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Henry Bushby Transcription Pages


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Formulae derived from Plaits &c.
Symbols: P, Plait knot series (formerly S.)
n, number of parts
B, bights A = arcs in torsions.
C, crossings
z, no. of cords (separate.) in knot
F, geometrical form (simplest.)
r, no. of repetitions of F.
x, coefficient of B.
y, " "C
[vertical]N, the numeral defining
the group & equal to regular
sequence of over, under &c. e.g.
I for plaits, II, III & so forth.
K any torsion group. no. of orig. cords.
S any undefined Group
i.k. irregular knot
r.k. regular knot

Pn xB//yC, z = F = , defines everything,
& means a knot in Plait series with
n parts, x bights, y crossings on z separate cords &c.
(1) x = y/(n-1)
(2) y = x(n-1)
(3) y given: find values of n.
Ans: Every measure, augmented
by 1, of y from 1 to y inclusive.
[e.g. y = 8: measures are 1, 2, 4, 8
(4) n & x given: find z.
Ans: z = GCM of n & x or, if
no GCM, z = 1.

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