And 4½2 = 20·25 counts required.

This may be proved correct by referring to the table of diameters on [page 335], where it will be seen that a plain cloth with 82½ threads per inch of 36’s is “perfect,” and a “two and two” twill with 82½ threads of 20¼’s counts is equally perfect.

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
sample.

Threads in
proposed cloth.

Counts in
sample.
   78 :

   55

√32

 :

√x

or as    782 :

   552

 32
6084  :

 3025 

 32

   32

 6050

9075 

6084)

96800

(15·91, or 16’s nearly = counts required

6084 

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.