154
THE THEORY OF SCREWS.
[160,
Explanation of Fig. 36.
General Section of the Cylindroid, showing—
(1) Cubic with the double point O.
(2) Asymptote of the cubic.
(3) The parabola, which is the envelope of the chords joining screws of equal pitch.
(4) Hyperbola having triple contact with the cubic, being envelope of reciprocal chords.
(5) Section of the principal plane. It is a tangent to the hyperbola.
(6) A tangent to the parabola, showing two screws, P and Q, of equal pitch.
(7) Common tangents to the parabola and the cubic, touching the latter at the two
principal screws.
(8) Any tangent to the hyperbola intersects the cubic in three points, two of which belong
to reciprocal screws (not shown).
Equations of Cubic.
x — '2y tan (0 - 25°),
= 20- 66 sin 20.
Equations of Hyperbola,
x = 1'6 ± 21'6 sec <p ± 47-5 tan ø,
y = - 12'8 + 32'8 sec <p.
Equation of Parabola.
y=-Sl-(5 + ^\\