In Fig. 651, C A B D represents the front elevation of a hood such as is frequently used upon a portable forge, KLMN its plan and E F H J a its side view. The opening A B at the top of the hood is round, as shown by L P of the plan, while the base C D where it joins the forge is nearly semi-elliptical, as shown, by K L M of the plan. In the side elevation E a shows the amount of flare and projection of the front of the hood, while the opening, shown in the front by C S D, appears as a simple straight line, a J. With these conditions given, the arch of the opening C S D of the front elevation can be determined in connection with the plan, by projection, as shown by the horizontal dotted lines, while if the arch of the front elevation be assumed arbitrarily then its line (a J) in the side view must be obtained by projection, and will be either straight or curved according to the nature of the curve employed in the front elevation,

Assuming the straight line a J of the side view as the true profile of the arch, its curve in either the front elevation or the plan must he determined, as a means of obtaining the pattern. As the flaring portion of the hood very much resembles a conical frustum having an oblique base, probably the simplest method of arriving at its true shape is to first determine the plan of this irregular frustum of which it is a part. Therefore produce the oblique line E a of the side elevation until it intersects the base line H J extended in the point G. Next set off from L on the center line of the plan a distance equal to H G of the side elevation, thus locating the point E. Through R, from a center to be determined upon the center line, draw the curve forming the front of the plan, with such length of radius as will make an easy junction with the curves of the back at K and M. It is not necessary that the curve K R M should be a perfect circle throughout; it may change as it approaches K and M so as to flow smoothly into the assumed curve of the back. It is simply necessary that no angle be produced at K and M, as such an angle would be continued through the surface of the hood toward the opening of the top.

Fig. 651. - Front and Side Elevations and Plan of Hood, Showing System of Triangulation.

Divide the circle of the top P L into any convenient num-ber of equal spaces, as shown by the small figures; also divide the outer curve of the plan R M L into the same number of spaces. For accuracy and convenience it will be found advisable to make the spaces shorter as the curve increases from M toward L until the end of the curve is reached at the point 11. Connect points of similar number in the two curves by solid lines, as shown; also connect points in the plan of the top with points of the next higher number in the plan of the base by dotted lines. In order to produce the curve of the opening correctly in the plan and the front elevation it will be necessary first to draw upon the side elevation lines corresponding to the solid lines just drawn across the plan. To accomplish this place the T-square at right angles to L R of the plan, and, bringing it successively against the points in the plan of the base R M L, drop corresponding points on L R, as shown. Transfer the spaces thus produced to the base line H G of the side elevation, numbering each point to correspond with the plan. By means of the T-square placed as before, drop points from the plan of the top to the center line L P (omitted in the drawing to avoid confusion of lines) and transfer the same to the line F E of the side elevation, numbering each point as before. Now connect points of corresponding number in the upper and lower lines of the side elevation by solid lines, as shown; then will these lines be the elevations of the solid lines drawn across the plan.

It may be here remarked that, as the pattern will be obtained from the plan, a correct front elevation of the opening, or arch, is not necessary to the work, but it it is desired it can ho obtained in the following manner: Place the T-square parallel to L R of the plan and, bringing it against the points in the plan of the base between R and M, drop corresponding points on the base line C D of the front elevation. Also in the same manner drop points from the curve of the top L P in plan upon A B of the front elevation, and connect points of corresponding number in the two lines by solid lines, as shown. From the points of intersection of the solid lines in the side elevation with the line a J (the profile of the arch), a, b, c, etc., carry lines horizontally across, as shown, intersecting them with lines of corresponding number in the front elevation. A line traced through the points of intersection as shown from S to D, will be the correct elevation of the opening in the front of the hood.

Fig. 652. - Diagrams of. Triangles.

