MECHANICS. 13 
A pulley is a circular disk inclosed in a case, turning about an axis passing 
through its centre, and provided on its circumference with a groove for the 
reception of a cord. © Pulleys are fixed or movable. 
In the fixed pulley (fig. 19), the case is stationary and attached to some 
object. At one end of the rope which passes over the pulley is the power, 
at the other end the resistance; the former must be equal to the latter ; and 
the advantage consists only in being able to give the power any desired 
direction. Thus,a weight may be raised by a power acting horizontally, or 
vertically downwards. Pulleys of this character (fixed pulleys) occur in 
jigs. 15, 16, 25, 26, 28, 29. 
Movable Pulleys, as represented in fig. 36, are distinguished from fixed in 
that the case of the pulley is movable. The cord, I, is fastened to a hook, 
passes under the pulley AB, which carries the weight W, and is then either 
elevated by the power P, or, as in fig. 37, passes over a second pulley to be 
drawn up from below. In the fixed pulleys, which are properly nothing 
more than means for changing the direction of motion, the weight must be 
equal to the power; in the movable, however, another condition occurs. 
Here the power is to the weight as the radius of the pulley to the chord of 
the arc of the pulley embraced by the rope. The most advantageous case 
is exhibited when the two sides of the rope are parallel, and the chord equal 
to twice the radius of the pulley. The power is here to the weight as 1: 2, 
that is, one pound of power will raise two of weight. In the double pulley, 
the same condition takes place, the second pulley being a fixed one, 
and only serving to change the direction in which the power is applied. 
In a single pulley, the proportion of 1:2 is the only one that can be 
attained, even in the most favorable cases; any desired proportion of weight 
to power can, however, be effected by a skilful combination of several pul- 
leys, fixed and movable. Of these combinations there are two kinds, those 
in which but one string is used, and those in which several are employed. 
Pl. 16, fig. 38, represents the first kind; figs. 39 and 40, the second. In 
jigs. 38 and 39, the weight, W, is attached to the movable pulleys, and the 
power, P, acts upon the last fixed pulley: in fig. 40, the relation is just the 
reverse, without changing the operation. As in one of these combinations 
all the strings must be stretched equally, and all except that on which the 
power operates must receive their tension from the weight—this tension, 
however, equalling that produced by the power—equilibrium will take place 
when the power is to the weight as 1 to the number of strings stretched by the 
weight. In fig. 38, or the power pulley, the pulleys are placed one above the 
other, and the statical relation of the machine is as 1:4; in fig. 39, where 
the pulleys are not immediately one above the other, and are united by 
several strings, every movable pulley connected with another by a special 
cord doubles the power of the machine ; hence it follows, that in this com- 
bination, although the weight is suspended to four pulleys only, A, A’, A”, A’”, 
the statical relation is as 1:16. The combination represented in fig. 40 is 
still more advantageous, in which the weight is fastened to the extremities 
of all the cords, the axis of the upper pulley alone being attached to a beam, 
while all the other pulleys are movable. Here, with three movable pulleys, 
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