These are not given for practical cutting, but are given as an example of scientific calculation in garment cutting. Although they are quite plain they may be called scientific conundrums, because the present generation of cutters knows nothing about them.
SCIENTIFIC CONUNDRUM IN THE SQUARE.
Mark a square of any unknown surface; divide one side into 20 equal parts, each part of which is a unit, or one number of the scale; use said 20 parts as a scale, representing the half breast circumference, and 2½ inches; with this scale make a diagram or draft of a vest, or coat, according to this work—all of which is done before the size of the square is known. When done, measure the square, or 20 parts of the scale, by inches.
Now, suppose the square turns out to be 20 inches; the size of the garment is 35 breast, or 17½ inches and 2½ inches. If the square turns out to be 22½ inches, the garment will be size 40, and so on, always 2½ sizes less than the square. If, however, the size of the square is too small to make a full size, multiply its units by any number whereby you can find a certain desired size. For instance: If the square contains 5 inches, each ¼ inch is a unit, or one part of the scale. Multiply the 5 inches by 4 and you have 20 inches. Now, take 4 units of the original, which represents here 1 inch, and your new scale will represent 20 inches divided into 20 parts, and will also cut size 35. If you multiply the 5-inch square by 3½, you will produce 18 inches, and if you take 3½ units as 1 unit, each unit will represent ¹⁄₂₀ of 18 inches, and the size of the garment will be 30½. If you multiply the 5 inches with 4½, you will obtain 22 inches, and by taking 4½ units as 1 unit for the scale, each unit will represent ¹⁄₂₀ part of 22 inches, and the size will be 39.
SCIENTIFIC CONUNDRUM IN THE CIRCLE.
Divide the half-diameter of a circle into 20 equal parts; then measure the half-diameter of the circle by inches, and if said result does not give a required size multiply the same as in a square; use the same units, and the same result will be obtained. All this must be done as in a square of 20, but afterwards the square of 17½ may be produced as shown in the diagram.
Fractional multiplication will result in the same thing, but may result in the fractional sizes, as 34½, 35¼ and 36¾, and so on. The six points of the compass will give all the base lines correctly on the square of 20 as well as on the square of 17½. It requires no scale, for one main point will give the other complete. The full diameter of the circle is 40 parts, and the triangle, as shown in Dia. [XII], contains 35, half of which is 20 and 17½, for which reason the square of 20 and the square of 17½ is adopted as a base.
With the aid of the above calculations a person can go to any cutter, obtain from him any graduated scale, and with it cut a garment before he knows the size thereof. Or he can select for himself a scale from any set for a certain size by simply finding a scale whose 20 units will correspond with the size. Should the scales contain too large or too small units, they may be multiplied or divided, and a new unit found by doubling or halving the units, or by dividing or multiplying them with any number, to gain the desired result.