w 
M E C 
M E C 
Roman Measures of Capacity for thing* dry, reduced to English Corn-measure. 
Peck. Gal. Pint. Doc. 
inch. 
O' 
TT 
°tV 
04 
1 
0.01 
0:04 
O.OS 
0.24 
0.48 
Ligu 
4 
la 
Cyath 
us 
Acetabulum. - 
6 
if 
24 
6' 
4 
Heir 
ilia 
48 
12 
8 
2 
Sextarius - - 
384 
96 
64 
16 
8 jSemimoduis 
'768 
192 
128 
32 
16 | 2 Modius 
Measure for horses, is the hand, which 
by statute contains four inches. 
^MEATUS AUDITORIES. See An a- 
1 TOMY. 
MECHANICS, that branch of practical 
! mathematics which considers motion and 
[ moving powers, their nature and laws, with 
: their effects in machines. 
The term mechanics is equally applied to 
j the doctrine of the equilibrium of powers, 
■ more properly called statics ; and to that 
science which treats of the generation and 
| communication of motion, which constitutes 
; mechanics strictly so called. See Statics, 
, Power, Motion, &c. 
The knowledge of mechanics is one of 
those things, says Mr. Mac Laurin, that 
serve to distinguish civilized nations from 
barbarians. It is by this science that the ut- 
most improvement is made of every power 
and force in nature ; and the motions of the 
| elements, water, air, and tire, are madesub- 
I servient to the various purposes of life ; for 
; however weak the force of man appears to 
be, when unassisted by this art; yet, with its 
aid, there is hardly any thing above his reach. 
It is distinguished by sir Isaac Newton into 
practical and rational mechanics ; the former 
of which treats of the mechanical powers, 
viz. the lever, balance, axis and wheel, pul- 
ley, wedge, screw, and inclined plane. 
Rational mechanics comprehends the whole 
theory of motion, shews when the powers or 
forces are given how to determine the mo- 
tions that are produced by them ; and con- 
versely when the phenomena of the motions 
are given, how to trace the powers or forces 
from which they arise. 
Mechanical powers are simple engines 
that enable men to raise weights, to move 
heavy bodies, and overcome resistances, 
which they could not do with their natural 
strength alone. Their importance to society 
is incalculable. Every machine whatever is 
composed of one or more of them, sometimes 
jof several combined together. 
In considering this science, it will be neces- 
sary at first to take some things for granted 
(that are not strictly true; and after the theory 
jis established, to make the proper allovv- 
I ances for them. 
1. That a small portion of the earth’s sur- 
face, which is spherical, may be considered as 
la plane. 2. That all bodies be supposed to 
(descend in lines parallel to each other ; for 
Ithough all bodies really tend to the centre of 
khe earth, yet the distance from which they 
Jfall is comparatively so small, that their incli- 
nation towards each other is inconsiderable. 
p. That all planes be considered as perfectly 
Imooth ; levers to be inflexible, and without 
- 0 1 0 3.84 
- 1 0 0 7.68 
thickness or weight ; cords perfectly pliable; 
and machines without friction and inertia. 
Three things are always to be considered 
in treating of mechanical engines; the weight 
to be raised, the power by which it is to be 
raised, and the instrument or engine by 
which this is to be effected. 
The mechanical powers are generally reck- 
oned six; the lever, the pulley, the wheel 
and axis, the inclined plane, the wedge, and 
the screw. 
These perhaps may be reduced to two; 
for the pulley and wheel are only assemblages 
of leve; >, and the wedge and screw are in- 
clined planes. 
To calculate the power of a machine, it is 
usually considered in a state of equilibrium ; 
that is, in the state when the power which is 
to overcome the resistance just balances it. 
Having discovered what quantity of power 
will be requisite for this purpose, it will then 
be necessary to add so much more as to over- 
come the friction and weight of the machine 
itself, and to give the necessary velocity. 
The lever is the simplest of all machines ; 
and is only a straight bar of iron, wood, or 
other material, supported on, and moveable 
round, a prop called the fulcrum. 
