Having now got a quarter of the pattern, it must be cut round, as shown, and transferred to the three other quarters, marked respectively in the figure A, B, C, which will be the pattern for a sphere. This is technically known as striking out a pattern gore by an intersection of lines, and this is quite near enough for the paper balloons, on which you must practise until you are sufficiently advanced in the science to enable you to begin on the proper material. There is another method which is still more accurate, in fact, will ensure absolute mathematical correctness, and that is by a calculation of a series of decimals corresponding with each of the seventeen perpendicular lines shown beneath ([Fig. 4]).
Fig. 4.
Suppose, for example, that the diameter of the balloon to be constructed is 20 ft., and that it is required to make it of 12 pieces; then, in order to draw the pattern for those pieces, find the circumference of the balloon, which is 62·83 ft., and, dividing it by 4, the quotient is 15·7 ft. Make, therefore, A D equal to 15·7 ft., and D E likewise of the same length. Divide the circumference, 62·83 ft., by 24, which is double the number of pieces that are to form the balloon, and the quotient, 2·618 ft., is the length of D C, and likewise of B D, so that B C is equal to 5·236 ft. Then, having divided the line A D into 18 equal parts, and having drawn the parallel lines from those points of division, find the length of each of those lines by multiplying 2·618 by the decimals annexed to that line. Thus 2·618, multiplied by 0·99619, gives 2·608 ft. for the length of f g, and, again multiplying 2·618 by 0·98481, the result gives 2·578 ft. for the length of h i, and so of the rest. In cutting the pieces after such a pattern, care should be taken to leave them about three-quarters of an inch all round wider than the pattern, which will be taken up by the seams; and the same rule must be borne in mind whether you are experimenting upon paper patterns, or upon the materials required for a large balloon. [Fig. 4] will illustrate the foregoing instruction, and those who like to take the trouble to prove the sum will take all the more interest in the manufacture of their balloon.
These decimals have been calculated by a mathematician, and are available for any sized balloon.
Fig. 5.
Now we come to the neck, the pattern of which may be drawn with a free hand, and maybe left to your own fancy, with this proviso—that the length ought not to exceed more than one-fifth of the whole length of the pattern. In [Fig. 5] you will see what the neck should be, the dotted line showing the spherical portion of the pattern gore.
Small gas-balloons are generally made of tissue-paper, varnished over with boiled oil, which gives them a very transparent and skin-like effect. Sometimes gold-beater’s skin is used, but it is very expensive, and paper answers the same purpose. Supposing that you are about to begin upon a paper balloon, the first thing to be done, before making your pattern gore, is of course to select your paper. Ordinary tissue is manufactured from the size of 20 × 30 inches square. There are other sizes made of a stronger quality, suitable for larger balloons than that of three feet circumference, upon which I recommend you to practise, as this is a handy size, while the above-sized paper—obtainable everywhere—cuts in well for the width to make the pattern gore, though, for length, you will have, probably, to paste two sheets together.
When you have a sufficient number of lengths ready for cutting out, place them, one on the top of another, on a flat board; then place the pattern gore on the top, and, with a sharp knife or razor, cut the whole out at once, taking care not to cut the pattern gore. You will do well also to place a few weights on the top to keep the whole lot in place. After you have cut one edge, move your pattern about a quarter of an inch away from the edge that is cut. This is to allow for the ‘lap,’ as it is called, whether in pasting a small balloon or sewing a large one, for bringing the gores together in case you have not made such allowance on the pattern. In pasting together—in the case of paper balloons, or sewing in the case of larger balloons—you should take care, for the sake of effect, to do so in alternate colours. Red and white, yellow and white, green and black, all make effective contrasts, but these minor details may be safely left to your own taste. Paste them, first in pairs, then in fours, &c., in the following manner. Having provided yourself with a large, smooth pasteboard, begin by laying upon it a white gore, and then place carefully over it a coloured one, showing the ‘lap’ on the one underneath to allow for the folding. You can do this by carefully manipulating the gores with the fingers, or, still better, by the means of a palette or any other flat knife. Then, with a ‘dabber,’ as it is technically termed—a clean duster will answer the purpose—press down the overlapping seam the whole length, and immediately hang it up to dry, and proceed to do the same thing with the others, never attempting to paste others together until the first are perfectly secure by drying. A little alum should be put into the paste you are using for the purpose.