[MONTGOLFIER BALLOONS.]
To project a pattern gore. With a radius of 5 inches, fig. 139, from the point a, on the line b o, describe a semicircle; divide the upper quadrant into three equal parts, in the points g, e, c. Carry the same distance, once down, to k. Draw the lines f g, d e, a c, h k, parallel to each other, and at right angles to the line b o. Draw the line a k, and prolong it to s, so that the distance k s shall be 10 inches, viz., twice the radius. From s, with the radius s k of 10 inches, describe the arc k n p. Draw o s parallel to h k; and, halfway between, m n.
As the distance from a to c is 5 inches, twice this will be 10, for the equatorial breadth of the gore; and, as it is intended to have 12 sheets of tissue paper (3 of each colour, yellow, blue, green, and red), and, consequently, 12 gores, 12 times 10 = 120, the half of which is 60, for the semi-circumference. Tissue paper is a very thin double-crown, 30 by 20. Lay down a straight line, b x, fig. 140, 60 inches in length, and divide it into 6 parts of 10 inches each; and draw parallels f g, d e, &c., at right angles to the meridian line b x. Measure the distance f g, fig. 139, and make f g, fig. 140, twice as much, half on each side; the same with d e, &c. Draw lines, connecting the extremities, till the fig. 140 is complete.
Instead of taking the trouble to construct fig. 139 with the compasses, the following measures will describe the pattern gore, fig. 140, at once; f g will be 5 inches, half to the left, half to the right, of the line b x; d e = 82⁄3 inches; a c = 10 inches; h k = 82⁄3 inches; m n = 7 inches; and o p = 63⁄4 inches.
These numbers are chosen to suit the size of the paper, to get the gores as large as possible, with the least waste: 60 inches are selected as the length of the gore, being twice the length of a sheet; 10 inches are 1⁄6 the length, and exactly half the breadth of the sheet; so the length and breadth are both employed, without the slightest waste.
The pattern gore should be of cartridge or imperial brown.
To Cut the Gores.
Lay the twelve sheets of tissue paper flat upon each other, as at fig. 141; cut the pattern gore into two pieces, along the line a c, fig. 140, and lay them on the tissue paper, fig. 141. Mark round them with a blacklead pencil, and cut them through with a strong pair of scissors.