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Henry Bushby Transcription Pages


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(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

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