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Henry Bushby Transcription Pages

VM533B94v2-p271.jpg

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271

See vi.229 [vertical strike through] (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] & xby 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 ^(two cords) in S6 <u>4B
[over] 20C. There-
fore it occurs alone in S3 2Bover 4C, for
S6 4B[over] 20C = S6, 4B[Over] 4(6-1)C. Divide [??]2),
4(=x) by 2 to get S32B[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 untwisted uncrossed endless cord.
(see also "F" on p256.)
[vertical strike through]

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