Non-homocentric Pencils. (OL 
Any form being assigned to the section by a plane per- 
endicular to the axis, and the position of the focal lines 
relative to the plane being defined, it is easy, by drawing 
Pigwl. 
{o) 


R 
plans and elevations of the rays through a number of points 
on the boundary of the section, to obtain graphically the 
section by any other plane parallel to the first. The two 
sections being drawn on card or metal, and erected in the 
correct relative positions, corresponding points may be 
joined by threads or wires and a model of the rays obtained. 
Model 1 represents the bounding surface of a pencil of 
elliptic section. The construction was simplified by taking 
for the first section an ellipse with its horizontal axis twice 
the length of its vertical axis, and letting the focal lines 
divide the distance between the two sections into three 
equal parts, the horizontal line being nearer the first section ; 
the second section is an equal and similar ellipse, with its 
longer axis vertical. 
Model 2 represents a pencil of rectangular section, and was 
constructed in a similar way. 
