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## Henry Bushby Transcription Pages

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__Summarised__227.__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.