14 PHYSICS. 
the weight is to the power required for equilibrium as 15:1; with 2 
movable pulleys, it will be as 2"*1—1:1. The combination in fig. 48, in 
which the cords A, A’, A”, work obliquely, is less advantageous and con- 
venient. 
Whuite’s Pulley is represented in front by fig. 42, and laterally in jig. 41, 
consisting of two blocks, Q and R, of which one is fixed and the other mova- 
ble. Each block has six concentric grooves, which act as so many single 
pulleys, the weight hanging to twelve cords, b, c, d,—n. Hence, with this 
number of pulleys, the relation between weight and power is 144:1. This 
combination, however, besides the slowness of movement, has the disadvan- 
tage that, from the small diameter of the lesser pulleys, the rigidity of 
the cords is so great as very sensibly to affect the action of the machine. 
The inclined plane, as the fourth simple machine, is represented in figs. 
44-46. AB is the base, BC the height, AC the length of the inclined plane, 
viewed as a right-angled triangle, up which the weight, M, is to be moved. 
Divide according to the parallelogram of forces, the weight, W, of M, acting 
vertically downwards, into two forces, one perpendicular to the direction of 
the inclined side of the plane, the other parallel to it; the former will be 
AB 
expressed by W cos. BAC =W cos. 8 =Waq the weight sustained by the 
BC 
resistance of the inclined plane, and the latter W sin. BAC = W sin. 6= ae 
expressing the amount of the force parallel in its direction to the inclined 
plane, necessary to produce equilibrium. Hence this force will be smaller 
as the inclination of the plane is less, or as the length of the plane is greater 
than its height. Should the force, as in fig. 46, act in a horizontal direction, 
or one parallel to the base of the plane, then the force, P, required to sustain 
X 
BC 
the weight, W, will be P = W tang. BAC =W tang. 6 = maps or the force 
is to the weight as the height of the plane to its base. The force is thus 
smaller in comparison with the weight to be sustained, as the height, BC, is 
smaller with respect to the base, BA; when, as in fig. 45, BC = AB, or 
BAC = 45°, then P=W, or the power is equal to the veight. Finally, if the 
height, BC, be greater than the base, AB, or BAC greater than 45°, the 
force must be greater than the weight. 
The wedge, the fifth simple machine, is illustrated by means of figs. 47 
and 48. It has in general the form of a three-sided prism (in the figure appear- 
ing as a triangle, ABC): upon the side AB, and perpendicular to it, a force 
operates in endeavoring to drive the opposite edge, C, into a body to be split, 
or between two bodies to be separated ; or, in case this has already been done, 
to retain it in its place. If, upon the wedge ABC (fig. 48), a force operates 
perpendicularly to its length, DC, endeavoring to drive it out, equilibrium 
occurs when the power is to the resistance as the sine of half the angle 
included between the two sides of the wedge, or sin. «, to the sine of the 
angle included between the direction of resistance and the side of the wedge. 
The power obtained is as the cosine of the latter angle. ig. 47 represents 
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