Pattern of Spout.—The arc of stretchout, Fig. 173, is drawn with a radius equal to the slant height of the cone, and with the apex as a center. The spacing of the half-profile is transferred to this arc with numbers to correspond. Where extension lines from points a, b, and c cut the slant height of the elevation, extension arcs are drawn over into the stretchout. All intersections should be traced out by starting from the profile, following each extension line to the miter line, and thence to a correspondingly numbered line in the stretchout. The miter cut of the pattern is obtained by tracing a curved line through these intersections. An arc whose radius is equal to the distance from the apex to the end of the spout completes the pattern. A lock on each side of the spout and a hem on the small end of the spout are added. A flange (not shown) should be added to the miter cut.
The Opening.—Upon any straight line, the distances a to b and b to c of Fig. 172 are set off. Since this is but half of the opening, this operation must be repeated as shown in Fig. 174. Measuring lines are drawn through each of these points. Upon the lines a the distance from point 2 to the center line of the half-profile of Fig. 172 is set off. Upon the lines a, the distance from point 1 to the center line of the half-profile of Fig. 172 is set off. Points c fall upon the center line of Fig. 174. A curve traced through the points thus obtained will give the shape of the opening.
The Funnel.—One side of the funnel should be extended inward until it meets the center line of the barrel. This will locate the apex of the whole cone, of which the frustum is a part. With any convenient point as a center, and a radius equal to the distance from this apex to the large end of the funnel, an arc of stretchout. Fig. 175, is drawn. A quarter-profile is placed above the elevation of the funnel in Fig. 171. This is divided into three equal parts. Since this is but a quarter-profile, twelve spaces must be transferred to the arc of stretchout in Fig. 175. The first and last points are connected to the apex by means of straight lines. The pattern is completed by an arc, drawn from the center of Fig. 175, whose radius is equal to the distance from the apex of the funnel to the point F in Fig. 171. The necessary locks and wire edge should be added.
58. Related Mathematics on Boat Pump.—Problem 30A.—The barrel of the boat pump is a cylinder whose diameter is 4″ and
