1 25 
MECHANICS. 
rising. By this means, the danger is pre- 
vented which might otherwise happen by the 
running down of the weight when left at li- 
berty. 
The pulley is a small wheel turning on an 
axis, with a drawing-rope passing over it: the 
small wheel is usually called a sheeve, and is 
so fixed in a box, or block, as to be moveable- 
round a pin passing through its centre. 
Pulleys are of two kinds: — 1. Fixed, which 
do not move out of their places; 2. Move- 
able, which rise and fall w ith the weight. 
When a pulley is lixed, as fig. 13, two equal 
weights suspended to the ends of a rope pass- 
ing over it, will balance each other ; for they 
stretch the rope equally, and if either of them 
is pulled down through any given space, the 
other will rise through an equal space in the 
same time ; and consequently, as the veloci- 
ties of both are equal, they must balance each 
other. This kind of pulley, therefore, gives 
no mechanical advantage ; so that you can 
raise no greater weight by it than you could 
do by your natural strength. Its use consists 
in changing the direction of the power, and 
sometimes enabling it to be applied with more 
convenience. By it, a man may raise a 
weight to any point, without moving from the 
place he is in ; whereas, otherwise, he would 
have been obliged to ascend with the weight: 
it also enables several men together to apply 
Jheir strength to the weight by means of the 
rope. 
The moveable pulley represented at A 
(fig. 14), is fixed to the weight W, and rises 
and falls with it. In comparing this to a le- 
ver, the fulcrum must be considered as at 
A; the weight acts upon the centre, and 
the power is applied at the extremity of 
the lever D. The power, therefore, being 
twice as far from the fulcrum as the weight 
is, the proportion between the power and 
weight, in order to balance each other, must 
be as 1 to 2. Whence it appears, that the 
use of this pulley doubles the power, and that 
a man may raise twice as much by it as by his 
strength alone. Or it may be considered in 
this way : Every moveable pulley hangs by 
two ropes equally stretched, and which must, 
consequently, bear equal parts of the weight ; 
but the rope A B being made fast at B, half 
the weight is sustained by it ; and the other 
part of the rope, to which the power is ap- 
plied, has but half the weight to support ; 
consequently the advantage gained by this 
pulley is as 2 to 1. 
When the upper and fixed block contains 
two pulleys, which only turn upon their axes, 
and the lower moveable block contains also 
two, which not only turn on their axis, but 
rise with the weight F (fig. 15), the advan- 
tage gained is as 4 to 1. For each lower 
pulley will be acted upon by an equal part of 
the weight ; and because in each pulley that 
moves with the weight, a double increase of 
power is gained, the force by which F may be 
sustained, will be equal to half the weight di- 
vided by the number of lower pulleys; that 
is, as twice the number of lower pulleys is to 
1, so is the weight suspended to the power. 
But if the extremity C (fig. 16) is fixed to 
the lower block, it will sustain half as much as 
a pulley; consequently here the rule will be, 
as twice the number of pulleys adding unity 
is to 1, so is the weight to the power. 
These rules hold good, whatever may be 
the number of pulleys in the blocks. 
If, instead of one rope going round all the 
pulleys, the rope belonging to each pulley is 
made fast at top, as in fig. 17, a different pro- 
portion between the power and the weight 
will take place. Here it is evident, that each 
pulley doubles the power : thus, if there are 
two pulleys, the power will sustain four times 
the weight. 
Fig. 8, is the concentric pulley, invented 
by Mr. James White. O, R, are two brass 
blocks, in which grooves are cut; and round 
these a cord is passed, by which means they 
answer the purpose of so many distinct pul- 
leys. The advantage gained is found by 
doubling the number of grooves in the lower 
block. 
It is common to place all the pulleys in 
each block on the same pin, by the side of 
each other, as in fig. 18 ; but the advantage, 
and rule for the power, are the same here as 
in figs. 1.5 and 16., 
A pair of blocks with the rope fastened 
round it, is commonly called a tackle. 
The inclined plane. This mechanical 
power is of very great use in rolling up heavy 
bodies, such as casks, wheelbarrows, &c. It 
is formed by placing boards, or earth, in a 
sloping direction. 
The force wherewith a body descends upon 
an inclined plane, is to the force of its abso- 
lute gravity, by which it would descend per- 
pendicularly in free space, as the height of 
the plane is to its length. For suppose the 
plane AB (fig. 19) to be parallel to the hori- 
zon, the cylinder C will keep at rest on any 
part of the plane where it is laid. If the 
plane is placed perpendicularly, as AB, fig. 
20, the cylinder C will descend with its whole 
force of gravity, because the plane contributes 
nothing to its support or hindrance ; and 
therefore it would require a power equal to iti 
whole weight to keep it from descending. 
Let AB (fig. 21; be a plane parallel to the 
horizon, and AD a plane inclined to it; and 
suppose the whole length A D to be three 
times as great as the perpendicular D B. In 
this case, the cylinder E will be supported 
upon the plane DA, and kept from rolling, 
by a power equal to a third part of the 
weight of the cylinder ; therefore a weight 
may be rolled up this inclined plane, by a 
third part of the power which would be suf- 
ficient to draw it up by the side of an upright 
wall. 
It must also be evident, that the less the 
angle of elevation, or the gentler the ascent is, 
the greater will be the weight which a given 
power can draw up ; for the steeper the in- 
clined plane is, the less does it support of the 
weight ; and the greater the tendency which 
the weight has to roll, consequently the more 
difficult for the power to support it: the ad- 
vantage gained by this mechanical power, 
therefore, is as great as its length exceeds its 
perpendicular height. 
To the inclined plane may be reduced all 
hatchets, chisels, and other edge-tools. 
The wedge is the fifth mechanical power or 
machine : it may be considered as two equally 
inclined planes, joined together at their 
bases; then D G (fig. 22) is the whole thick- 
ness of the wedge at its back A BG D, where 
the power is applied; E F is the depth or 
height of the wedge ; B F the length of one 
of its sides; and OF is its sharp edge, which 
is entered into the wood intended to be split; 
by the force of a hammer or mallet striking 
perpendicularly on its back. Thus, A li 
(fig. 23) is a wedge driven into the cleft 
C£D of the wood F G. 
When the wood does not cleave at any dis- 
tance beforp the wedge, there will be an equi- 
librium between the power impelling the 
wedge downward, and the resistance of the 
wood acting against the two sides of the 
wedge, when the power is to the resistance as 
half the thickness of the wedge at its back is 
to the length of either of its sides ; because 
the resistance then acts perpendicular to the 
sides of the wedge. But when the resistance 
on each side acts parallel to the back, the 
power that balances the resistances on both 
sides will be, as the length of the whole back 
of the wedge is to double its perpendicular 
height. 
When the wood cleaves at any distance 
before the wedge (as it generally does), the 
power impelling the wedge will not be to the 
resistance of the wood as the length on the 
back of the wedge is to the length of both its 
sides, but as half the length of the back is to 
the length of either side of the cleit, esti- 
mated from the top or acting part of the 
wedge. For, if we suppose the wedge to be 
lengthened down from the top C E, to the 
bottom of the cleft at D, the same proportion 
will hold ; namely, that the power will be to 
the resistance as half the length of the back 
of the wedge is to the length of either of its 
sides: or, tvhich amounts to the same thing, 
as the whole length of the back is to the 
length of both the sides. 
The wedge is a very great mechanical 
power, since not only wood, but even rocks, 
can be split by it ; which it would be impos- 
sible to effect by the lever, wheel and axle, 
or pulley ; for the force of the blow, or stroke, 
shakes the cohering parts, and thereby makes 
them separate more easily. 
The screw (fig. 24.) is the sixth arid last me- 
chanical power, but cannot properly be called 
a simple machine, because it is never used 
without the application of a lever or winch to 
assist in turning it ; and then it becomes a 
compound engine of a very great force, 
either in pressing the parts of bodies closer to- 
gether, or in raising great weights. It may 
be conceived to be made by cutting a piece 
of paper, ABC (fig. 25), into the form of an 
inclined plane, or half-wedge; and then wrap- 
ping it round a cylinder (fig. 26), the edge of 
the paper AC will form a spiral line round 
the cylinder, which will give the thread of the 
screw. It being evident that the winch must 
turn the cylinder once round, before the 
weight of resistance can be moved from 
one spiral winding to another; therefore, 
as much as the circumference of a circle 
described by the handle of the winch is 
greater than the interval or distance between 
the spirals, so much is the force of the screw. 
Thus, supposing the distance of the spirals to 
be half an inch, and the length of the wjnch 
twelve inches, the circle described by* the 
handle of the winch where the power acts 
will be 76 inches nearly, or about 152 half- 
inches, and consequently 152 times as great 
as the distance between the spirals: and 
therefore a power at the handle, whose in- 
tensity is equal to no more than a single 
pound, will balance 152 pounds acting against 
the screw ; and as much additional force as 
