Previous to entering into any detail of other particu lars, we shall lay before our readers such general remarks as occur upon what is termed the fabric of cloth ; a mat ter which we conceive to be not only of the most essential importance, but which has been most unaccountably ne glected, even by those who practise the manufacture, and who, with I cry few exceptions, regulate their opera tions in this respect by no fixed or determinate rule, but generally are contented merely to copy what they are taught, without any other guide to detect error, than actual experience, which very frequently is dearly pur chased. Vet we conceive it possible, that this important point may be reduced to such a degree of mathematical precision, as might render it capable of conclusive de monstration, or at least that the approximation may he so near, as to guard the person who will be at pains to adopt it, from almost the slightest danger of great error, even in regulating the fabric of any species of cloth to which he has not been previously accustomed. For the better understanding of this method, it may be necessary to consider, very briefly, that quality of yarn, which is called its grist or fineness.
If a thread of yarn be considered as a cylinder, its weight must be in the compound ratio of its magnitude and density. Now, yarn being made up in hanks of a determinate length, this length may be considered as the altitude of the cylinder, and consequently its grist or fineness is the area of the base ; and then as the areas of cylinders are in proportion to their circumscribing squares, the square root of the square will be equal to the diameter of the base. When yarn of any kind is warped, and stretched in a loom, to undergo the sub sequent operation of being woven into cloth, the threads which compose the warp arc parallel to each other, and their parallel situation is preserved by the utensil called the reed, through the intervals between the divisions of which a certain number of threads pass, The number of divisions in this reed, therefore, ascertains the num her of threads of warp which are to be woven into cloth of any determinate breadth. Now the breadth of every thread or cylinder being the diameter of its base, and the reed being the scale which regulates the number of these threads in a given measure, the ratio which the one bears to the other ascertains the number of threads, and their contiguity to each other in the cloth. Let then the square root of the mass in any determinate length of yarn be taken as the measure of the diameter of the base of a thread, and let the number of the reed which will form a proper fabric be known, and any other will be found to form a similar fabric. From this arises a very simple
analogy or proportion, which may be thus stated : Let the weight of one kind of yarn be expressed by a, and that of another by b. Let a be properly woven in a reed or scale, which contains 1200 intervals or divisions, in 37 inches, which is the common measure of the linen reed. Then to ascertain the proper reed for b, the proportion will be as ? a is to 1200 so is V b to the reed required. Hence as a is to 144, so is b to the square of the reed required. Suppose now that a represents cotton yarn No. 60, and b represents No. 100, then As 60 : 144 : : 100 : 14,400, the root being 15.49 nearly, which is the answer. From this the following simple arithmetical proportion will arise for practical use.
1st, If the yarn is known, and the number of the reed wanted, As the name or designation of the first yarn given To the square of the given reed, So is the name or designation of the second yarn To the square of the reed required.
2d, If, as before, the yarn and reed are known, and the yarn wanted to fit any other reed, As the square of the given reed To the yarn, So is the square of the other reed To the yarn required.
In actual practice, the following objection, which is very plausible, will readily occur to practical manufac turers, and, at first sight, will probably induce almost the whole of them to reject these rules as erroneous and inconclusive. They will assert, and with truth, that a manufacturer who would implicitly adopt and follow these rules, would either make all his fine goods so dense and heavy in the fabric as to disgust his customers, or that his coarse goods would be so flimsy in the texture, as to be totally useless. To this it is only necessary to reply, that it arises from no error in the calculation, nor want of truth in the general principle, but in what was premised as a general requisite in cloth at the outset ; namely, that durability and thickness is the first object in coarse goods, and beauty and transparency in fine. It would afford but a slender recommendation to a birth-day dress, to possess that warmth and durability which would form the chief excellence of a watch-coat, or blanket ; and it would be equally useless, to give to the coarse ma nufacture, which is valuable in proportion to the shelter which it affords from the inclemency of wind and wea ther, qualities which could only afford gratification to the eye, by the sacrifice of every comfort.