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Henry Bushby Transcription pages

VM533B94v4-p262.jpg

Revision as of May 29, 2014, 6:07:32 AM
edited by JLee
Revision as of Jun 2, 2014, 6:34:49 AM
edited by JLee
Line 1: Line 1:
263<br>
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I<sub>2</sub> Only<br>(5) odd c gives c-1 knots <sup>c-1</sup>/<sub>2</sub> of (c+1)<br><sup>c-1</sup>/<sub>2</sub> of (c+2)}[bracket with line above]<u>[Oro?]</u><br>odd c give <s>same</s> ^<i>c-1 knots</i> for <u>not.</u><br>But some will be repetitions.<br>
I2 only<br>
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(6) Required: knots with y.c. Proceed<br>as follows:-<br><u>A.</u> Suppose y is odd.<br>(i) <u>[Oro?]</u>: - y c can be derived from<br>r.k. y-2, & r.k y-1.<br>(ii) With r.k.(y-2) join 1 to all even nos.<br>"<u>[Oro?]</u>" up to & including 1 [Sideways U] y-2. This will give<br><sup>y-3</sup>/<sub>2</sub> knots of y crossings.<br>Then with r.k (y-1) join 1 ^<i><u>[Oro?]</u></i> to all odd<br>nos. ^<i>except 5</i> up to & including 1 [Sideways U] y. This will <br>give <s><sup>y-3</sup>/<sub>2</sub> of y crossings.</s> <s><u>y-3</u></s> <sup>4-3</sup>/<sub>2</sub> knots. <br>(iii) <s> As y is odd these are no fresh knots</s> ^<i> With. r.k. y join 1 <u>not </u> to all even nos. up </i><br><s>as yet ascented in the "not" series.</s>^<i><s>by</s> to y-1 (i.e. y) excluding 2. This gives <sup>y-3</sup>/<sub>2</sub> knots.</i><br><u>B</u>. Suppose y is even.<br><s>(i)</s> <u>[Oro?]</u>:- y , c can be derived from <br>r.k y-2 & r.k y-1.<br>(i) With r.k. (y-2) join 1 to all even nos. <u>[Oro.?]</u><br>to y-2.<br><s>as in <u>A</u>.i.</s> This gives <sup>y-2</sup>/<sub>2</sub> <s>4</s> knots.
(ii) Then with r.k (y-1) join 1 to all odd<br>
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Nos. ^<i>"<u>[Fro?]</u>" to y-1 except 5.</i><s>as in <u>A-i.</u></s> This gives y-4[over]z <s>c</s> knots.<br>
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(iii) with r.k.y, join 1 to all even<br>
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nos ^<i><u>"not"</u></s> up to & including y <s>+1</s>., but ^<i>excluding 2&</i>com-<br>
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mencing with 1[symbol]4. This will give<br>
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y-2[over]z knots different from B.i.<br>
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The totals thus obtained therefore<br>
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are:-<br>
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y odd: <s>y-3+y-2[over]2 = 2y-4[over]2 = y-2</s><br>
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y-3+y-3+y-3[over]2 = 3(y-3)[over]2<br>
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y even: y-2[over]2 + y- <s>2</s>4[over]2 + y-2[over]2 = 3y-8[over]2.<br>
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<u> For example</u>: Required [liks?] with 6c.<br>
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<u>B.</u> (i) 6-2=4, 6-2=5.<br>
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With 4 join 1 ^<i>[Oro?]</i> to all even nos. up to<br>
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4, [rig?] 2,4. This gives 6-2[over]2=2. They are<br>
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the Weaver & Endless chain.<br>
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(ii) With 5 join 1  ^<i><u>[Fro?]</u></i> to odd nos. up to 5, <s>[rig?]</>,<br>
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<s>3, 5.</s> excluding 5. <s>This gives</s> [rig?] 3. This gives<br>
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6-4[over]2 = 1. It is the Timber Hitch.<br>
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(iii) With r.k.6 join 1, ^<i><u>not</u></i> to even nos.<br>
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up to 6, excluding 2. [rig?] 4,6. This gives<br>
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<s>4</s>6-2[over]2 = 2. They are Ended Chain & 1z Granny.<br>
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Total 6-2+6-4+6-2[over]2 = 18-8[over]2 = 5.<br>
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[Vertical diagram and caption in a square box:] 6c <s>i 6</s> 2z. <s>not get found. = I[subscript]4 2[over]6 reversed.] [Vertical text outside the square box:] Also Reef, "A", p179.
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Revision as of Jun 2, 2014, 6:34:49 AM

I2 Only
(5) odd c gives c-1 knots c-1/2 of (c+1)
c-1/2 of (c+2)}[bracket with line above][Oro?]
odd c give same ^c-1 knots for not.
But some will be repetitions.
(6) Required: knots with y.c. Proceed
as follows:-
A. Suppose y is odd.
(i) [Oro?]: - y c can be derived from
r.k. y-2, & r.k y-1.
(ii) With r.k.(y-2) join 1 to all even nos.
"[Oro?]" up to & including 1 [Sideways U] y-2. This will give
y-3/2 knots of y crossings.
Then with r.k (y-1) join 1 ^[Oro?] to all odd
nos. ^except 5 up to & including 1 [Sideways U] y. This will
give y-3/2 of y crossings. y-3 4-3/2 knots.
(iii) As y is odd these are no fresh knots ^ With. r.k. y join 1 not to all even nos. up
as yet ascented in the "not" series.^by to y-1 (i.e. y) excluding 2. This gives y-3/2 knots.
B. Suppose y is even.
(i) [Oro?]:- y , c can be derived from
r.k y-2 & r.k y-1.
(i) With r.k. (y-2) join 1 to all even nos. [Oro.?]
to y-2.
as in A.i. This gives y-2/2 4 knots.