Derivatives Formed by Rearranging Ends or Picks- The number of what maybe termed fundamental weaves is comparatively small, but the weaves that may be derived from them are innumerable. Thus, if a simple twill weave is shown out in design paper, several other weaves maybe obtained from it by rearranging either the ends or the picks. Designs thus obtained are termed derivatives.

## Twill Derivatives

To illustrate how derivative weaves are obtained, a regular 45° twill, Fig. 20, is taken and three other weaves formed from it. Suppose that it is desired to form a derivative weave by rearranging the ends of Fig. 20 in 1, 4, 7, 2, 5, 8, 3, 6 order; that is, the first end of the new weave is to be like the first end in Fig. 20, the second end of the new weave like the fourth end of Fig. 20, the third end like the seventh, the fourth like the second, and so on. It will be seen that com- mencing with the first end of Fig. 20, every third end is taken until by this method the first end is reached again, when the design commences to repeat. Fig. 21 shows the twill in Fig. 20 rearranged in this order, Suppose that it is desired to arrange the ends in the twill in Fig. 20 in 1, 2, 5, 6, 3, 4, 7, 8 order. Fig. 22 shows that the first and second ends are like the first and second ends in Fig. 20; that the third end is like the fifth in Fig. 20; the fourth is like the sixth; the fifth like the third, and so on.

These two examples show that a number of weaves may be obtained from a regular twill weave, or in fact from any weave. After deriving a weave from a twill still other weaves may be obtained by rearranging the ends of the derivative. When a weave is to be rearranged in its picks, the same process is employed as when rearranging the ends. These two examples show that a number of weaves may be obtained from a regular twill weave, or in fact from any weave. After deriving a weave from a twill still other weaves may be obtained by rearranging the ends of the derivative. When a weave is to be rearranged in its picks, the same process is employed as when rearranging the ends. Suppose, for example, that it is desired to rearrange the picks of Fig. 20 by taking the first 3 picks, missing the next 3, taking the next 3, and so on until the weave repeats. Fig. 23 shows the twill in Fig. 20 rearranged in this manner; the first 3 picks of Fig. 20 are copied for the 1'irst 3 picks of Fig. 23; the next 3 picks of Fig. 20 are skipped; the next 3, that is the seventh, eighth, and first, are copied for the fourth, fifth, and sixth picks of Fig. 23; and so on until the weave repeats. In rearranging any weave in either its ends or picks, the repeat becomes an important matter and should always be carefully considered. Take, for example, Fig. 23, it will be noticed that the first pick of this figure is like the first pick of Fig. 20, and also that in working out this new weave the sixth pick of Fig. 23 will be the same as the first pick, but the weave does not repeat on this pick, since the next pick, the seventh, is not like the second. However, after working out 12 picks, the weave repeats, since the next, or thirteenth, pick is like the first, the fourteenth like the second, the fifteenth like the third, and so on.In selecting an order by which to rearrange either the ends or the picks of a weave, care should be taken to select one that will cause the weave to repeat correctly.

For example, suppose that it was attempted to rearrange the ends of an 8-end twill by moving in twos; that is, taking one and skipping one; the order would be 1, 3, 5, 7, when it would come back to 1 again and continue in the same order. This,,of course, would be a repeat in a certain sense of the pose, for example, that it is desired to rearrange the picks of Fig. 20 by taking the first 3 picks, missing the next 3, taking the next 3, and so on until the weave repeats. Fig. 23 shows the twill in Fig. 20 rearranged in this manner; the first 3 picks of Fig. 20 are copied for the first 3 picks of Fig. 23; the next 3 picks of Fig. 20 are skipped; the next 3, that is the seventh, eighth, and first, are copied for the fourth, fifth, and sixth picks of Fig. 23; and so on until the weave repeats In rearranging any weave in either its ends or picks, the repeat becomes an important format and should always be carefully considered. Taking, for example, Fig. 23, it will be noticed that the first pick of this figure is like the first pick of Fig. 20, and also that in working out this new weave the sixth pick of Fig. 23 will be the same as the first pick, but the weave does not repeat on this pick, since the next pick, the seventh, is not like the second. However, after working out 12 picks, the weave repeats, since the next, or thirteenth, pick is like the first, the fourteenth like the second, the fifteenth like the third, and so on.In selecting an order by which to rearrange either the ends or the picks of a weave, care should be taken to select one that will cause the weave to repeat correctly. For example, suppose that it was attempted to rearrange the ends of an 8-end twill by moving in twos; that is, taking one and skipping one; the order would be 1, 3, 5, 7, when it would come back to 1 again and continue in the same order. This of course, would be a repeat in a certain sense of the word but would not be a repeat of the weave, since all of the ends of the original weave would not be used. When it is desired to learn in what order the ends may be taken to make the weave repeat when rearranging the ends or picks of a weave by means of taking one end and skipping a certain number, find two numbers that, when added together, will equal the number of ends or picks on which the weave is complete but that cannot be divided into each other or into the number of ends or picks of the weave without a remainder. When twills are rearranged in this manner they are said to be rearranged in salin order. Suppose that it is desired to rearrange the ends of a twill that is complete on 12 ends and 12 picks. It will be seen that 7 and 5 are two numbers that cannot be divided into each other or into 12 without a remainder but that when added together will equal 12. Therefore, the ends of the weave may be rearranged by moving in sevens or fives. That is, if the ends are arranged on a base ot 7, the first end of the weave is copied, while the next six are missed, and so on, which will give the following order: 1, 8, 3, 10, 5, 12, 7, 2, 9, 4, 11, 6; here the weave will commence to repeat and consequently will not need to be continued. On the other hand, take two numbers such as 8 and 4; these added together make 12, but it will be noticed that 4 can be divided into 8 and also into 12. It would not therefore be possible to rearrange a 12-end twill with either of these numbers. To show that this is correct suppose that it is attempted to rearrange the ends of a 12-end weave on a basis of 4, that is, ‘ taking the first end and missing the next 3 ends. The order will be 1, 5, 9, and if the next 3 ends are missed it will be seen that it is necessary to take the first end again, when exactly the same ends will be taken, and consequently only these 3 ends will be used, which will not give a repeat of the weave.