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 6, where sin 6 is the eccentricity of the 

 ellipse. Also 6 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 

 ^i be the point in which the ordinate through X meets the first circle and 

 X., be the point in which a ray drawn from X^ to the centre meets the second 

 circle. Then this point X 2 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. 



