In the above question the given cloth is plain, with 103 threads per inch, and the proposed cloth is a “two and two” twill. Taking the same number of threads in each case, we get—

Ends + Intersections in
proposed twill cloth.

Ends + Intersections
in given plain cloth.

4+2

 :

4+4

   103   : x
or

6

 :

8

   103  
    8  
6)824 

Ends required in twill cloth =

   137⅓

It must not be forgotten that it is necessary to take an equal number of ends of each pattern in this class of calculation. In more complex patterns it is often advisable to take the number of ends which is the L.C.M. of the ends in the two patterns in order to get a complete number of intersections in each case.

Another Example.—If a “two and two” twill cloth is made with 137 threads per inch, and it is proposed to make a cloth with the same counts of yarns in a “5 up, 2 down, 1 up, 2 down” twill, how many threads per inch are required to keep the same firmness?

In 40 ends of the proposed cloth there are 16 intersections, and in 40 ends of the sample cloth there are 20 intersections.

Then as

40 + 16

:

40 + 20