is sufficient to overcome the friction, will 
raise the 152 pounds; and the velocity of 
the power will be to the velocity of the 
weight, as 152 to 1. Hence it appears, that 
■ the longer the winch is, and the nearer the 
spirals are to one another, so much the 
greater is the force of the screw. 
A machine for shewing the force or power 
of the screw may be contrived in the following 
manner: — Let the wheel C have a screw 
(fig. 24) on its axis, working in the teeth of the 
wheel D, which suppose to be 48 in number. 
It is plain, that for every time the wheel C 
j and screw' are turned round by the winch A, 
the wheel D will be moved one tooth by the 
ji screw ; and therefore, in 48 revolutions of 
the winch, the wheel D will be turned once 
round. Then, if the circumference of a cir- 
cle, described by the handle of the winch A, 
is equal to the circumference of a groove 
round the wheel D, the velocity of the han- 
dle will be 48 times as great as the velocity of 
any given point in the groove. Consequent- 
ly, if a line G goes round the groove, and 
has a weight of 48 pounds hung to it, a 
power equal to 1 pound at the handle will ba- 1 
lance and support the weight. To prove 
this by experiment, let the circumferences of I 
the grooves of the wheels C and D be equal 
to one another ; and then if a weight H, of 
1 pound, is suspended by a line going round 
the groove of the wheel C, it will balance a 
weight of 48 pounds hanging by the line G ; 
and a small addition to the weight H will 
cause it to descend, and so raise up the other 
weight. 
If a line G, instead of going round the 
groove of the v'heel D, goes round its axle I, 
the power of the machine will be as much in- 
creased as the circumference of the groove 
exceeds the circumference of the axle; which 
supposing to be six times, then one pound 
at H will balance six times 48, or 288 pounds, 
hung to the line on the axle : and hence the 
power or advantage of this machine will be 
as 288 to 1. That is, a man who by his na- 
tural strength could lift a hundredweight, 
will be able to raise 288 cwts. by this engine. 
If a system of pulleys was applied to the 
cord H, the power would be increased to an 
amazing degree. 
When a screw acts in a wheel in this man- 
ner, it is called an endless screw. 
When it is not employed in turning a 
wheel, it consists of two parts: the first is 
called the male or outside screw ; being cut 
in such a manner, as to have a prominent 
part going round the cylinder in a spiral man- 
ner, which prominent part is called the 
thread of the screw ; the other part, which is 
called the female, or inside screw, is a solid 
body, containing a hollow cylinder, whose 
concave surface is cut in the same manner as 
the convex surface of the male screw, so [hat 
the prominent parts of the one may fit the 
concave parts of the other. 
A very considerable degree of friction al- 
ways acts against the power in a screw ; but 
this is fully compensated by other advan- 
tages; for on this account the screw con- 
tinues to sustain a weight, even after the 
power is removed, or ceases to act, and 
presses upon the body against which it is 
driven. Hence the screw will sustain very 
great weights ; insomuch that several screws 
properly applied, would support a large build! 
■MECHANICS. 
mg, whilst the foundation was mending, or 
renewed. 
OF COMPOUND MACHINES. 
Though it is evident from the principles 
delivered above, that any one of the mecha- 
nical powers is capable of overcoming the 
greatest possible resistance, in theory; yet, 
in practice, if used singly for producing very 
great effects, they would be frequently so 
unwieldy and unmanageable, as to render it 
impossible to apply them. For this reason, 
it is generally found more advantageous to 
combine them together ; by which means the 
power is more easily applied, and many other 
advantages are obtained. In all machines, 
simple as well as compound, what is gained 
in power is lost in time. Suppose that a man, 
by a fixed pulley, raises a bpam to the top of 
a house in two minutes, it is clear t hat he 
will be able to raise six beams in twelve mi- 
nutes ; but by means of a tackle, with three 
lower pulleys, he will raise the six beams at 
once, with the same ease as he before raised 
one; but then he will be six times as long 
about it, that is, twelve minutes: thus the 
work is performed in the same time, whether 
the mechanical power is used or not. But 
the convenience gained by the power is very 
great; for if the six beams are joined in one, 
they may be raised by the tackle, though it 
would be impossible to move them by the 
unassisted strength of one man. 
Consequently, if by any power you are 
able to raise a pound with a given velocity, 
it will be impossible, by the help of any ma- 
chine, to raise two pounds with the same ve- 
locity ; yet, by the assistance of a machine, 
you may raise two pounds with half that ve- 
locity, or even one thousand with the thou- 
sandth part of that velocity ; but still there is 
no greater quantity of motion produced, 
when a thousand pounds are moved, than 
when one pound is moved ; the thousand 
pounds moving proportionally slower. 