In the lever there are three circumstances 
to be principally attended to : 1. The ful- 
crum, or prop, by which it is supported, or 
on which it turns as an axis, or centre of mo- 
tion : 2. The power to raise and support the 
weight: 3. The resistance or weight to be 
raised or sustained. 
The points of suspension are those points 
where the weights really are, or from which 
they hang freely. The power and the weight 
are always supposed to act at right angles to 
the lever, except it is otherwise expressed. 
The lever is distinguished into three-sorts, 
according to the different situations of the 
fulcrum or prop, and the power, with respect 
to each other. I. When the prop is placed 
between the povver and the weight. 2. When 
the prop is at one end of the lever, the power 
at the other, and the weight between them. 
3. When the prop is at one end, the weight 
at the other, and the power applied between 
them. 
A poker, in stirring the fire, is a lever of 
the first sort : the bar of the grate upon which 
it rests is the fulcrum ; the fuel, the weight 
to be overcome ; and the hand is the power. 
The lever of the first kind is principally used 
for loosening large stones ; or to raise* great 
weights to small heights, in order to get ropes 
under them, or other means of raising them 
to still greater heights; it is the most common 
species of lever. 
ABC, Plate Mechanics, fig. 1 . is this lever, 
in which B is the fulcrum, A the end at which 
Q2 
M E C 1 23 
the power is applied, and C the "end where 
the weight acts. 
To find when an equilibrium will take 
place between the power and the weight, in 
this as well as in every other species of lever, 
it is necessary to recollect, that when the mo- 
menta, or quantities of force, in two bodies are 
equal, they will balance each other. Now let 
us consider when this will take place in the 
lever. Suppose the lever All (fig. 2) to be 
turned on its axis, or fulcrum, so as to come 
into the situation DC ; as the end D is farthest 
from the centre of motion, and as it has 
.moved through the arch AD in the Same time 
as the end B moved through the arch BC, it 
is evident that the velocity of AB must have 
been greater than that of B. But the mo- 
menta being the products of the quantities. of 
matter multiplied into the velocities, the 
greater the velocity, the less the quantity of 
matter need be to get the same product. 
I herefore, as the velocity, of A is the greatest, 
it will require less matter to produce an equi- 
librium than B. 
Let us next see how much more weight B 
will require than A to balance it. As the radii 
ot circles are in proportion to their circum- 
ferences, they are also proportionate to similar 
parts of them ; therefore, as the arches AD, 
CB, are similar, the radius or arm I3E bears 
the same proportion to EC that the arch 
AD bears to CB. But the arches AD and 
CB represent the velocities of the ends of 
the lever, because they are the spaces which 
they moved over in the same time ; therefore 
the arms DE and EC may also represent 
these velocities. 
It is evident then, that an equilibrium will 
take place when the length of the arm AE 
multiplied into the power A, shall equal EB 
multiplied into the weight B; and conse- 
quently, that the shorter EB is, the greater 
must be the weight B; that is, the power and 
the weight must be to each other inversely, 
as their distances from the fulcrum. Thus, 
suppose AE, the distance of the power from 
the prop, to be 20 inches, and EB, the dis- 
tance of the weight from the prop, to be eight 
inches, also the weight to be raised at b to 
be five pounds, then the power to be applied 
at A must be two pounds ; because the dis- 
tance of the weight from the fulcrum eight, 
multiplied into the weight five, makes 40 ; 
therefore 20, the distance of the power from 
the prop, must be multiplied by two, to get 
an equal product, which will produce an 
equilibrium. 
It is obvious, that while the distance of the 
povver from the prop exceeds, that of the 
weight from the prop, a power less than the 
weight will raise it, so that then the lever 
affords a mechanical advantage : when the 
distance of the power is less than that of the 
weight from the prop, the power must be 
greater than the weight to raise it ; when both 
the arms are equal, the povver and the weight 
must be equal, to be in equilibrio. 
The second kind of lever, when the weight 
is between the fulcrum and the power, is re- 
presented by fig. 3. in which A is the ful- 
crum, B the weight, and C the power. The 
advantage gained by this lever, as in the first, 
is as great as the distance of the power from 
the prop exceeds the distance of the weight 
from it. Thus if the point a, ou which the 
povver acts, is seven times as far from A as 
