Obtaining Moulds

of the semi-cone. Next describe the plan of the frame (it may be pointed out here that this all might be done upon the original plan ; a separate drawing is used only to avoid confusion of lines). and set off upon the development along the radiating lines points at a like distance front the edge of the envelope that the edges of the frame are, in plan from the line a b as measured on the correspondingly numbered radial line, and so obtain a series of points through which to draw the mould. For example, points 2-x-o on the development are made equal to points z-x- o in the plan.

To obtain the Face Mould of Frame, Fig. 6.—Again draw f he plan of trame and the containing cone. Assuming the head to be made in two pieces, which it may easily be, draw the line i-a, joining the extremities of the curve; parallel with this draw a second line tangent to the curve. This shows thickness of stuff required to get the head out of. Next divide the line i-a into a number of parts, as a, b, c, d, e. Through these points draw perpendiculars to the centre line A-1, cutting the side of the cone ; with the points i. 3. 4,5 upon the centre line as centres, and the distance of each point from the side of the cone as radii, describe arcs as shown in dotted lines. Intersect these by projectors from the points b, c, d, I, drawn parallel with the centre line A-C, thus obtaining points i', 2', 3', 4', 5'. Next erect perpendiculars to 1 -a from points 1, d. c, b, a, and make them equal in length to the similarly numbered dotted ordinates in the plan, and draw the curve through the points so found. In practice the back edge would be gauged parallel from the front, but geometrically it may be obtained in like manner to the soffit edge by producing the projectors as shown at 2', 3", 4" 5".

The principle upon which the above construction is based is that any section of a cone passing through both sides, as shown by the line a-i produced, forms an ellipse ; also any section of a cone parallel with its end or perpendicular-to its axis is a circle (in the case of a semi-cone, a semicircle). If then we iind the size of the cone at various

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