This section is from the book "Practical Sheet And Plate Metal Work", by Evan A. Atkins. Also available from Amazon: Practical Sheet And Plate Metal Work.

An article may take the shape of a portion of an elliptical cone of the above description - that is, one whose centre line is not square to the base.

The setting out of the pattern for an object of this character can be done in a similar mariner to that shown in connection with the oblique cone (Chapter XVIII (Articles Of Unequal Overhang. Oblique Cone).). A side-elevation is first drawn (Fig. 172) and the half-plan of the top. The line T t is drawn up square to 0 6 produced, and then with t as centre and t 1, t 2, etc., as radii, the points are turned down on to 0 6, giving the points 1', 2', etc. These latter points are then joined to T. Now, using T as centre and T 0, T 1', as radii, the arcs of circles are swept out. The compasses are next fixed to the length of one of the six parts of the semi-ellipse, and, commencing at 0 on the pattern, the points 1, 2, 3, etc., are stepped from arc to arc. The inner curve is obtained by drawing the radial lines on the pattern and cutting these by the arcs run around from the points where the corresponding lines intersect the bottom line a d.

Fig, 171.

The ends of the frustum will, of course, be similar in shape, and if it is desired to obtain the width of the ellipse at the bottom, this can be done by drawing c b' square to T c, and making c b' equal to c 3, joining b' to T, and then drawing c' b" square to T c', then c' b" will be the half width of the ellipse at the bottom of the frustum.

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