When the cutting machine was completed, the given measure of was was effected by turning a handle or winch 18 revolutions. consequently 18 became the constant measure of the hvpothenue ; and from I: ese the i CI tical shift was equal to the perpendicular cf the triangle ; the horizontal shift to the base ; the angle of obliquity, contained between the base and hypotheouse. constituted the deviation from the horizontal line, and its comple ment the deviation from the perpendicular. If this table be geometrically examined, it will not be found abso lutely correct ; but taken as an appreximation for a prac tical purpose, its greatest del iation will not exceed part of an inch, which was deemed sufficiently near.
From this table a very correct practical rule was found for straight lines in direction of obliquity, and the curved lines were constructed in a similar man ner, by supposing every cm ve to be the arc of a circle of some specified dimension. That none of them could be geometrically circular, mill be obvious from the sim ple consideration, that be in ; a sin of loop or chainwork. the to nde Dry of the thread or yarn was always in a direct straight line when sire o bed, z nd consequently all circular curl, s were tis steel as inscribed polygons, the number of ii hose sides was to great, and the mea sure of each so minute, as to render the deviation from an actual circle imperceptible to thee ye.
The Pol•gonic Tables. a few of .vhich are annexed as specimens, were then calculated, to show by inspection the angle which each would form with it horizontal straight line, and these were instantly found merely by referring to the tables. In order to apply these tables to the formation of any pattern required, the usual and perhaps the easiest way, was generally to draw the pat tern upon a very enlarged scale. To calculate the num ber of loops required was the next object, and this in straight lines was easy from actual measurement, 32 loops being always allowed for an inch. The curves being always supposed to be arcs of some circle, were found by the common analogy which the circumference of a circle bears to the diameter, the medium propor tion as 115 to 355 being generally used. Were more minute calculation necessary, elliptical, parabolic, and hyperbolic curves, might have been very minutely found ; but it never appeared necessary in a business which only required a sufficient portion of accuracy to please the ey e, to expend time upon such extreme nicety. These
were the general rules observed in this business; and the Tables, with short explanations of each, will be found at the conclusion of the article.
The cloth frame being loosely suspended, and its mo tion regulated by the cylinder above, it was further sus pended by the centre from one end of the lever H, the other end of which was connected by means of two stout iron wires, with a piece of iron furnished with a small friction wheel, and acting on the rim of the perpendicular traverse wheel directly under its centre. The tendency of the frame to descend, produced a gentle pressure of the friction-wheel against the rim of the traverse, and according to its shape the frame was either lowered or raised at every shift of the wheel.
The communication between the cloth frame and the horizontal traverse, was effected merely by a small con necting bar of iron between the edge of the cloth frame and the wheel, the rod being placed directly level with the centre of the wheel. The pressure against the wheel was very simply effected, merely by tying a piece of whip cord to the frame, and after passing it over a pulley, suspending a small weight to the other extremity of the cord. A screw was also attached to the breast-beam, which the cloth frame could be raised at pleasure, to present fresh cloth, by shifting a notch in the suspensary rod C. Thus ten or twelve rows could be wrought with out shifting the beams upon which the cloth was stretch ed. The general motion was communicated by a leather belt passing over the pulley at N, and the machine could be engaged or disengaged at pleasure, by means very similar to those used for other machinery. When a flower was finished, the ratchet-wheel moved a small lever, which instantly stopped the machine, in order to prevent accidents. There were three treddles below, moved by 0 ipers upon the cross shaft, by which all the motions were given. The first, P 1, served to set fur the needle frame, so as to produce the perforation of the cloth by the needles; the second, P 2., set in mo tion that pat t of the machinery which supplied the needles with thread, and which is afterwards to be de scribed; and the third, P 3, moved the ratchet-wheel one tooth between every perforation. These were the chief motions in front of the machine. Some idea of those behind may he formed by inspecting Fig. 2, which is a eiew taken directly behind the machine.