6.« MECHANIC S. 
When bodies are compofed of moleculac which are of 
the fame fize and fubftance, and fimilarly pofited through¬ 
out, they are faid to be homogeneous ; fuch are the bodies 
which we (hall conlider; and in which the mafs will ma- 
nifelllybe proportional to theextenfion or the magnitude, 
fo that the one may be fubftituted for the other in our in- 
veftigations. The vertical lines which would be defcribed 
by bodies if fubjerted to the free artion of gravity, are fre¬ 
quently called lines of direElion. Since they would, if pro¬ 
duced, meet at the centre of the earth, they cannot, ftrictly 
fpeaking, be parallel ; but, with refpert to any body or any 
fyftem of bodies connected for mechanical purpofes, the 
whole fpace occupied by all their particles mull be fo very 
minute compared with the magnitude of the earth, that 
their feveral lines of direction may be confidered as parallel 
without any danger of fenfible error; jult as we fpeak of a 
moderate portion of the earth’s furface as a plane, although 
it is, in fatt, nearly fpherical. Hence, then, the artions of 
gravity upon a body, or fyftem, may be confidered as thofe 
of parallel forces applied to their various particles. 
By the definition of the centre of gravity, when it is fup- 
ported the body is in, equilibrio; and, front the nature of 
equilibrium, it can only be produced fingly by the exercife 
of a force equal and oppofite-to the refultant of all the other 
forces arting upon the feveral particles of the body, that is, 
fince in this cafe the forces are parallel, by a force equal to 
the weight of the body applied at the centre of parallel 
forces; confequently the centre of gravity coincides with the 
centre of parallel forces . 
Varying the pofition of the body, will not caufe any 
change in the centre of gravity; fince any fuch mutation 
w ill he nothing more than changing the directions of the 
forces, without their ceafing to be parallel ; and, if the 
forces do not continue the fame, in confequence of the 
body being fuppofed at different diftances from the earth, 
ftill the forces upon all the moleculae vary proportionally, 
and their centre remains unchanged. 
When a heavy body is fufpended by any other point 
than its centre of gravity, it will not reft unlefs that centre 
is in the fame vertical line with the point of fufpenfion ; 
for in all other pofitions the force which is intended toen- 
fure the equilibrium will not be dirertly oppofite to the 
refultant of the parallel forces of gravity upon the feveral 
particles of the body, and of courle the equilibrium will 
not be obtained. 
If a heavy body be fuftained by two or more forces, 
their directions muft meet either at the centre of gravity 
of that body, or in the vertical line which paffes through it. 
Thus, let B (fig. 61.) be a heavy body whofe centre of 
gravity is G ; it will be at reft if the firing a B, by which 
it is fufpended, hang vertically, whether the ftring itfe|f 
be fixed at a, or be attached to two other firings whole 
lengths are b a, c a, and fixed at b and c. If the ftring a B 
were either longer or Ihorter, the point a continuing fixed, 
and the pofitions of b and c being unchanged, the body 
would ftill hang at reft, and the brings ba, ca, under the 
fame tenfion. If the body were removed vertically to the 
dotted fituation in the diagram, it would be luftained in 
that pofition by the firings bd and ce, which would fuffer 
the fame tenfion as when they were united in the point a. 
If inftead of the firings we applied props fg, hi, in the 
lame directions on the oppofite fides of the body, their 
feet f, h, being fixed ; or if other props tnn, op, were ap¬ 
plied, either parallel to the former, or having their direc¬ 
tions meeting in the vertical line q G ; the body would ftill 
be fupported ; and, if the directions of the props and of the 
firings were parallel, the compreffion in the one cafe would 
be equal to the tenfion in the other. Eitherthe compref¬ 
fion or tile tenfion may in every cafe be readily eflimated 
by means of the parallelogram of forces, &c. the weight of 
the body being known. 
