712 



C H A I N W O R K. 



T*ambour- and, on the contrary, the resolution of any one direct 

 ing- force into any two oblique forces ; which composition 

 """Y"" ' and resolution are abundantly confirmed from me- 

 chanics." 



Upon the application of this theorem, that pro- 

 found and illustrious philosopher founded the first 

 rational and satisfactory explanation of the causes of 

 the elliptical orbits of the planets, and accounted for 

 the causes by which the whole system of the universe 

 is regulated } and the recent discoveries of La Place, 

 and other eminent philosophers of the French school, 

 are merely extensions of the same general law, invol- 

 ving the effects produced by the gravitation of the 

 planets towards each other, as well as towards the 

 sun. To apply this principle to the construction of 

 the tambour machine, or any other requiring exten- 

 sively varied motion, it was only necessary to produce 

 two direct motions, which, as being the most simple 

 and efficient mode of construction, were placed at 

 right angles to each other, one being in a vertical, 

 and the other in a horizontal direction ; and as it is 

 easier to communicate motion to one body than to 

 many, it was found better that the motions which 

 produced a relative change of position between the 

 cloth and the needles, so as to regulate the successive 

 points of perforation, should be given to the former 

 rather than to the latter. In the first construction of 

 the machine, the motion given to the cloth frame 

 was effected by two screws, one placed vertically, and 

 the other horizontally. As the machine in this state 

 was wrought by the operator's hands and feet, and 

 entirely under the guidance of his discretion, the 

 screws were turned by his hands, by two small 

 winches, so calculated, that when either winch was 

 turned to the extent of a quarter or quadrant of one 

 revolution, a shift of the cloth, equal to ^d part of 

 an inch, was produced. This was found a proper 

 length when the motion was directly given by one 

 screw, either vertically or horizontally. But when 

 any intermediate angle was to be formed, it required 

 that the shift should be less in both screws, as the 

 oblique line produced by the combined action of both 

 screws was always greater than either side apart, in 

 the same ratio that the hypothenuse of a right angled 

 triangle exceeds that of either of the sides. When 

 the screws were judiciously turned, this operation 

 suceeded very well ; but as the ratio of the one to 

 the other constantly varied, even the most care- 

 ful operators, totally ignorant of the most simple 

 elementary principles of trigonometry, were in con- 

 stant danger of error ; and when entrusted to women 

 or boys, which considerations of economy rendered 

 peculiarly desirable, it was found impossible to place 

 much reliance upon the quality and regularity of the 

 work. These reasons, therefore, induced the inven- 

 tor seriously to endeavour to find some remedy, which, 

 by fixing the motions of the machine under regular 

 mechanical laws, should entirely remove both the 

 blunders and inaccuracies of human agency, and this 

 he was enabled to effect by removing the screws, and 

 substituting the traverse wheels. When this point 

 was gahied, very little more was necessary to render 

 the machine entirely automatic, and this was speedily 

 effected. 



In order to form a rule by which a pair of wheels 

 may be formed, to produce a straight line at any 



angle of obliquity, nothing more was necessary Tambour-, 

 than to construct a table of trigonometrical calcula- in S- 

 tions from 1 to 89 inclusive, the measure of the S *^Y-^" / 

 hypothenuse being always the side given = T V of an 

 inch ; but to execute such minute measures with ac- 

 curacy, it became necessary to invent a machine for 

 the regulation of those divisions. In order to effect 

 this, he availed himself partly of the principle of the 

 common clock-makers' cutting engine, and partly of 

 the best description which he could find of Mr Rams- 

 den's celebrated machine for dividing astronomical 

 instruments. Combining these with such variations 

 as suited his particular object, he contrived a cutting 

 engine, by which he was enabled to cut with consi- 

 derable precision and accuracy to divisions so mi- 

 nute as the 1200th part of an inch, and this was 

 found quite competent for every practical purpose. 



When the cutting machine was completed, the 

 given measure of -fa was effected by turning a handle 

 or winch 18 revolutions, consequently 18 became 

 the constant measure of the hypothenuse ; and from 

 these the vertical shift was equal to the perpendicu- 

 lar of the triangle ; the horizontal shift to the base ; the 

 angle of obliquity, contained between the base and 

 hypothenuse, constituted the deviation from the ho- 

 rizontal line, and its complement the deviation from 

 the perpendicular. If this table be geometrically ex- 

 amined, it will not be found absolutely correct ; but 

 taken as an approximation for a practical purpose, its 

 greatest deviation will not exceed T ^g-th part of an 

 inch, which was deemed sufficiently near. 



From this table a very correct practical rule was 

 found for straight lines in every direction of obli- 

 quity, and the curved lines were constructed in a si- 

 milar manner, by supposing every curve to be the 

 arc of a circle of some specified dimension. That 

 none of them could be geometrically circular, will be 

 obvious from the simple consideration, that being a 

 succession of loop or chainvvork, the tendency of the 

 thread or yarn was always in a direct straight line 

 when stretched, and consequently all circular curve* 

 were treated as inscribed polygons, the number of 

 whose sides was so great, and the measure of each so 

 minute, as to render the deviation from an actual 

 circle imperceptible to the eye. 



The Polygonic Tables, a few of which are annexed 

 as specimens, were then calculated, to show by in- 

 spection the angle which each would form with a 

 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 pattern upon a very enlarged 

 scale. To calculate the number 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 sup- 

 posed to be arcs of some circle, were found by the 

 common analogy which the circumference of a circle 

 bears to the diameter, the medium proportion as 115 

 to 355 being generally used. Were more minute 

 calculation necessary, elliptical, parabolic, and hyper- 

 bolic 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 eye, to expend time upon such extreme nicety. 

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