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Henry Bushby Transcription pages

VM533B94v4-p157.jpg

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157
In every group I, II, III &c. alike,
where y is less than n, - as it is
in the 1b knots - the complication
reduces to O1 & is a circle. Thus
II5 1b/4c, though not a Torsion
does so, and P3 II5 1b/2c, not a Torsion,
does so. With torsions it follows
under the N(N + 1) rule; the fact
that with other groups x(d[?]) also
gives the new n, points to some
still more general law.
The Torsion Rule may also be
expressed thus:-
(n - 1)n xB/yC = (x - 1)x nB/n(x - 1) C
or
N(N + 1) xB/xNC = (x - 1)x (N + 1)B/(N + 1)(x - 1)C
or
Kn xB/x(n - 1)C = Kx nB/n(x - 1)C
where N = Numeral Group I, II &c, and
K = Torsion Group.

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