| 18 | + 282⁄7 | = 462⁄7. |
| 18 | ||
| × 100 | = 388⁄9 % of 282⁄7 counts. | |
| 462⁄7 | ||
| 282⁄7 | ||
| × 100 | = 61⅑ % of 18's counts. | |
| 462⁄7 |
This last example shows clearly that the weight of the constituents varies inversely according to the yarn counts, the higher the counts the lower the weight and vice versâ. The matter is more prominent in problems where a resultant counts is given with two weight ratios, the counts to produce these being sought by calculation.
Example 44.—A garment is required equal to 12's counts composed of two yarns where one-third of weight is on the face and two-thirds on the back. Find two counts which will fulfil these conditions.
The counts are inverse to the weights; if the proportion had been direct we should have stated: ⅓ of 12's, but seeing that the ratio is inverse we state: 3⁄1 of 12's = 36's for one yarn.
The other thread is ⅔ of 12, which inversely gives 3⁄2 of 12 = 18. For proof—
| 36 × 18 | |
| = 12's counts. | |
| 54 |
Example 45.—Find two yarns one having one-fifth of the weight and the other four-fifths to give a resultant counts = 12's.
| ⅕ of 12, inverse | = 5⁄1 × 12 | = 60's counts. |
| ⅘ of 12, inverse | = 5⁄4 × 12 | = 15's counts. |
These counts are 60's and 15's and they together produce a thread = 12's.
Example 46.—A three-fold yarn is equal to a counts of 8's, the first thread gives one-seventh of the weight, the next three-sevenths and the next four-sevenths, find each counts in the folded thread.