The correct plan of the opening may be obtained by placing the T-square parallel to L R and bringing it against the various points of intersection through which the curve S D was traced and cutting the solid lines of corresponding number in the plan, giving the points a. b, c, etc. In case the development of the curve S D has been omitted, measure the horizontal distance of each of the points a, b, c, etc., in a J of the side elevation from the line F H and set off the same on the center line of the plan from L toward N. Thus the horizontal distance of point a from the line F H is set off from L on the center line of the plan, thus locating the point N or a, the extreme point of projection of the hood. In the same manner the projections of points b, c, etc., of the side elevation, or in other words, their distances from F H are set off from L of the plan, as shown between N and T. Now place the T-square at right angles to L Rand, bringing it against these points last obtained, cut the corresponding solid lines of the plan, thus locating the points a. b, c, etc., of the plan, as before. A line traced through these points will be the correct plan of the curve of the opening.

Before the pattern can be begun it will be necessary to first obtain the correct distances represented by the solid and dotted lines across the plan. This is accomplished by means of two diagrams of triangles, shown in Pig. 652, as follows: Draw the vertical line A B, in length corresponding to the hight of the hood, as indicated by F H in the side elevation. At right angles to A B draw B C, in length corresponding to P R or 1 1 of the solid lines of the plan. From B set off also the spaces B 2, B 3, B 4, etc., corresponding in length to the lines 2 2, 3 3, 4 4, etc., of the plan. Connect the points in B C with the point A by solid lines. Then will these lines represent the true distances between points 1 and 1, 2 and 2, etc., of the plan. The second diagram of triangles is constructed in a similar manner. The vertical line E D is drawn, equal to F H of the side elevation. E F is- set off at right angles to it, in length equal to the dotted line 1 2 of the plan. From E are set off the distances E 3, E 4, etc., corresponding to the lines 2 3, 3 4, etc., of the plan. The points thus established in F E are then connected with D by means of dotted lines. Then will these lines represent the true distances between points 1 and 2, 2 and 3, etc.,-of the plan.

Fig. 653. - Pattern of Hood.

To develop the pattern, first draw any vertical line, as L Z of Fig. 653, representing the center of the hack, which make equal to the hight of the hood F H. As the base of the hood is perfectly straight from L to the point 11, set off on a horizontal line from the point Z, in Fig. 653, a distance equal to L 11 of the plan, and draw 11 L of the pattern. With L as center, and 11 10 of the small circle in plan as radius, describe a short arc. Then, from 11 of the base in pattern as center, and 11 D of the second diagram of triangles as radius, describe a short arc intersecting the one first drawn, thus establishing the point 10 of the upper line of the pattern. Then from this point as center, with A 10 of the first set of triangles as radius, describe a short arc, and from 11 of the base of the triangular portion of the pattern, with 11 10 of the outer curve of the plan as radius, describe another arc intersecting it, thus establishing the point 10 in the lower line of the pattern. Proceed in this manner, using alternately the spaces in the inner line of the plan, the hypothe-nuses of the dotted triangles, the hypothenuses of the triangles indicated by solid lines, and the spaces in the outer line of the plan, obtaining the several points, as shown. Then lines traced through these points will be the pattern of the envelope of the shape indicated by F E G H of the side elevation, or in other words, of the frustum of which the hood forms a part. It now remains to cut away such a portion of this pattern as represents the part G a J of the side elevation. To accomplish this it is simply necessary to obtain the positions of the points a, b, c, etc., of the plan and side elevation upon the lines 11,2 2. 3 3, etc., of the pattern.

With the blade of the T-square set parallel to the base line G H of the side elevation bring it against the points of intersection made by the line a J with the radial lines, and cut the vertical line F H, as shown by the short dashes drawn through it. Transfer the points thus obtained in F H to the vertical line A B of the first set of triangles. Then with the blade of the T-square at right angles to A B, and brought successively against the points in it, cut the hypothenuses of the several triangles corresponding in number to the lines from which the points were derived in the side elevation, all as indicated by the letters a, b, c, d, e and f. The distances of these points from A may now be transferred to lines of corresponding number in the pattern, measuring from the upper line, as shown by a, b, c, etc. Then a line traced through these points, as shown from N to M, will give the shape of the front or arch of the hood, and L P N M Z will be the half pattern of the hood.