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
! )
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 extreme0-@
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 ! )
---- 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
-UUNDER-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-UUNDER-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-OUNDER-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
Copyright 2005 Sept - Charles
Hamel / Nautile -
Overall rewriting in August 2006 .
Copyright renewed. 2007-2012 -(each year of existence)