the work will then be turned tapering as the tool is
traversed from _a_ to _b_, because the axis _x--x_ is at an angle with
the movement of the tool. Furthermore the amount of taper or the
difference between the diameters at the ends for a given length, will
depend on how much center _h_{1}_ is set over from the central position.

[Illustration: Fig. 1. Taper Turning by the Offset-center Method]

[Illustration: Fig. 2. Examples of Taper Work]

The amount of taper is usually given on drawings in inches per foot, or
the difference in the diameter at points twelve inches apart. For
example, the taper of the piece shown at _A_, Fig. 2, is 1 inch per
foot, as the length of the tapering surface is just twelve inches and
the difference between the diameters at the ends is 1 inch. The conical
roller shown at _B_ has a total length of 9 inches and a tapering
surface 6 inches long, and in this case the taper per foot is also 1
inch, there being a difference of 1/2 inch in a length of 6 inches or 1
inch in twice that length. When the taper per foot is known, the amount
that the tailstock center should be set over for turning that taper can
easily be estimated, but it should be remembered that the setting
obtained in this way is not absolutely correct, and is only intended to
locate the center approximately. When a taper needs to be at all
accurate, it is tested with a gage, or by other means, after taking a
trial cut, as will be explained later, and the tailstock center is
readjusted accordingly. There are also more accurate methods of setting
the center, than by figuring the amount of offset, but as the latter is
often convenient this will be referred to first.

=Setting Tailstock Center for Taper Turning.=--Suppose the tailstock
center is to be set for turning part _C_, Fig. 2, to a taper of
approximately 1 inch per foot. In this case the center would simply be
moved toward the front of the machine 1/2 inch, or one-half the required
taper per foot, because the total length of the work happens to be just
12 inches. This setting, however, would not be correct for all work
requiring a taper of 1 inch per foot, as the adjustment depends not only
on the _amount_ of the taper but on the _total length_ of the piece.

[Illustration: Fig. 3. Detail View of Lathe Tailstock]

For example, the taper roller _B_ has a taper of 1 inch per foot, but
the center, in this case, would be offset less than one-half the taper
per foot, because th