Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

SURFACES OF REVOLUTION

121

itself. In Fig. 118, S-s, is the horizontal trace of a meridian plane
parallel to V. This plane intersects the circumference of the
circle of the gorge at M and N. Therefore m' and n' are two points
in the vertical projection of the required meridian curve.
For the same reason r' and q' are two more points in the vertical
projection of the curve, since R and Q are the two points in which
this same meridian plane intersects the base of the surface.
To find other points of the curve, draw horizontal planes, for
example T. This plane cuts the generatrix D-E-F at X (x,, x')
and cuts the surface itself in the circumference of a circle whose
horizontal projection is x,-x,,,-x,, and whose vertical projection
is x"-x"'. This circumference intersects the meridian plane at
X (x,,, x"), also at X (x,,,, x"'), locating two points in the required
curve.
Since the surface is symmetrical with reference to the plane of
the circle of the gorge, the meridian curve in vertical projection
will be symmetrical with reference to the vertical projection of the
circle of the gorge. Therefore, having determined the points x"
and xtt in the vertical projection of the curve, corresponding points
y" and y"' below m'-n' may be obtained by drawing U-u' parallel
to mn-n' and at the same distance below m'-n' as T-t' is above, and
by taking y" and y"' at the same distance from a'-' as x" and x"'.
By this process we may find as many points in the curve as may
be desired.