| A | |
| 1 + A⁄B | = R, |
but
| A | A + B | ||
| 1 + | = | ||
| B | B |
and making the fraction proper we obtain the rule—
| AB | |
| = R. | |
| A + B |
Stated in words the rule is "To find the resultant counts of two threads folded together, multiply the two counts together and divide by their sum."
It often happens that a counts of a given size is required from two single yarns as in the frequent case of yarns running down before the contract for goods has been delivered. In such instances the resultant counts required is known and given one of the constituent singles, the other can be obtained by the rule: "Multiply the two counts together and divide by the difference." This can be proved in a general way from the last-found formula—
Example 29.—
| A × B | |
| = R | |
| A + B |
in this equation the following also holds good