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## Henry Bushby Transcription Pages

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263

(ix.) In any series, Sx, xB are ac-

companied by x(n-1)C and no more.

Hence B = __C__ x-1 & C = x(n-1)B.

(x) It follows that when B>1, C = 0

or >__n__, and a true knot results

except in S, when C must always =

0. But when B = 1, a twist knot

results. (i.) Therefore in S1 every “knot”

is without crossings & consists in fact

of a simple circle, which is equivalent

to saying that no knot exists; and

in every other series there is one

”knot” – the first – which is a twist

knot. Further it follows from ix that

this twist knot is the highest series in which

a “knot” containing its no. of crossings can occur.

(xi) Since the relation of C to B is

constant (ix.) any regular knot may

be indicated by the expression,

Sx __xB__ x(n-1)C provided it be remembered

that this is not a fraction. Moreover