e respective centres _v_ are
used for the parts from _w_ to _w'_ and from _t_ to _t'_ respectively.

[Illustration: Fig. 82.]

[Illustration: Fig. 83.]

The most correct method of drawing an ellipse is by means of an
instrument termed a trammel, which is shown in Figure 83. It consists of
a cross frame in which are two grooves, represented by the broad black
lines, one of which is at a right angle to the other. In these grooves
are closely fitted two sliding blocks, carrying pivots E F, which may be
fastened to the sliding blocks, while leaving them free to slide in the
grooves at any adjusted distance apart. These blocks carry an arm or rod
having a tracing point (as pen or pencil) at G. When this arm is swept
around by the operator, the blocks slide in the grooves and the
pen-point describes an ellipse whose proportion of width to length is
determined by the distance apart of the sliding blocks, and whose
dimensions are determined by the distance of the pen-point from the
sliding block. To set the instrument, draw lines representing the major
and minor axes of the required ellipse, and set off on these lines
(equidistant from their intersection), to mark the required length and
width of ellipse. Place the trammel so that the centre of its slots is
directly over the point or centre from which the axes are marked (which
may be done by setting the centres of the slots true to the lines
passing through the axis) and set the pivots as follows: Place the
pencil-point G so that it coincides with one of the points as C, and
place the pivot E so that it comes directly at the point of intersection
of the two slots, and fasten it there. Then turn the arm so that the
pencil-point G coincides with one of the points of the minor axis as D,
the arm lying parallel to B D, and place the pivot F over the centre of
the trammel and fasten it there, and the setting is complete.

[Illustration: Fig. 84.]

To draw a parabola mechanically: In Figure 84 C D is the width and H J
the height of the curve. Bisect H D in K. Draw the diagonal line J K
and draw K E, cutting K at a right angle to J K, and produce it in E.
With the radius H E, and from J as a centre, mark point F, which will be
the focus of the curve. At any convenient distance above J fasten a
straight-edge A B, setting it parallel to the base C D of the parabola.
Place a square S with its back against the straight-edge, setting the
edge O N coincident with the line J H. Place a