MECHANICS. 15 
the wedge when the force acts abnormally, or not in the direction of the 
length of the wedge, by which means the wedge is driven in obliquely. In 
this case, the resistance is to the power as radius to the difference of half the 
angle included between the sides of the wedge, and the angle made by the 
direction of resistance with the side of the wedge. In any case, the right- 
angled wedge may be looked upon as an inclined plane, and the isosceles 
wedge as the combination of two equal inclined planes. The wedge 
is the more powerful as the angle included between its sides is greater ; it is 
driven in, however, more easily as this angle is less: The wedge is princi- 
pally used for splitting, in which the power acts by percussion, so that, 
practically, no accurate calculations can be made from the principles referred 
to above. 
The screw is merely an inclined plane wound around a cylinder. Con- 
struct a rectangle ( pl. 17, fig. 1), divide two opposite sides into any equal 
number of equal parts, unite the points of division, 1, 2, 3, 4, &c., of the one 
side, with 2, 3, 4, 5, &c., of the other, by the lines aa’, cc’, dd’, ee’, and sup- 
pose the rectangle lapped around a cylinder, the circumference of whose 
base exactly equals an undivided side of the rectangle; then the lines aa’, 
cc’, dd', &c., will form on the cylinder a continuous curved line, called a 
screw line, and each single winding is called a turn of a screw. The height 
of a turn of the screw is the distance between two contiguous turns, or 
between the two points of the screw line lying vertically one above the 
other (as a,c, or 1, m). If, now, a prismatic body be wound around the 
cylinder on the screw line, it will form the winding or thread of the screw ; 
and the whole taken together will be a screw spindle, or male screw, when 
the thread is on the outside of the cylinder: it is a female or mother screw 
when the thread is applied to the inside of the cylinder or cylindrical cavity. 
According as the prismatic body wound around the cylinder is a three or 
four-sided prism, the thread of the screw is called sharp (pl. 17, fig. 2) or 
flat (fig. 3), where A is the spindle, and Q the mother or female screw. 
This female screw consists of a prismatic body, DE, in whose cylindrical 
hole a thread, B, is situated. The male and female screws differ in the 
thread being applied to a cylindrical convexity for the former, and to a 
cylindrical concavity for the latter. The thread of the screw may have 
other forms than that of the three or four-sided prisms; these are, however, 
the most convenient and generally used. 
Male and female screws can only be used in combination with each other, 
and even in cases where one seems to be absent (as the female of a wood 
screw), itis formed by the one that is present in the material itself. Strictly 
speaking, the screw, althuugh always included among them, does not belong 
to simple machines, as it can never be applied without the assistance of a 
lever to turn the spindle in the nut. 
In the movement of a screw three cases may present themselves: either 
the spindle is fixed and the nut is turned, thus advancing along the former ; 
or the nut is fixed and the spindle moves in it; or, finally, both male and 
female move, uniformly, but with different velocities, often in different 
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