Let A B C D in Fig. 470 represent the elevation of the article, of which A1KLB1MI is the plan. The plan is constructed by means of the centers O, P, F and F1, as indicated. The patterns, therefore, are struck by radii obtained from sections of the several cones of which the article is composed. At any convenient place draw the line P2 P1, Fig. 480, indefinitely, corresponding to P of the plan, and upon it construct a section of the article as it would appear if cut on the line A1 P of the plan. Therefore set off, at right angles to it, A2 P3, equal to A1 P. Make P3 D2 equal to the straight hight of the article, as shown by R D of the elevation. Make D2 A3 of the diagram equal to D1 P of the plan. Draw A2 A2, which will correspond to A D of the elevation, prolonging it until it meets P2 P1 in the point P1. Then P1 A2 is the radius of the outside line of the pattern of the portion between K and I of the plan, and P1 A3 is the radius of the line inside of the same part.
Fig. 479.-Plan and Elevation.
Fig. 480. - Diagram of Small Cone.
Fig. 481. - Diagram or Middle Cone.
Fig. 482. - Diagram of Large Cone.
An Oral or Egg-Shaped Flaring Pan.
In like manner draw the line O1 O2, Fig. 481, corresponding to 0 of the plan, and construct a section taken on the line O B1, as shown by O3 B3 C3 C3 Produce B2 C3 until it meets O3 O1 in the point O1. Then O1 C2 and O1 B2 are the radii of the pattern of that portion of the article contained between L and M of the plan.
Draw the line F3 F3, Fig. 482, which shall correspond to F or F1 of the plan. Make F3 E equal to the straight hight of the article, and lay off F3 L3 at right angles to it, equal to F1 L of the plan, and E l2 equal to F1l of the plan. Draw L3 l2, which produce until it meets F3 F2 in the point F2 Then F3 l2 and F2 L2, respectively, are the radii of the pattern of those parts shown by K L and I M of the plan.
To lay off the pattern after the several radii are obtained, as described above, draw any straight line, in length equal to F3 L3, as shown by F4 K in Fig. 483, and from F4 as center, with F2 l2 and F2 L3, Fig. 482, as radii, strike arcs, as shown by k1 l1 and K L1, which in length make equal to the corresponding arcs of the plan K L and k l, as shown. Draw L1 F4, and upon it set off from l1 toward F4, a distance equal to 0' C3 of Fig. 481, establishing the point 03, from which strike the arc l1 m1 in length equal to l m of the plan. In like manner, from the same center, with radius O1 B2, of Fig. 481, strike the arc L1 M1, equal in length to L M of the plan. Draw M1 O3, which produce in the direction of F5 making M1 F1 equal to K F4, from which center continue the inner line of the pattern, as shown by m1 i1 which in length must equal m i of the plan. In like manner, from the same center, with radius F3 L3 of Fig 482, describe the arc M1 F1 and draw I1 F5 Set off on this line from i' a distance equal to P1 A3 of Fig. 480, thus establishing the center P3. Describe the arc i k, in length equal to i k of the plan. In like manner, from the same center, with the radius P1 A3 of Fig. 480 describe the arc I1 K1, in the length equal to I K of the plan. Place the straight edge against the points P3 and K3 and draw K3 k, thus completing the pattern.
From inspection it is evident that the pattern might have been commenced at any other point as well as at K k of the plan. If the joint is desired upon any of the other divisions between the arcs, as L l, M m, or I i, the method of obtaining it will be so nearly the same as above narrated as not to require special description. If the joint is wanted at some point in one of the arcs of the plan, as, for example, at X x, draw the line X x across the plan, producing it until it meets the center by which that are of the plan is struck. In laying off the pattern, commence with a line corresponding to X F1, in place of F4 K1, and from it lay off an arc corresponding to the portion of the arc in the plan intercepted by X x, as shown by X L l x. Proceed in other respects the same as above described until the line k K2 is obtained, against which there must be added an arc corresponding to the amount cut from the first part of the plan by X x, as above described, or, in other words, equal to X K k x; of the plan.
Fig. 483. - The Pattern of an Oval or Egg-Shaped Flaring Pan,