The warp of a web being longitudinally stretched in parallel straight lines, and the woof or waft being inser ted at right angles to it, the substance produced as cloth will bear a strong analogy to the form of a raft of wood, consisting of two platforms of square beams, laid across each other and fastened together; or if we suppose that a number of cylindrical pieces of wood, such as the top masts or yards of a ship, are laid parallel to each other, and that cords or ropes are interwoven between them to keep them together, we shall have a very exact repre sentation of a piece of cloth, on a scale of such magnitude as will admit of all the proof of actual measurement. In cloth, even of the finest kinds, the length, breadth, and number of the component threads or cylinders, in the piece, may he ascertained with equal precision; but, from the smallness of the diameter of every thread, it becomes impossible to measure them actually, with any degree of accuracy. The length and the weight or mass, however, being known, the diameter may be found by a calculation, which hears evident marks of great exactness, and we may then safely assume that no difference can arise, pro vided the densities of all threads are the same. Upon this point, however, there has been some difference of opi nion, and the subject has been so little investigated in a scientific manner, that it would be perhaps presumptuous to draw any absolute conclusion upon the subject. We shall therefore only observe, that the argument upon which the increase of density in fine yarn above coarse chiefly rests, is this, that in spinning fine yarn, a greater number of revolutions of the wheel arc necessary to give the twist sufficiently to produce a sufficient cohesion of the fibres, than in coarse. This is incontrovertibly true; and as the filaments or fibres, by this twisting, assume the form of a screw orI I t_lo point to he decided is, simply whether, by this excess of twisting, the fibres of fine 'am are not brought more closely into contact than those of coarse ; and consequently that the diameter of the thread is diminished in the same proportion that the twisting is increased. It must be obvious, that where the
circumference exposes a small surface, many more re volutions will be required than where it presents a large one, before all the fibres can be sufficiently stretched ; and, consequently, that fine yarn will always require more twisting than coarse to give it the same tenacity. But as every thread, from the stoutest cable to the finest which human art and industry can produce, contracts in length, by the operation of twisting, there scents reason enough to conclude, that the compressing power ex erted acts either entirely upon the length, or that what is exerted on the diameter, must bear a very small pro portion indeed to the other. We may therefore infer, that the nearest approximation to actual truth will be, to consider a rope or thread like any other solid cylinder, and that the difference of density will not very material ly affect the calculation. Upon this principle we shall easily arrive at a very considerable degree of mathemati cal precision, and upon the whole come nearer to actu al truth, than by any other hypothesis yet known.
In Plate CXCIII. will be found some figures, expla natory of ti hat further remarks may be necessary on this subject as connected with fabric ; and it trill also be useful in conveying correct ideas of the varieties of tex ture most generally used, both in the substantial and flimsy descriptions of woven goods.
Figure 1st of Plate CXCII1. may be supposed to re present any solid body composed of various parts, lashed together. If the darkened squares are so many parallel beams of wood, connected by cordage, we arrive at once at a precise idea of texture. The length of these beams is known b) measurement ; the breadth of the whole of the aggregate number of pieces of wood, add ed to the space which the cords occupy between each, and which will be more or le.ss, in proportion to the thickness or diameter of these cords. It h also obvious,