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DIRECT FOLLOW-ON of PAGE 11
Please be aware that, despite the attention given to proofing and proofing again ,there may persist some
mistakes ( "may" that is  like when a bookseller state " books may have reminder marks"  : you can be
dead certain the book has them  ! )


----------------------------USER's RECIPE----------------------------------

I will really appreciate feed-back positive or negative and with suggestions from those of
you who will try it

( → )  means  LEFT to RIGHT
(←)   means RIGHT to LEFT


Line "ABOVE"
 is written LEFT to RIGHT (→) in the order as read RIGHT to LEFT (←)
AS IN ARABIC on BOTTOM rim .

It is linked to the yellow ODD B.R.T.L   half-period so they have to be read on the same
slanting orientation as the yellow upward going with right to left slant vector so
read when in use   ( → ) LEFT to RIGHT AS WE DO IN WESTERN SOCIETIES



Line "UNDER"
is written LEFT to RIGHT (→) in the order as read LEFT to RIGHT (→) 
as we usually do on TOP rim  .

It is linked with the blue EVEN T.R.B.L  half-period so they have to be read on the same
slanting orientation as the blue downward going  with right to left slant vector so
read  (←) RIGHT to LEFT AS IN ARABIC

------------------------------------

 BOTTOM rim sequence written in the order ( ← )  TO BE READ IN USE  ( → )
0        2        4        1        3        0        2                   
@      @      @      @      @      @      @      @
          2        0        3        1        4       2        0          
 TOP rim sequence written in the order ( → )  TO BE READ  READ IN USE  (←)


We don't use  the @ as there is no crossing to be made there ( BIGHT rim , border ).

------------------------------------

 BOTTOM rim sequence written ( ← )  TO BE READ IN USE  ( → )
0        2        4        1        3        0        2                   
@      @      @      @      @      @      @      @
          2        0        3        1        4       2        0          
 TOP rim sequence written ( → )  TO BE READ  READ IN USE  (←)

0 & 0  have no crossing on its bight row so is written as "starting" the sequence but "linked"
with a @ that will not receive a crossing row coding.
and  0 and (L+1)th row crossing are rim bight crossing with no crossing so  here they are
not given a BIGHT number.

------------------------------------

BOTTOM rim sequence written ( ← )  TO BE READ IN USE  ( → )
0        2        4        1        3        0        2            this is relating to the ODD    B.R.T.L      
@
     /          \         /         \        /        \        
@
          2        0        3        1        4       2        0    this is relating to the EVEN  T.L.B.R
 TOP rim sequence written ( → )  TO BE READ  READ IN USE  (←)

------------------------------------
So

we use the ABOVE line to know what crossing the ODD  Bottom.R.T.L   are making,
we use the  BELOW line to know what crossing the EVEN   Top.L.B.R are making.

If we use what we already know

For the left side numbered sequence of  crossing row  bottom to top ( ↑ )
0 and 7  are without any crossing so are not really put to use (place holding only)
even 2 - 4 - 6  are OVER for the yellow B.R.T.L half-period      upward going
even 1 - 3 - 5 are UNDER for the yellow B.R.T.L half-period    upward going

For the right side numbered sequence  of  crossing row  top to bottom ( ↓ )
0 and 7  are without any crossing so are not really put to use (place holding only)
even 2 - 4 - 6 are OVER for the blue T.R.B.L half-period     downward going
even 1 - 3 - 5 are UNDER for the blue T.R.B.L half-period   downward going


we can write

------------------------------------

BOTTOM rim sequence written ( ← )  TO BE READ  ( → )
U        O      U       O       U        O       U
0        2        4        1        3        0        2            this is relating to the ODD    B.R.T.L      
 @      /          \         /         \        /        \        @
          2        0        3        1        4       2        0    this is relating to the EVEN  T.L.B.R
          U      O        U       O      U       O       U
TOP rim sequence written ( → )  TO BE READ  READ  (←)

------------------------------------

 This will be reduced to

------------------------------------

BOTTOM rim sequence written ( ← )  TO BE READ  ( → )
0        1       2        3       4         5        6       7    number of CROSSING ROW on left
none  U      O        U       O        U       O   none
0        2        4        1        3        0        2            this is relating to the ODD    B.R.T.L      
@        \         /         \        /        \        /      @
          2        0        3        1        4       2        0    this is relating to the EVEN  T.L.B.R
none   O       U       O       U       O      U     none  
7         6        5       4        3        2       1       0     number of CROSSING ROW on right
TOP rim sequence written ( → )  TO BE READ  READ  (←)

------------------------------------

the 2 extreme 0-@  pair being just there as place-holding items ( just as digit 0 is just a place
holding digit giving meaning to the other digits 1 to 9 in numbers ! )

Let us have a look at the :
- laying of the FOURTH half-period
downward going from right to left makes UNDER -UNDER

- laying of the FIFTH half-period
upward going from right to left makes UNDER-UNDER

- laying of the SEVENTH half-period
upward going from right to left makes UNDER-UNDER-UNDER-OVER

   here are the laying of the other half period :
SECOND           THIRD           SIXTH         EIGHTH          NINTH          TENTH

so it is

---- free run
---- UNDER
---- UNDER
---- UNDER-UNDER
---- UNDER-UNDER
---- UNDER-UNDER
---- UNDER-UNDER-UNDER-OVER on the 7th half-period this is the first OVER
---- UNDER-UNDER
---- UNDER-UNDER-UNDER-OVER-UNDER-OVER
---- UNDER-OVER-UNDER-OVER-UNDER-OVER

This so we  have a visual checking of the validity of what is said here

NOTE that is the start is AN OVER instead of an UNDER the working of crossings
will be easier, sober !

To be thoroughfuly verified one again (done )

So for half-period 4
 it is EVEN we know it is a   T.L.B.R so we will have to use the below row of digits
Bight concerned among the 5 possible ( 0 to 4) is for half-period 4
(4 - 2) / 2 = 1 so from BELOW row of digit we start with "1" that is an UNDER  and
we read for BIGHT that were made to exist BEFORE "1" and "1" itself as it can cross itself.
so we have U -U      
UNDER-UNDER

So for half-period 5  
 it is ODD we know it is a   B.R.T.L so we will have to use the above row of digits
Bight concerned among the 5 possible ( 0 to 4) is for half-period 5
(5 - 3) / 2 = 1 so from ABOVE row of digit we start with "1" that is an UNDER  and
we read for BIGHT that were made to exist BEFORE "1" and "1" itself as it can cross itself.
so we have U-U    
UNDER-UNDER

So for half-period 7  
 it is ODD we know it is a   B.R.T.L so we will have to use the above row of digits
 Bight concerned among the 5 possible ( 0 to 4) is for half-period 7
(7 - 3) / 2 = 2 so from ABOVE row of digit we start with "2" that is an UNDER  and we
read for BIGHT that where made to exist BEFORE "2" and "2" itself as it can cross itself.
so we have  U-U-U-O      
   UNDER-UNDER-UNDER-OVER

May be it is too cumbersome to have the bottom rim in the "above" position  and the top rim
 in the "below" position so let us make a mirroring

What I did till now  I did so as to "maintain comparability" between HALL's mandrel and
Nautile's cylinder ( just a Pi/2 ( 90° ) CW from cylinder to mandrel or CCW from
mandrel to cylinder.

Let us have the BOTTOM rim in LOW position and the TOP rim UP
sequence the right way up for cylinder

 


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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

Url : http://charles.hamel.free.fr/knots-and-cordages/