No real gain of force is, therefore, ob- 
tained by mechanical contrivances ; on the 
contrary, from friction, and other causes, 
force is always lost; but by machines we are 
able to give a more convenient direction to 
the moving power, and to apply its action at 
some distance from the body to be moved, 
which is a circumstance of infinite import- 
ance. By machines also, we can so modify 
the energy of the moving power, as to obtain 
effects which it could not produce without 
this modification. 
In machines composed of several of the 
mechanical powers, the power will be to the 
weight, when they are in equilibrio, in a pro- 
portion formed by the multiplication of the 
several proportions which the power bears to 
the weight in every separate mechanical 
power of which the machine consists. 
Suppose a machine, for instance, com- 
posed of the axle in the wheel, and a pulley; 
let the axle and wheel be such, that a power 
consisting of one-sixth of the weight will ba- 
lance it ; and let the pulleys be such, that by 
means of them alone, a power equal to one- 
fourth of the weight would support it: then, 
by means of the axle in the wheel, and the 
pulleys combined, a power equal to one-fourth 
of one-sixth, that is, of the weight, will be 
in equilibrio with it. 
In contriving machines, simplicity ought 
127 
particularly to be attended to ; for a com- 
plicated machine is not only more expen- 
sive, and more apt to be out ot order, but 
there is also a greater degree of friction, in 
proportion to the number ot rubbing parts. 
Whatever may be the construction of a 
machine, its power will always be in propor- 
tion to the velocity of the power to the 
weight ; and so that this is obtained in the 
greatest degree that circumstances will ad- 
mit, or that are necessary, then the fewer 
parts the better. 
It is evident, from the principles already 
laid down, that the velocity of a wheel is to 
that of a pinion, or smaller wheel which is 
driven by it, in proportion to the diameter, 
circumference, or number of teeth in the pi- 
nion to that of the wheel. Thus, il the num- 
ber of teeth in a wheel are 60, and those of 
the pinion 5, then the pinion will go 12 times 
round for once of the wheel, because 60, di- 
vided by 5, gives 12 for a quotient. 
Hence, if you have any number of wheels 
acting on so many pinions, you must divide 
the product of the teeth in the wheels by 
those in the pinions; and the quotient will 
give the number of turns of the last pinion in 
one turn of the first wheel. Thus, it a wheel 
A (fig. 27) of 48, acts on a pinion B ot 8, on 
whose axis there is a wheel C of 40, driving a 
pinion D of 6, carrying a wheel E ot 36, 
which moves a pinion F of 6, carrying an in- 
dex; then the number of turns made by 
the index, will be found in this manner: 
4 8 x 40 x 3^6—8 0 12 0 — 940 , the number of 
turns which the index will make while the 
wheel A goes once round. 
Any number of teeth on the wheels and 
pinions having the same ratio, will give the 
same number of revolutions to an axis : thus, 
«^X V X Vto 00 = 240 ’ as before. It 
therefore depends upon the skill of the engi- 
neer, or mechanic, to determine what num- 
bers will best suit his design. 
It is evident, that the same motion may be 
performed, either by one wheel and pinion, 
or by many wheels and pinions, provided the 
number of turns of all the wheels bear the 
same proportion to all the pinions which that 
one wheel bears to its pinion. 
When a wheel is moved immediately by 
the power, it is called a leader; and if there 
is another wheel on the same axis, it is called 
the follower. Thus A, being moved immedi- 
ately by the power, is to be considered as a 
leader, ancl B as a follower ; the wheel C be- 
ing driven by B, becomes a leader, and D a 
follower; E (fig. 28) is a leader, and the cy- 
linder F may be considered as a follower. 
Sometimes the same wheel acts both as a 
leader and a follower ; as in fig. 29, where 
B is moved by A, and consequently is a 
follower, while, as it drives C, it is also a 
leader. Therefore, as to multiply both the 
divisors and dividend by the same number 
does not alter the quotient; in mechanical 
calculations, every wheel that is both a lead- 
er and a follower, may be entirely omitted. 
The power of a machine is not at all al- 
tered by the size of the wheels, provided the 
proportions to each other are the same. 
On the application of men and horses, as 
moving powers in machinery, fyc. A horse 
draws with the greatest advantage, when the 
line of draught is not level with lys breast, but 
.11 
