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.

GENERATION ANMD CLASSIFICATION OF LINES 79

If, under the same conditions, the circuit is contra-clockwise,
the helix is called a left-handed helix.
A helix is completely known when the radius, the pitch, and
the direction of the circuit (whether right-handed or left-handed)
are given.
214. To represent the Helix. See Fig. 86. Let A-B represent
the axis of the helix, assumed for convenience perpendicular to H.
With a, as a center and with a,-d, as a radius, equal in length
to the radius of the helix, draw the circle d,-d,,-d,,,-. -dx. The............~~~~I f if1X

circumference of this circle will be the
horizontal projection of the helix,
since the generating point retains a
constant radial distance from the axis.
Let D (d,, d') represent the position of the generating point when
in H. Beginning with d, divide the
circumference of the circle into any
number, say eight, equal parts. The
points of division are d,, d,,, d,,,..
dox. Lay off upon a'-6t, downward
from G-L, a distance ar-e' equal to
the pitch of the helix. Divide this
distance a'-e' into the same number
of equal parts as the circumference

I t '~a H L
d d
dI, |,
_:5
d

J- --- ---
bF
FIG. 86

of the circle has been divided into, and through the points of division, 1, 2, 3, 4, *., e', draw horizontal straight lines.
While the generating point is making one circuit of the axis
it moves through a vertical distance equal to a'-e'. Therefore,
since the two motions are uniform, while the generating point is
making any fractional part of the circuit it must move through
the same fractional part of the total vertical distance.
When the generating point is on H its horizontal projection is
at d, and its vertical projection is at d'.
When the generating point has made one eighth of its circuit
its horizontal projection will be at d,,. Its vertical projection must
be on a straight line through d,, perpendicular to G-L, and on
straight line through 1 parallel to G-L, and therefore at d".