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Henry Bushby Transcription pages

VM533B94v4-p009.jpg

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9.
Required: Reversibles of 12c. 16c.
[sigma] diffces are 2, 4, 6, 8 etc.
16 is divisible by 2, 4, 8 only.
Values of [sigma] are 3, 5, 9. _ 3 knots.
Therefore, except in the case of 2c, of
which there is 1 knot, given y (the
coefficient of c) there are as many
knots as there are measures equal
to 2 or multiples of 2 ^ less than y which will
divide y, & values of [sigma] = these +1.
Example : Required, reversibles of 24.
24 is divisible by 2 _ [sigma] = 3
[symbol] 2 x 2 _ [sigma] = 5
[symbol] 3 x 2 _ [sigma] = 7
[symbol] 4 x 2 _ [sigma] = 9
[symbol] 6 x 2 _ [sigma] = 13[bracket] 5 = AND.
These knots are not necessarily on /z.
Determination of z.
In [sigma] = 3, z = 1 except in the case of
2c, 2 + 6 (or a multiple of 6)c, in which
case z = 2. Every 3rd knot is on 2z.
(p 10 follows) 1st = 1 ([sigma]-1)c

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