Among cotton looms the positive take-up motion is generally used. The cloth as woven is, by this arrangement, drawn on the cloth roller a certain distance at every pick, the amount of take-up being regulated by wheels. Fig. 26 shows a sketch of the arrangement. The construction is similar for almost all looms, but there are different gears and sizes of wheels used. In Dickinson’s gear the rack wheel of 50 teeth receives its motion from a pawl, worked by one of the slay swords. On the same stud is the change wheel: this gears with the stud wheel, 100 teeth, firmly connected with the pinion of 12 teeth, driving the beam wheel 75. The beam or sand roller is 15 inches in circumference, and is covered with glued sand, perforated tin, or some pointed substance, to hold the cloth firmly. The fabric is wound on the cloth roller below this by means of contact with the sand roller. The change wheel is varied to give changes of picks in the cloth, a larger wheel giving fewer picks in the quarter inch. Each gear has a constant number associated with it, called a dividend. If the number of teeth in the change wheel be divided into this dividend, it gives the picks in a quarter inch of cloth. Imagining that a change wheel, having the effect of only one tooth in a revolution, could be applied, then the dividend is the number of picks that the loom would run before the sand roller advanced a quarter of an inch. Suppose 528 dividend is taken, this represents a change wheel supposed to have one tooth. If a wheel of 66 teeth be put on, only 1/66 as many picks to the quarter will be inserted--_i.e._, 528/66 = 8 picks. The method of obtaining the dividend for any ordinary gear is-- (Rack wheel × Carrier wheel × Beam wheel)/ (Pinion wheel × number of 1/4 inches in circumference of taking-up roller) afterwards adding 1-1/2 per cent. for shrinkage of the cloth after being released from the tension of the loom. Thus, Dickinson’s gear is-- (50 × 75 × 100)/(12 × 60) = 520. Add 1-1/2 per cent. = 7.8 ----- Dividend 527.8 The principal gears in use in Lancashire are:--