In Fig. 449 let A B C be the elevation of the cone and D E F the plan of the same. To obtain the envelope set the compasses to the space B A, or the slant hight of the cone, as a radius, and from any convenient point as center, as B1 of Fig. 450, strike an arc indefinitely. Connect one end of the arc with the center, as shown by A1 B1.

With the dividers, using as small a space as is convenient, step off the circumference of the plan D E F, counting the spaces until the whole, or exactly one half, is completed, as shown in the upper half of the plan. Then set off on the arc A1 C1 of the pattern, commencing at A1, the same number of spaces as is contained in the entire circumference of the plan. Connect the last point C with the center B1. Then B1 A1 C1 will be the pattern for the envelope of the cone ABC.

Fig. 449.   Plan and Elevation.

Fig. 449. - Plan and Elevation.

Fig. 450  Pattern.

Fig. 450 -Pattern.

The Envelope of a Right Cone.

It is not necessary that all of the spaces used in measuring the circumference of the plan should be equal. It frequently happens that when the space assumed between the points of the dividers has been stepped off upon the circumference of the base, a space will remain at the finish smaller than that originally assumed. In that case the required number of full spaces can be stepped off upon the arc of the pattern, after which the remaining small space may be added, thus completing the correct measurement of the pattern.