r axis
of the work, whether an attachment is used or not. The importance of
this will be apparent by referring to Fig. 13. To turn the taper shown,
the tool _T_ would be moved back a distance _x_ (assuming that an
attachment is used) while traversing the length _l_. As an illustration,
if the tool could be placed as high as point _a_, the setting of the
attachment remaining as before, the tool would again move back a
distance _x_, while traversing a distance _l_, but the large end would
be under-sized (as shown by the dotted line) if the diameters of the
small ends were the same in each case. Of course, if the tool point were
only slightly above or below the center, the resulting error would also
be small. The tool can easily be set central by comparing the height of
the cutting edge at the point of the tool with one of the lathe centers
before placing the work in the lathe.

[Illustration: Fig. 14. Plan View showing Method of Turning a Taper with
the Compound Rest]

=Taper Turning with the Compound Rest.=--The amount of taper that can be
turned by setting over the tailstock center and by the taper attachment
is limited, as the centers can only be offset a certain distance, and
the slide _S_ (Fig. 9) of the attachment cannot be swiveled beyond a
certain position. For steep tapers, the compound rest _E_ is swiveled to
the required angle and used as indicated in Fig. 14, which shows a plan
view of a rest set for turning the valve _V_. This compound rest is an
upper slide mounted on the lower or main cross-slide _D_, and it can be
turned to any angular position so that the tool, which ordinarily is
moved either lengthwise or crosswise of the bed, can be fed at an angle.
The base of the compound rest is graduated in degrees and the position
of these graduations shows to what angle the upper slide is set. Suppose
the seat of valve _V_ is to be turned to an angle of 45 degrees with the
axis or center, as shown on the drawing at _A_, Fig. 15. To set the
compound rest, nuts _n_ on either side, which hold it rigidly to the
lower slide, are first loosened and the slide is then turned until the
45-degree graduation is exactly opposite the zero line; the slide is
then tightened in this position. A cut is next taken across the valve by
operating handle _w_ and feeding the tool in the direction of the arrow.

[Illustration: Fig. 15. Example of Taper Work Turned by using Compound
Rest]

In this particular instance the compound res