=To change the Counts=, the pattern and threads per inch remaining the same.
If a sample cloth has 78 threads per inch of 32’s yarn, and it is proposed to make a cloth of the same weave with 55 threads per inch, what counts of yarn are required to keep the same “firmness”?
This is simple enough. The diameters of yarns vary as the square root of their counts, and therefore as the threads in one cloth are to the threads in another, so will the square root of the counts in one be to the square root of the counts in the other.
Threads in Threads in proposed Counts in sample. cloth. sample.
78 : 55 ∷ √32 : √x or as 78^2 : 55^2 ∷ 32 6084 : 3025 ∷ 32 32 ---- 6050 9075 ----- 6084 )96800(15·91, or 16’s nearly = counts 6084 required ----- 35960
On referring to the table of diameters (p. 335), it will be found that a plain cloth with 78 threads of 32’s is “perfect,” and that a plain cloth with 55 threads of 16’s is also perfect. Therefore the above calculation is correct.
=To change the Threads per Inch=, the counts and pattern remaining the same.
If a sample has 78 threads per inch of 32’s, and it is proposed to weave a cloth of the same pattern, but with 60’s yarns, find the number of threads per inch required to keep the same firmness.
This is simply a continuation of the previous statement.
If the two counts are known, the number of threads will vary as the square roots of the counts; thus--
Counts in Counts in Threads in sample. proposed cloth. sample. √32 : √60 ∷ 78 : _x_ or as 32 : 60 ∷ 78^2 : _x_^2 6084 60 ------- 32)365040 11407½ √11407 = 106.8 threads required.
The above may be proved correct by referring to the table of diameters. A plain cloth with 78 threads per inch of 32’s is “perfect,” and so is a plain cloth with 106½ threads per inch of 60’s.
The same principle must be employed if the warp and weft are of different counts, or if the threads per inch are not equal in warp and weft.
_Example._--A sample cloth is made with 78 ends per inch of 32’s and 91 picks per inch of 44’s. How many picks will be required to keep the same firmness, if the weft only is changed to 60’s?
Counts in Counts in sample. proposed cloth. √44 : √60 ∷ 91 : _x_ or as 44 : 60 ∷ 91^2 : _x_^2 8281 60 ------ 44)496860 ------ 11292 = _x_^2 ------ and √11292 = 106½ ∴ picks per inch required = 106½