68] THE REPRESENTATION OF THE CYLINDROID BY A CIRCLE. 61
If from any point X a perpendicular XR be let fall on AP, then the pitch
of the screw through X is XR tan 0, where sin 0 is the eccentricity of the
ellipse. Also 0 is the angle between the normal to the plane and the nodal
axis.
Fig. 17.
Let two circles be described, one with the major axis of the ellipse as
diameter and the other with the line joining the two foci as a diameter. Let
Xy be the point in which the ordinate through X meets the first circle and
X2 be the point in which a ray drawn from X} to the centre meets the second
circle. Then this point X2 on this inner circle will be exactly the circular
representation of the screws on the cylindroid with which this chapter com-
menced. There is only one such circle, for the distance between the foci is
the same for every tangential section, and so is the distance from the centre
to the axis of pitch.