through c, 
the intersection of these lines will pass through 
the centre of gravity. 
After the plan of Borelli, Weber balanced a 
plank across a horizontal edge, and stretched 
upon it the body of a living man: when the 
whole was in a state of equilibrium, in which 
the method of double weighing was adopted, 
by accurate measurements he found the total 
length of the body 
m.m. in. 
= 1669.2 = 65.30853 
the distance of the centre of gravity below the 
vertex == 721.5 = 28.406455 
above the sole of the foot 
= 947.7 = 37.310949 
above the trausverse axes of the hip-joints 
= 87.7 = 3.454729 
above the promontory of the sacrum 
= 847) 0(341519 
As the horizontal plane of the centre of gravity 
lies between three-tenths and four-tenths of an 
inch above the promontory of the sacrum, it 
must traverse the sacro-lumbar articulation 
which is intersected by the mesial plane, be- 
cause the body is symmetrical, and by the 
transverse vertical plane, the sacro-lumbar arti- 
culation must, therefore, contain the common 
point of intersection of all three planes, which 
coincides with the position of the centre of gra- 
vity of the body when standing; but this point 
varies in different individuals in proportion to 
the difference of the weight of the trunk to that 
of the legs, as well as by any change of the 
position of the limbs. 
The centres of gravity of particular figures 
may be found geometrically and analytically, 
as shewn in mechanical treatises; but these 
methods require computations too detailed for 
our limits. 
The attitudes and motions of every animal 
are regulated by the positions of their cen- 
tres of gravity, which, in a State of rest and 
not acted on by extraneous forces, must lie in 
vertical lines which pass through their bases 
of support. Thus, if g (fig. 210, a and B) be the 
common centre of gravity of two bodies whose re- 
spective centres of gravity are g, H, in A 
