According to these principles, the manner in which a load borne
on poles between two bearers is distributed between them may be
ascertained. As the efforts of the bearers and the direction of the
weight are always parallel; the position of the poles relatively to the
horizon makes no difference in the distribution of the weights between
the bearers. Whether they ascend or descend, or move on a level plane,
the weight will be similarly shared between them.
If the beam extend beyond the prop, as in _fig. 86._, and the
weight be suspended at a point not placed between them, the props must
be applied at different sides of the beam. The pressures which they
sustain may be calculated in the same manner as in the former case.
The pressure of the prop B may be considered as a power sustaining the
weight W by means of the lever B C. Hence, the pressure of B,
multiplied by B A, must be equal to the weight W multiplied by
A C. Therefore, the pressure on B bears the same proportion to the
weight as A C does to A B. In the same manner, considering B
as a fulcrum, and the pressure of the prop A as the power, it may be
proved that the pressure of A bears the same proportion to the weight
as the line B C does to A B. It therefore appears, that the
pressure on the prop A is greater than the weight.
(246.) When great power is required, and it is inconvenient to
construct a long lever, a combination of levers may be used. In
_fig. 87._ such a system of levers is represented, consisting of
three levers of the first kind. The manner in which the effect of the
power is transmitted to the weight may be investigated by considering
the effect of each lever successively. The power at P produces an
upward force at P′, which bears to P the same proportion as P′ F
to P F. Therefore, the effect at P′ is as many times the power
as the line P F is of P′ F. Thus, if P F be ten times
P′ F, the upward force at P′ is ten times the power. The arm
P′ F′ of the second lever is pressed upwards by a force equal
to ten times the power at P. In the same manner this may be shown to
produce an effect at P″ as many times greater than P′ as P′ F′
is greater than P″ F′. Thus, if P′ F′ be twelve times P″ F′, the
effect at P″ will be twelve times that of P′. But this last was ten
times the power, and therefore the P″ will be one hundred and twenty
times the power. In the same manner it may be shown that the weight is
as many times greater than the effect at P″ as P″ F″ is greater than
W F″. If P″ F″ be five times W F″, the weight will be five
times the effect at P″. But this effect is one hundred and twenty times
the power, and therefore the weight would be six hundred times the
power.
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