When a body ftands upon a plane, if a vertical line pafs- 
jng through the centre of gravity fall within the bale on 
which the body ftands, it will not fall over; but, if that 
vertical line palfes without the bafe, the body will fall, un¬ 
lefs it be prevented by a prop or <r cord. Wiien the ver¬ 
tical line falls upon the extremity of the bafe, the body 
may ftand, but the equilibrium may be diiturbed by a very 
trifling force ; and, the nearer this line pafles to any edge of 
the bafe, the more eafily may the body be thrown over ; the 
nearer it falls to the middle of the bafe, the more firmly 
the body ftands. „ 
The various motions of animals, if attentively confi¬ 
dered, will appear to be regulated confiftently with the 
principles juft dated. Thus, when a man endeavours to 
rife from his feat, he thrulls forward his body, and draws 
his feet backward till the vertical line from the centre of 
gravity falls juft before his feet; this enables, or indeed 
compels, him to rife; and, to prevent falling forward, he 
advances one of his feet till the vertical line of direction 
is brought between his feet, in confequence of which he 
may ftand firmly. In walking, he firlt extends his hind- 
moil leg and foot almoit to a right line, and at the fame 
time bends the knee of his fore-leg a little ; by this means 
his body is thruft forward, and the line of direction from 
its centre of gravity falls beyond the fore-foot, on which 
account he is ready to fall, but prevents it by immediately 
taking up the other foot, and putting it forward beyond 
the line of direction'. After the fame manner, he thrulls 
himfelf forward by the leg which is now the hindmoft, till 
the line of direction from the centre of gravity be beyond 
his fore-foot, when he again fets his hind-foot forward ; 
and thus he continues the motion of walking at pleafure. 
While walking, a man always fets down one foot before 
the other is taken up ; fo that at each (tep he has both 
feet upon the ground. But in running he takes one up 
before he fets the other down ; fo that his feet touch the 
ground alternately for moments of time, and in the inter¬ 
mediate portions he does not touch it at all. In walking 
up hill, a man bends his body more forward than in walk¬ 
ing on a horizontal road, that the line of direction may 
he thrown before his feet: in walking down hill he rather 
leans backward, to prevent the line of dirertion from being 
too forward, which would occafion his fall. In carrying 
a burthen, a man always leans the contrary way to that in 
which the burthen lies, in order that the common centre of 
gravity of both mayhave itslineof dirertion betweenhisfeet. 
When a quadruped, as a horfe, moves, he leans forward, 
all at once lifting up one of his fore-feet and one of his 
hind-feet; when the right leg before is pulhed forward, 
the left leg behind is moved on at the fame time ; and, 
this motion being made, the left leg before takes its turn 
conjointly with the right leg behind, and fo on ; as the 
body, when Handing, is fupported by four props which 
form a rertangle, the molt commodious mode of moving 
is to change the pofitions of two feet at a time diagonally, 
and thus to caufe the centre of gravity of the animal’s 
body to make but a fmall movement, and to remain al¬ 
ways very nearly in the dirertion of the two points of 
fupport. This rule of motion is always obferved, but 
with thefe differences : in the pace there are four times in 
the complete movement; if the fore right-leg be moved 
firft, the left leg behind follows the initant after; then the 
left fore-leg has its turn, which is followed the next in- 
ftant by the right foot behind. Thus, the fore right-foot 
comes firlt to the earth, the left foot behind next, the left 
fore-foot third, and the right hind-foot laff; fo that there 
are four motions, and three intervals, of which the firlt 
and laff are Ihorter than the middle one. In trotting, he 
takes up two feet together, and fets down two together, 
diagonally oppofite. In galloping he takes up his feet one 
by one/ and fets them down one by one ; but he llrikes 
with the two fore-feet nearly at once, and the two hind- 
feet nearly at once; all the time the line from the centre 
of gravity lies forward, fo that the animal requires the 
fore-feet to come to the ground at Ihort intervals to pre¬ 
vent a fall. If the various motions of other animals be 
confidered, they will all be found conformable to the fame 
principles. But it would be tedious to enter further into 
the detail in this place. 
Tq 
