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## Henry Bushby Transcription Pages

### VM533B94v2-p271.jpg

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271

__See vi.229__
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(xv.) The *^possible* geometrical [?fr..]*^,F,* of any regular

knot, ~~is~~ S [?symbol] xB</u>[over]x([?symbol]-1)C, is repeated (interlaced)

Z times in the knot Sz[?symbol] __z x B__[over] zx(z[?symbol]-1)C

~~which is always on z cords.~~

When a regular knot is on more than

1 cord some F is always *^possible to be* repeated in it.

(It is not always actually repeated in a diagrame as drawn.)

The knot therefore in which F occurs

singly on 1 cord can be found by dividing

__[?symbol]__ & __x__by __z__ wherever they occur in the

expression of the knot containing the

repetition, S[?symbol] __xB,/u>[over ] [?symbol](z-1)C, Z being the
number of the cords. For instance, a
given F occurs twice __[over] 20C. There-

*^(two cords)*in S6 <u>4B

fore it occurs alone in S3

__2B__over 4C, for

S6

__4B__[over] 20C = S6,

__4B__[Over] 4(6-1)C. Divide [??]2),

4(=x) by 2 to get S3

__2B__[over] 2(3-1)C=S3

__2B__[over] 4c.

The converse process is equally simple. A

reference by this process to S1 always im

plies an

(see also "F" on p256.)

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