.

=Turning Taper or Conical Surfaces.=--Conical or taper surfaces are
turned in a vertical boring mill by swiveling the tool-bar to the proper
angle as shown in Fig. 13. When the taper is given in degrees, the
tool-bar can be set by graduations on the edge of the circular base _B_,
which show the angle _a_ to which the bar is swiveled from a vertical
position. The base turns on a central stud and is secured to the saddle
_S_ by the bolts shown, which should be tightened after the tool-bar is
set. The vertical power feed can be used for taper turning the same as
for cylindrical work.

[Illustration: Fig. 14. Turning a Conical Surface by using the Combined
Vertical and Horizontal Feeds]

Occasionally it is necessary to machine a conical surface which has such
a large included angle that the tool-bar cannot be swiveled far enough
around to permit turning by the method illustrated in Fig. 13. Another
method, which is sometimes resorted to for work of this class, is to use
the combined vertical and horizontal feeds. Suppose we want to turn the
conical casting _W_ (Fig. 14), to an angle of 30 degrees, as shown, and
that the tool-head of the boring mill moves horizontally 1/4 inch per
turn of the feed-screw and has a vertical movement of 3/16 inch per turn
of the upper feed-shaft. If the two feeds are used simultaneously, the
tool will move a distance _h_ of say 8 inches, while it moves downward a
distance _v_ of 6 inches, thus turning the surface to an angle _y_. This
angle is greater (as measured from a horizontal plane) than the angle
required, but, if the tool-bar is swiveled to an angle _x_, the tool, as
it moves downward, will also be advanced horizontally, in addition to
the regular horizontal movement. The result is that the angle _y_ is
diminished and if the tool-bar is set over the right amount, the
conical surface can be turned to an angle _a_ of 30 degrees. The
problem, then, is to determine what the angle _x_ should be for turning
to a given angle _a_.

[Illustration: Fig. 15. Diagram showing Method of Obtaining Angular
Position of Tool-head when Turning Conical Surfaces by using Vertical
and Horizontal Feeding Movements]

The way angle _x_ is calculated will be explained in connection with the
enlarged diagram, Fig. 15, which shows one-half of the casting. The sine
of the known angle _a_ is first found in a table of natural sines. Then
the sine of angle _b_, between the taper surface and center-line of the