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 " " = 54lb. 40’s { " " = 40lb. { Egyptian " = 50lb. 50’s { American " = 28lb. { Egyptian " = 37lb. 60’s " " = 30lb. 70’s " " = 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. REED COUNTING. Before entering into the calculations regarding the weight of cloth, it is necessary to familiarise ourselves with some method of counting the ends of warp in the cloth. On the Exchange the system adopted both for ends and pick is their number per quarter inch--_e.g._, a 16 by 14 means 16 ends per 1/4-inch, or 14 picks per quarter. The methods used in the manufactory are based on the counts of reed. Formerly many systems of reed counts prevailed, each town or district having a method peculiar to itself; thus, Blackburn counts, Preston counts and many others were at one time adhered to in their respective districts, but have now fallen into disuse, and almost been forgotten. The Stockport counts is commonest in Lancashire, and is based on the number of dents or splits of the reed in two inches, and as cloth is generally wrought two ends on a dent, this system is often taken as the number of ends in one inch. It is in use in almost every Lancashire manufacturing district, being adopted in consequence of its simplicity and suitability for calculation purposes.