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

119

a distance from the point in which the axis pierces H equal to the
distance which the generatrix is to be from the axis. D-E-F
represents the generatrix in a position parallel to V and between
the axis and V.
From the nature of the generation every point of the generatrix
will generate the circumference of a circle whose plane is perpendicular to the axis and whose radius is equal to the distance of
the point from the axis.
Since, by Section 199, C-E
is the straight line perpendic-
ular to both A-B and D-E-F, \
S r, s
the point E of the generatrix'
is nearer to the axis than any d
other point of the generatrix,
and will generate the circum- G ' a'.L
ference of the smallest circle ___ \ / 't _
of the surface. This circle
is horizontally projected in ee
mn,-o,-n,-m and vertically
projected in m'-n', and is U ---- y" y u
called the circle of the gorge.
It will be observed that as
we increase the distance from b' f\
E, other points upon the gen- FIG. 118
eratrix above or below E will
generate circumferences of circles of gradually increasing radii.
It will be also observed that the circumference of the circle
generated by a point of the generatrix at any given distance
above the plane of the circle of the gorge will have the same
radius as the circumference of the circle generated by a point of
the generatrix at the same distance below the plane of the circle
of the gorge.
This shows that the surface is symmetrical with reference to
the plane of the circle of the gorge.
The circumference of the circle d,-p,-q, —r,, generated by the
point D, the point in which the generatrix D-E-F pierces H, is
called the base of the surface.