119 (#173) ############################################ WOOLLEN YARN SPINNING o 43 43.8 Thus if 4° (Ex. 4) is the drafting angle, the following deduc- tions may be made :- D* 43 = T whence II x Cot. of O 3•14 Cot. 4° 43 = I turn per i in. to give 4º. 3.14 X 14 For ist 18 in. (no draft) 18 X I 18 turns of spindle For ist and 2nd 18 in. (2 draft) 36 X 1.4 = 50 turns of spindle For ist, 2nd, and 3rd 18 in. (1} draft) 54 X 1•7 = 92 turns of spindle For ist, 2nd, 3rd, and 4th 18 in. (1š draft) 72 x 2 = 144 turns of spindle To effect the insertion of this necessary twist with an actual regular turning of the spindle, it is obvious that the speed of the carriage must be so reduced that the second movement of 18 in. occupies V2 of the time the first 18 in. took; the third movement of 18 in. takes V3 of the time of the first 18 in.; and the fourth movement of 18 in. takes ~ 4 of the time of the first 18 in. If now it be taken that the spindles turn once per second it will be obvious that- the ist period of 18 in. will require 18 secs. the 2nd 18 in. 50 18 = 32 secs. the 3rd 18 in. 92 50 42 secs. 18 in. 144 92 52 secs. seconds for completion 144 : The time taken for each period may be put into the form- (18 * I) VI 18 seconds for 18 in. (18 x 2) v2 = 50 seconds for 36 in. (18 x 3) V3 92 seconds for 54 in. (18 x 4) VA 144 seconds for 72 in. from which the general rule may be adduced that - the 4th . See p. 292. 119
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