The work is
then removed and the tailstock is shifted along the bed until the
distance _a--b_ between the extreme points of the centers is exactly 1
foot. The center is next offset a distance _b--c_ equal to one-half the
required taper per foot, after which a parallel strip _D_, having true
sides, is clamped in the toolpost. Part _D_ is then set at right angles
to a line passing from one center point to the other. This can be done
conveniently by holding a 1-foot square (preferably with a sliding head)
against one side of _D_ and adjusting the latter in the toolpost until
edge _E_ of the square blade is exactly in line with both center points.
After part _D_ is set, it should be clamped carefully to prevent
changing the position. The angle between the side of _D_ and an
imaginary line which is perpendicular to axis _a--b_ is now equal to
one-half the angle of the required taper.

The axis of the part to be turned should be set parallel with line _E_,
which can be done by setting the cylindrical surface which was
previously finished, at right angles to the side of _D_. In order to do
this the work is first placed between centers, the tailstock being
shifted along the bed if necessary; the tail-center is then adjusted
laterally until the finished cylindrical surface is square with the side
of _D_. A small try-square can be used for testing the position of the
work, as indicated in Fig. 8. If the length of the work is less than 1
foot, it will be necessary to move the center toward the rear of the
machine, and if the length is greater than 1 foot, the adjustment is, of
course, in the opposite direction.

[Illustration: Fig. 9. A Lathe Taper Attachment]

=The Taper Attachment.=--Turning tapers by setting over the tailstock
center has some objectionable features. When the lathe centers are not
in alignment, as when set for taper turning, they bear unevenly in the
work centers because the axis of the work is at an angle with them; this
causes the work centers to wear unevenly and results in inaccuracy.
Furthermore, the adjustment of the tailstock center must be changed when
turning duplicate tapers, unless the length of each piece and the depth
of the center holes are the same. To overcome these objections, many
modern lathes are equipped with a special device for turning tapers,
known as a taper attachment, which permits the lathe centers to be kept
in alignment, as for cylindrical turning, and enables more accurate work