(277.) Two systems of pulleys, called _Spanish bartons_, having
each two ropes, are represented in _fig. 123._ The tension of
the rope P A B C in the first system is equal to
the power; and therefore the parts B A and B C support a
portion of the weight equal to twice the power. The rope E A
supports the tensions of A P and A B; and therefore the
tension of A E D is twice the power. Thus, the united
tensions of the ropes which support the pulley B is four times the
power, which is therefore the amount of the weight. In the second
system, the rope P A D is stretched by the power. The rope
A E B C acts against the united tensions A P and
A D; and therefore the tension of A E or E B is twice
the power. Thus, the weight acts against three tensions; two of which
are equal to twice the power, and the remaining one is equal to the
power. The weight is therefore equal to five times the power.
A single rope may be so arranged with one moveable pulley as to support
a weight equal to three times the power. In _fig. 124._ this
arrangement is represented, where the numbers sufficiently indicate the
tension of the rope, and the proportion of the weight and power. In
_fig. 125._ another method of producing the same effect with two
ropes is represented.
(278.) If several single moveable pulleys be made successively to act
upon each other, the effect is doubled by every additional pulley:
such a system as this is represented in _fig. 126._ The tension
of the first rope is equal to the power; the second rope acts against
twice the tension of the first, and therefore it is stretched with
a force equal to twice the power: the third rope acts against twice
this tension, and therefore it is stretched with a force equal
to four times the power, and so on. In the system represented in
_fig. 126._ there are three ropes, and the weight is eight times
the power. Another rope would render it sixteen times the power, and so
on.
In this system, it is obvious that the ropes will require to have
different degrees of strength, since the tension to which they are
subject increases in a double proportion from the power to the weight.
Public-domain text, read in full here on John Shaqi.
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