Cotton Manufacturing - Christopher Parkinson Brooks

20’s cotton equals 30’s worsted,
(20 × 840)/560 = 30’s
20’s cotton equals 56’s linen,
300 : 840 :: 20’s : 56’s.
20’s cotton equals 20’s silk.
20’s English equals 16·93’s French.
1·18 : 1 :: 20’s : x
x = (1 × 20)/1·181 = 16·93

Double Yarns (Cotton).—Two-fold yarns are numbered according to the single yarn counts—thus, 2/80’s = two ends of 80’s twined together, which would wrap 40’s. Actually, to make the resultant count 40’s, the single yarn should be finer than 80’s, because the twist put in the folded yarn contracts it in length and causes the two-fold to be really coarser than would appear. However, neglecting this, suppose we twine one end of 40’s and one of 20’s, the counts would not be 15’s, as a first glance would indicate, but 13·33. This can be proved by taking the weight of a lea of 40 = 25 grains, and of 20’s = 50 grains; total, 75. 75 divided into 1000 gives the counts as 13-1/3. Another rule is, multiply the two counts and divide by their sum—

(40 × 20)/(40 + 20) = 800/60 = 13-1/3
3/300’s = 100’s.
3-fold yarn of 40’s, 80’s, and 120’s would be 21·81.
A lea of 40’s = 25 grains.
A lea of 80’s = 12-1/2 "
A lea of 120’s = 8-1/8 "
——
45-5/6
1000/(45-5/6) = 21·81

Or take the highest count and divide it by each of the others and by itself, then divide the total of the quotients into the highest—

120 ÷ 80 = 1-1/2
120 ÷ 40 = 3
120 ÷ 120 = 1
——
5-1/2
120/5-1/2 = 21·81

Testing Yarns.

In addition to wrapping warp yarn to ascertain actual counts, it is frequently tested as to strength; the lea from the reel is placed between two hooks on a testing machine, and by a wheel worm and screw the lower hook is moved downwards, increasing the tension on the yarn. By an index finger this tension is indicated on a face plate, and when the lea is broken the finger stops at the highest weight or strain that the yarn has stood. Below is a table, which will give a general idea of the comparative strength of mule twists, having, for the American cotton, the standard turns in—i.e., square root of counts multiplied by 3-3/4.

20’s	American Cotton	= 80lb.
30’s	American Cotton	= 54lb.
40’s {	American Cotton	= 40lb.
40’s {	Egyptian Cotton	= 50lb.
50’s {	American Cotton	= 28lb.
50’s {	Egyptian Cotton	= 37lb.
60’s	Egyptian Cotton	= 30lb.
70’s	Egyptian Cotton	= 26lb.

In yarn the diameters of the threads do not vary inversely as the counts, but inversely as the square root of the counts. Thus, 16’s is not four times as thick as 64’s, but twice as thick, the square roots being four and eight respectively.