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Henry Bushby Transcription pages

VM533B94v4-p008.jpg

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8.
Plait or Twist Knots as on p152 [ft?].
of vol 1.
Their [double underline] reversibiltiy.
The law of reversibilty for these knots
is as follows:-
Let [sigma] = any odd no. of strands >1
Then [sigma]-1 is the difference of an
Arithmetical series of which it is also
the first [terin?], and in this series every
[terin?] represents a reversible Plait (Twist)
Knot with crossing equal to the [terin?].
But except in the case of [sigma]=3 the first
[terum] duplicates a knot in n ^(not the) preceding
series, and therefore, when all the series
are being considered from 3([sigma]) onwards,
it is best, except with [sigma]=3, to make
2([sigma]-1) the 1st [terin?].
Thus: Required reversible knots: [sigma]=5.
[sigma] = 5, [sigma] - 1 = 4 = 1 st terin (since the series
alone is being considered.
Are = 4c, 8c, 12c, 16c, 20c . . . . . knots.
(p g follows)

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