√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.

One advantage gained by a knowledge of the principle of cloth “balance” is that the number of picks per inch which a given pattern or weave will take can easily be obtained by calculation. This is of great advantage to designers for Jacquard weaving, as it often occurs that a design is made and the cards cut for a pattern which will not admit of the required number of picks of the given counts being put in the cloth, which a slight alteration in the ground weave would have rendered possible.

To alter the Weight.—If the weight of a cloth is required to be altered, and the same firmness kept, the threads per inch and counts can be found on the same principle.

If a cloth is made heavier it must be done by using coarser yarns and fewer threads; it cannot be done by using more threads, and preserve the same “firmness” or “perfection.”

Suppose a sample piece of cloth weighing 10 lbs. is made with 93 threads of 45’s, and it is proposed to make a piece of the same length and width, but weighing 15 lbs. To find the threads per inch and counts of yarn to keep the same firmness.

The weights of two cloths will vary as the square roots of the counts if they are of the same perfection.

Therefore—

To find the threads per inch required of the above counts—

Then to make a piece of the same perfection or firmness as the sample piece, and to alter the weight from 10 lbs. to 15 lbs., the counts must be changed from 45’s to 20’s, and the threads per inch from 93 to 62.

To prove this is correct take a piece 20 inches wide, 102 yards long, 93 threads per inch both in warp and weft of 45’s yarns.

The weight of this sample piece will be—

20 × 102 × 93840 × 45 = 5 lbs. of twist;

and as there is the same weight of weft, the total weight of the piece will be 10 lbs.

Now calculate the weight of a piece of the same length and width with 62 threads per inch of 20’s yarns:—

20 × 102 × 62840 × 20 = 7½ lbs. of twist;

and with the same quantity of weft, the total weight of the piece will be 15 lbs.

This proves the calculation to be correct so far as altering the weight goes.

To see if both cloths are of the same firmness, the table of diameters may be referred to. It will there be seen that a plain cloth with 93 threads per inch of 45’s yarn is “perfect,” and also that the altered cloth with 62 threads of 20’s is equally perfect.

It thus proves the principle of the calculation to be correct.

A lighter cloth may be made, and the same firmness kept. The formula is the same in both cases. If a cloth is made lighter it must be done by using finer counts and more threads. It cannot be done by using fewer threads, as the firmness could not be kept and the required weight obtained.

In altering the weights of cloths some allowance would have to be made for the difference in milling-up with different counts of yarns and numbers of threads. If a cloth is made heavier, thicker yarns would be used, and the warp length to give a certain length of piece would be different in the sample to the altered cloth. But this is a comparatively small matter, which can be adjusted with a slight alteration in the basis of the structure.