forward and tooth No. 1 on the
stop. After this cut is completed, the lever is reversed which rotates
the cutter one tooth, and the return movement places tooth No. 2 in the
working position. This operation is repeated until the tenth tooth
finishes the thread. It is often necessary, when using a single-point
thread tool, to re-sharpen it before taking the finishing cut, but with
a circular tool this is not necessary, for by using the different teeth
successively, the last tooth, which only takes finishing cuts, is kept
in good condition.

=Cutting Screws to Compensate for Shrinkage.=--Some tool steels are
liable to shrink more or less when they are hardened; consequently if a
very accurate hardened screw is required, it is sometimes cut so that
the pitch is slightly greater than standard, to compensate for the
shrinkage due to the hardening operation. As the amount of contraction
incident to hardening is very little, it is not practicable to use
change gears that will give the exact pitch required. A well-known
method of obtaining this increase of pitch is by the use of a taper
attachment.

For example, suppose a tap having 8 threads per inch is to be threaded,
and, owing to the contraction of the steel, the pitch must be 0.12502
inch instead of 0.125 inch. The lathe is geared to cut 8 threads per
inch or 0.125 inch pitch, and then the taper attachment is set to an
angle _a_, Fig. 28, the cosine of which equals 0.125/0.12502; that is,
the cosine of angle _a_ equals _the pitch required after hardening_,
divided by the _pitch necessary to compensate for shrinkage_. The angle
is then found by referring to a table of cosines. The tap blank is also
set to the same angle a by adjusting the tailstock center, thus locating
the axis of the work parallel with the slide of the taper attachment.
When the carriage moves a distance _x_, the tool point will have moved a
greater distance _y_ along the work, the difference between x and y
depending upon angle _a_; hence the tool will cut a thread of slightly
greater pitch than the lathe is geared to cut.

To illustrate by using the preceding example, cosine of angle _a_ =
0.125/0.12502 = 0.99984. By referring to a table of cosines, we find
that 0.99984 is the cosine of 1 degree, approximately; hence, the taper
attachment slide and the work should be set to this angle. (The angle
_a_ in Fig. 28 has been exaggerated in order to more clearly illustrate
the principle.)

[Illustration: