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Bing Dual-Independent "Alcohol-proof" Float Kits
>>>A Bing, NOT BMW product!
Copyright, 2014, R. Fleischer
The MAIN advantage of these kits is that you do not ever (probably) have to replace the
floats. That does NOT apply to the float needles, of which there were two basic types.
The VITON tipped ones have the same easy-to-lose fine wire clip as on the stock
carburetors. That clip insures positive float needle operation.
If the original floats (which DO AGE) are really bad, and/or the float needle is bad, things will certainly
improve with PROPER installation of these PRICEY kits!
IN MY OPINION, installation of these kits when the old parts were worn, often considerably, is the
HONEST & TRUE reason that SOME find improvements with fuel mileage.
Adjustment of these dual-independent float kits is more involved than with the stock floats.
These kits can have real nasty problems, so read all of this article.
Introduction to these kits:
I do NOT recommend Bing so-called alcohol-proof float kits for everyone (dual independent floats).
(I will get much deeper into them after this section)
you are willing to fiddle with these, & understand the limitations & cautions, they are
OK with me.
Bing said, years ago, that they gave increased mileage & performance due to stability
of the fuel level
during turns. I somewhat agree, but mostly only in an airplane or with serious
racetrack use where
the bike is leaned to truly extreme angles. These independent floats were originally
advertised as being
for engines where the carburetors were facing more left and right than on our
Airheads...& more or less fore
& aft. One must think about the way the floats are hinged & operate, &
then you will see that Bing's old
claims for our bikes were hardly reality. As to their NOT being affected
by 'alcohol'....that may be true. But, as seen in my Bing article where I get into extreme long-term
testing of alcohols, alcohol-laced fuels, and a LOT more, alcohol is not the REAL problem that seems
to cause deterioration of the floats, particularly weight increase, and probably mass center change.
For EITHER the stock OR Independent kits, you MUST replace the FLOAT NEEDLE regularly....as
it is the SAME needle, for BOTH stock and the Bing Independent Float Kit. These kits are very pricey.
Consider what the kits cost, your labor in installing and maintenance, etc., versus purchasing new floats
every 30,000 to 50,000 miles. How many miles/time/etc., between the cost of a regular stock float
replacement, versus the cost of Bing's Kit.
The Kit float level is somewhat difficult to adjust, having TWO flimsy brass arms. The arms contact the
floats via small pins on the floats; if not close to correct alignment the carburetors can flood.
There is NO provision for an overflow/vent for the float bowl, as in the stock
float bowls. Thus it is possible for the bike, especially on the left side-stand,
to fill a cylinder with INCOMPRESSIBLE fuel which can destroy a piston
upon you trying to start the bike. The overflowing fuel might flow to
the ground from a further up carburetor body port, & not into the cylinder.
I would not count on that. Having fuel in the left cylinder, even a quite modest
amount, and then, during starting, have the RIGHT cylinder fire-up, will cause
enormous pressures in the LEFT cylinder...and a LOT of damage.
However, the separate floats seem to be stable for any type of gasoline's (so far), and MIGHT last almost
The VERY earliest kits used metal (zinc casting) bowls. Few are likely around.
Next came kits you may see, these kits were sold with deep reddish-brownish plastic bowls. Those bowls
have been known to develop cracks, often microscopic, that cause weeping of gasoline, typically along a
vertical corner. The latest Bing Independent kit bowls are...again... zinc metal, similar in material to the
original stock bowls.
There is a problem with the plastic bowls. Those sometimes developed microscopic cracks, typically
vertical-running in a corner. Later, Bing went back to zinc bowls. The zinc bowls were rather costly to
purchase from Bing if you needed to replace a plastic one (they stopped selling plastic ones).
bowls are EXPENSIVE, NOT available from BMW (BMW regular carb parts prices are often MUCH
cheaper than Bing's!!). BMW does not sell these kits, nor parts (except the float needles, & the upper
body parts which are common to all the Bing CV carburetors.
NOTE: The old method of turning the carburetor upside down for adjusting the float level is no longer
used for the STOCK one piece white floats...but it IS for these Bing dual independent floats! At least per
Bing's instruction sheets. However, by using one's finger, carefully, one can adjust the float bridge of
these Bing kits, while the carburetors are on the bike...and Bing's latest sheets reflect both methods of
adjustment. Note that adjusting even the stock floats using the upside-down method is somewhat tricky,
particularly with the sprung tip type of float needle. Best you do NOT use that method.
For these independent float conversions, here are some adjustment specifications:
To adjust while on the bike, maintain the arms parallelness to each other, 7 adjust for 0.412" from the
With carburetor upside down the most outward part of the brass hinge unit, the top of its flat area, should
be 10.5 mm and parallel to the base...AND...BOTH of these arms MUST be parallel to each other. For
the old model 55 carburetors this was 8.5 mm. Once in operation, one could remove a bowl quickly,
& the center area to top of the fuel should be very close to 1-5/32". NOTE that after first installing &
adjusting one of these Bing independent float kits, they must be RE-ADUSTED after maybe a dozen hours
of riding. This is because the float needle breaks in, & effects of fuel on the needle & float. I think the
BRASS hinge unit tends to change a bit, something to do with its hardness & tempering grade? It is
important that the spring loaded plunger on the float needle be in good condition, & the spring inside it
not sacked out nor rusted/frozen, or the mixture will be variable due to changes in the fuel level.
arm lower edge to the carburetor body, at the point your finger VERY LIGHTLY pressing on the arm
assembly, causes the float needle plunger tip to NOT QUITE start moving upwards.
When ON the bike, that adjustment is easier to do by observing the point gas just stops or just starts
flowing....that is the parallel point, or, should be. The part of the arm to look at for the parallel-ness is
the BOTTOM of the arm.
Once in awhile deposits of fuel residues will get into the
needle spring and cause it to malfunction.
The float needle tip also wears out. Thus, the float needle should be replaced at regular intervals,
just like the original stock ones, and they ARE the same part....as delivered from BMW or Bing.
I recommend 30,000 miles. It appears that the floats will NOT require replacing on the Bing KITS,
at least no reports, so far.
Links to .pdf articles on this website. These are actual Bing Bulletins. There is an explanation of
how the Bing Dual-Independent Float kit conversions are supposed to work, & how they are to be
adjusted, according to BING. Please read these Bulletins before reading further in this article.
This is the original 1984 dated bulletin describing the new kit.
This is what Bing in the USA produced, & if you read it carefully, it differs a bit from
the above bulletin.
ALSO, the sketch does not show that the distance is 8.5 mm, which is 0.335", for the model 55
Bing claims/claimed mileage increases. That is NOT likely ON A MOTORCYCLE, unless you were
previously running rich from wrongly adjusted or bad floats; or, are so aggressive that you lean the
bike WAY OVER like actually racing on a twisty race-course; or, you are doing VERY aggressive
off-roading, with the bike often-times assuming very large angles from vertical. In my opinion, there
will be no appreciable mileage increase from normal, even aggressive touring. I measured ZERO
mileage improvement using very aggressive riding in steep tight twisties.
Bing ORIGINALLY offered these kits in various types, depending on your carburetor model number.
These kits were offered for the slide carburetors as well as the CV carburetors.
Kits were numbered #1 through 4 for BMW motorcycles:
#1: type 53 for R50, R60/5, and the /6 carbs.
#2: type for CV carburetors with 4 screws in the top cover.
#3: type for CV carburetors with 2 screws in the top cover.
#4: type for ALL 40 mm carburetors.
Kits #1 and #2 had the square grey float needles, requiring no needle clip.
kits #3 and #4 had the larger, triangular, brass, viton tipped needle with the needle clip.
In the clickable pdf that has a sketch, the 10.5 mm distance, which is 0.413", does not show
that the bridge & carburetor base are also PARALLEL. This was added in a much later
USA bulletin (which I have).
carburetor...but that model is not used on the BMW Airheads. The various types of Bing carburetors
are used on vehicles other than BMW motorcycles, and if interested for some reason or other, know
that the 53 carburetor (which is used on some Airheads) was made in 24-27 mm; the 84 in 28-32, the
54 in 34-40, and the 55 in 40-55. The 64 and 94 were the CV types.
Included in my personal files are original Bing Engineering bulletins from 1984.
Bing promoted their new float system for transverse to direction engines, and for special industrial
that these kits were developed originally for small aerobatic aircraft & only later Bing decided
engines, ultra-light aircraft, etc., that had special inclination performance requirements. It is my
it could sell many more, perhaps at a handsome profit, to motorcyclists and others, for whom there
was REALLY no advantage, ONLY DISADVANTAGES (except floats life). As noted, I have the
original Bing engineering bulletins on these kits, from the early 1980's...and most are clickable,
see well above for the links.
Bing furnished, through its Bing Agency International in the USA, another bulletin that
explained how Bing wanted you to think about the kit's operation, using a glass of liquid as
an example, as liquid sloshed back & forth, with acceleration & deceleration, and how,
supposedly, this worked on BMW bikes (BUT....remember, our carbs are rearward and angled,
NOT a transverse engine!
Bing said that there is a lean-ness, then richness, power changed,
& you subconsciously added more throttle to compensate. I say: take this with a grain of salt!
"My Airhead motorcycle came with the twin independent float conversion... why do the gurus "hate"
them? I also would like to know what IS the proper procedure for adjusting the float levels on carbs
with this conversion, assuming I am going to do it myself ..."
(and other inquiries.....)
I passed on what I knew about this kits as far back as 1984, and I later did articles
on these kits, including discussing the original engineering behind their development,
which Bing would very probably prefer I not post.
NOTE that BMW never installed
them,... it would hardly have cost them anything...there are several reasons they did
not, & I discuss those in this article.
Primarily, there is the lack of an BOWL "overflow" that has "guru's" (and maybe BMW?) most upset.
All the stock CV Bing carburetors, as delivered by BMW, have an overflow capability at a vent port
on the carburetor body, which is rather high up; and does have a goodly capacity for flow.
This is in addition to the tiny diameter vertical 'overflow' (vent) pipe coming out of the bottom of
the bowl. Neither of these may prevent some flow into the left cylinder, especially if the bike is on
the side-stand, and the float needle is leaking a fair amount of fuel into the bowl, that is, at a much
higher level...and rate... than designed....or; thinking about it another way, the float & its float needle
are NOT shutting off the fuel, as the float bowl level rises to the proper preset amount.
Side-stand's vary in their angle which is another factor. There is a great danger in trying to start the
engine with liquid gasoline in the left cylinder. It does not take very much gasoline, as you try to
crank the engine, to have what is called a 'liquid' or hydrostatic lock, which, especially if the right
cylinder fires; can lead to busted pistons, bent rod, etc. With the Bing independent float kits,
there is NO DIRECT BOWL VENT, which acts somewhat as an overflow. You can see this
by looking at the Bing bowls in the kit, versus your stock bowl...there is NO vertical tiny pipe
in the conversion kit bowls. Frankly, I was surprised to see this, as Bing could certainly
have included one.....for ROAD BIKES, or OFF ROAD BIKES.
While I am often considered as one of the so-called "guru's", I actually have nothing too Pay attention to my advice to always turn
much against use of these Bing Independent Float Kits, or alcohol-proof kits, or however
Bing Agency in the USA presently advertises and sells them.
Just be sure your petcocks work
properly (don't leak internally either) ....and are in the OFF position (horizontal lever position)
if using the side-stand; OR using the center-stand.
off your petcocks when the engine is off (Bing ALSO cautions this). This is especially important
if using the side-stand. ****OFF is NOT "auf"!!!! if your petcocks are so marked.****You will have to adjust the flimsy float bridge in the kits a few times, perhaps only twice. Usually,
after that, they settle down & are reliable. You will still have to replace the float needle now & then,
perhaps 30K-60K intervals, same as with the stock floats.
The twin independent floats in these kits ""seem"" to last forever in any type of gasoline or time/miles
(NOT so the float needle).....but the adjustment brass-looking bridge is thin, flimsy & is poorly
heat-treated. It is possible that this was done on purpose, to be fair about this. That brass-looking
bridge needs to be adjusted properly at first install, & then once or twice more after being in use for
awhile. Bing says readjust (implying once) after 5 hours, I say this is not enough, & should be checked
again after maybe a month or more, and then maybe at yearly....or even longer, intervals; typically they
are OK after they settle down. Depends on mileage.
The float needles in all the CV carburetors were (very early models) a solid metal, and later Viton
(or? rubber) tipped, and are now, per Bing, the same part number, no matter if the tip is black, gray,
red, etc. Some early metal ones were square, not triangular, in their bodies. The float needles in the
Bing dual-independent kits are the same part as the later stock types. Float needles wear out...and
allow overflowing with the kit...and also with stock carburetors. USUALLY, there is a teeny bit of
foreign matter lodged in the float needle seat or on the needle tip that you can remove by jiggling the
float with the fuel turned ON, but, eventually the needles become unusable. The 'rubber' hoses will
deteriorate over time, more or less depending on the additives in the gasoline you use. The interior
of the hose is what deteriorates...leaving tiny rubber particles...and they cause problems in the float
seat area....the needles then leak, fuel level rises, overflows on your foot (and hopefully NOT into
the cylinder(s). Can be worse if on the left side-stand.
Tipped float needles are made of VITON...or were. How they handle alcohol in modern fuels is a
good question. SOME forms of VITON are OK in nearly all types of alcohol. MOST Viton material
is pretty good in ETHANOL. UNfortunately, gasoline ingredients vary...a LOT.
BMW dealerships generally charge LESS for Bing carburetor parts than Bing Agency does, but the
dealerships may...or may not... stock the independent float kit parts (as they are not BMW parts)...
although the FLOAT needles are the same).
At this point, if you have not looked at ALL FIVE bulletins/etc, links well above in this article,
NOW is the time to do so. Read them at this point, before proceeding.
CAUTION! If you are not familiar with Bing carburetors, you need to know that the thin round
metal rod that holds the float bridge to the two carburetor support bosses, goes into, and is removed
from, the support bosses from only one side. The rod is KNURLED at ONE end. The OTHER end
goes in FIRST. When removing the old rod, remove it knurled end first; using a very thin rod at the
NON-knurled end, and a very tiny hammer or even the plastic handle of some tool as a VERY light
tapping-impact tool!!...be GENTLE. You can devise a very thin rod for use as a punch, by grinding
a nail, remove sharp end or reshaping it.
Under NO CIRCUMSTANCES put much force on that float rod. When installing, tap it in or squeeze
it in very gently. Remember: install the NON-knurled end of the rod first. That way, the knurled rod
end goes into the knurled boss end, lastly.
Be truly careful. You will have a VERY bad day if you break a boss.
Be careful to avoid miss-adjustment of the bridge....it could then cause rubbing, or uneven, even angular float
Be careful about the two vertical float pins in each float bowl....those pins have been known to be bent, and
operation. If you miss-adjust the bridge, you can get all sorts of problems, from flooding to mixture problems.
This is NOT a difficult job, just be slow, cautious, careful.
need gentle straightening...otherwise the floats might stick at the bottom (more, later on....).
On the Bing CV carbs, as STOCK, with the die-cast aluminum-looking (probably zinc) float bowls, there are
two round holes, in the forward corners of the float bowls. ONE is plugged off, with the opposite one similarly
plugged for the other carburetor, as there are left side & right side bowls. The one NOT plugged off is a 'well',
with a small brass jet at the very bottom. That jet, on the stock or kit bowls, SHOULD be checked for clogging.
The well is where the main body of the carburetor has a small tube that dips down into the well. CHECK THAT!
This is where the enrichener (mis-named choke) gets its fuel. Check the tube to be sure it is OK. On rare
occasions folks have had carburetors with water in them & if the water freezes, the tube can split, & then you
must repair that damage, with a sleeve. Note also, that the well/cavity needs an INTACT bowl gasket, that is
the big funny cork gasket that fits into a groove at the bottom of the carburetor (float bowl removed). If that
gasket has a crack or missing piece in the area of the 'well', the enrichener may not work correctly.
The Bing "alcohol-proof" kits PLASTIC BOWLS (that I have seen so far) do NOT have ANY corners plugged,
but the jet is for use in only ONE of the wells. Many early Bing kits were furnished with the jet in a baggy,
UNinstalled. That was so YOU could install the jet in the correct corner. Your newly acquired bike, if it has
these kits, should already have the jet properly installed at the correct corner...but do check that. Check
this because as I noted, Bing shipped some kit bowls with NEITHER corner plugged off. It is possible
that someone has a bowl with NO corner jet installed! The proper corner FOR THE JET is the one
that mates to the DOWNward pipe coming from the carburetor body corner. If the jet is not properly
installed in the Bing Dual Independent kit, the 'choke' (enrichener) will not work correctly. In the stock
metal bowls, you cannot fit the wrong left or right bowl due to the plug in one corner.
The jet is there to fill the 'well' in a controlled way, so that a very rich initial STARTING mixture is
possible....and after approximately 10 seconds of running, the bowl is supplied by the quantity allowed
by the JET. The downwards going tiny diameter pipe may have one or two teeny side holes, which
modifies this, as far as bowl level that can be sucked up easily, but the idea here still holds true. Thus,
a jet not in the correct corner could allow some washing down of the cylinder walls with lots of fuel over
too many seconds of operation .... not so nice. So, the thing here is, DO NOT install the wrong bowl
at left or right; be sure the jet is in the proper corner. EASY to see which goes where...the carburetor
has a very tiny thin diameter pipe, going downwards; it must go into the JETTED bowl corner.
All of the metal dual-independent bowls I have personally seen have the jets already mounted in the
proper corner. If you order a bowl, you are going to get the metal one; there is a LEFT & a RIGHT,
due to this corner jet location.
If the float guide pins are bent, the floats can hang up!
I have also seen some floats with poorly peened tubes in the floats themselves, an easy to fix.
Here are some hints from my own work on these:
1. Bowl CENTER to top of gasoline, ~1-5/32". This is APPROXIMATE & is for 40 mm carbs.
2. Carb is supposed to be upside down for the original installation instructions. If adjustment is checked
& done with carburetor on the engine, which is fine for future checks, the lower part of the spring-loaded
plunger type needle, that is, the plunger itself, must be such that the plunger is JUST being
touched/pressured, but the plunger has not moved upwards yet, for both the parallel and distance
measurement. That is 0.413". Excessive pressure will depress the needle plunger and give a false reading.
This measurement can be done by holding a flat wide steel rule against the lower part of the carb body &
using another narrower rule marked at 0.413" MINUS the wider rule thickness, vertically from that, noting,
using fingertip & hardly the slightest pressure on the bridge, where the bottom of the bridge finger (either)
is parallel & the measurement is correct. This is a pretty accurate adjustment point, rather better than #1,
which can be used, with 'QUICK' bowl removal, as a double-check on your work. Better is on the
workbench, but NOT necessary. See 5 and 6, below.
3. Hairclip is not used at float bridge tang area on 64-32/1 through 20.
4. The spring loaded plunger type of float needle has a tiny hole in the bottom. That hole, the bridge tab,
is mechanically coupled by a very easy-to-loose teensy wire clip. The purpose is to make for very
positive opening of the needle port. Assembly of the needle, clip, & float bridge are best done on the
workbench, on a piece of old white bed sheet. YOU CAN do it on the bike, if careful...and do put a
sheet on the floor! I always stock extra wire clips.
From here, I will assume the new twin independent floats kits were properly installed:
First, turn the carburetor upside down. Adjust the tab on the bridge piece & the arms themselves,
5. If the carburetor is OFF the bike:
so the arms are parallel to the carburetor base and even with each other. Use a very small
screwdriver, very carefully, to adjust the tab. The arms must also be parallel with the carburetor
base & also the two arms parallel to each other. This condition must exist in future checks too.
The distance per the Bing sketch of 10.5 mm (0.413") must exist.
6. If the carburetor is ON the bike:
You have to lift the arm assembly very VERY gently with a fingertip, and NOT ..NOT!....allowing the
spring loaded plunger (if you have that type) in the float needle to be more than just barely touched.
You CAN feel the resistance though...just do NOT depress the needle plunger. Same adjustment(s)
are to be done. When carburetor is ON the bike, that above adjustment MAY be easier for you to do
by observing the point gas just stops or just starts flowing....that is the parallel point, or, should be.
The part of the arm to look at for the parallel-ness is the BOTTOM of the arm, as viewed as if the
carburetor was ON the bike. BOTH arms must be equal and parallel.
For 5. and 6: When using a small screwdriver, you bend the tab against the steel retaining pin. You will see
what I mean when you try to figure out how to bend the tab. DO NOT BE HAM-FISTED.
A little known problem with the individual independent floats themselves is that there really is a top & bottom
to SOME of them. Bing ignores this. Because of the tight fit at the bottom combined with the slight upward slope
(and very close to the bowl rod) of the bottom of the 'new' float bowls, the floats CAN, sometimes, 'stick', to the
bottom of the bowl. They can also stick at or near the bottom if the pin is bent even slightly!! Usually, but
NOT always, this 'potential problem' does not cause a problem due to the motorcycle vibration during operation.
Be careful to install the floats on straight up pins. Another thing to watch for is that the center metal pipe area
(that is part of the float itself) is such that the broad-rivet head of that pipe is DOWNWARDS, towards the bottom
of the bowl. It is possible to actually 'feel' this float grabbing at the bottom, especially if the rounded larger head
area is up (or pin bent), instead of properly down...which raises the floats very slightly off the floor of the float
bowl. I had one bowl that I saw that this was exceptionally poor....so I installed the floats rivet pipe head
downward, and I put a very small and very thin washer over the bowl's rods first.
8. http://bmwmotorcycletech.info/bing-tech-bulletin.pdf has a sketch, near the bottom of the page, of
the float bridge adjustment with the carburetor on the workbench, upside down. The RIGHT end
of the arms (the two arm ends MUST be parallel) have a wider area on the right-most part of those arms.
You could describe it as wider by a small amount. The UPPER surface of that wider part must be not
only be parallel to the carb base body, and both arms even to each other....but the DISTANCE from this
upper surface arm part to the carburetor base must be 10.5 mm...which is 0.412 inch. This covers
all the CV carb models used on our Airheads (there is a different specification for ONE model of Bing
not used on the Airheads...it is listed on the sketch above, model 55 carburetor, the distance is 8.5 mm).
9. After some hours of use, reset the bridge if needed, at the least do check it. The bridge will change its
adjustment slightly due to its heat treatment (I THINK),....and some settling-in of the tip of the float needle.....
teeny changes in the internal float needle spring parts, etc. You will probably do this with the carburetors
attached to the motorcycle, rather than remove them to the workbench. Mind my previous comments on
how to do this with the carburetor ON THE BIKE.
You WILL have to change the float needle now & then, perhaps at 30,000 to 60,000 mile intervals. Rechecking
adjustment is mandatory at that time...same as a stock carburetor. The adjustment of these twin independent
float kit units is, as you have seen, more time consuming than the simple adjustment method of the stock floats.
The lifting of the float bridge to see the exact contacting of the float needle pin plunger end is tricky. Certainly,
no matter how done, you must be VERY gentle with the fingertip....to see the correct adjustment.....and
to NOT distort the brass bridge. It might be a lot easier for you to turn the gas on & lift VERY gently
to the point the gas JUST shuts off, then lower your finger to the point the gas JUST starts flowing.
That is the parallel point....or should be. Be careful with that bridge. It is flimsy, & if you lift at one a
rm with any real pressure, you can distort it..... both arms must remain parallel to each other, as well
as the final adjustment being parallel to the carburetor body.
10. Once installed & in operation, one can turn off the fuel petcock(s), remove a bowl quickly to avoid
excessive fuel getting into the bowl. The BOTTOM of the BOWL CENTER AREA to the TOP OF THE
FUEL should be very close to 1-5/32". This was for a 40 mm Bing CV carburetor. I have not checked
a 32 mm. When I do, will post it here.
Revisions:02/18/2005: Clarifications and final release
05/22/2005: Add extensive notes, yellow background
05/24/2005: add 4 scanned pages, modify descriptions, minor other things
08/24/2005: Go over article and clarify some details
06/24/2007: Edit the article for clarity, add more cautions.
01/10/2008: Rechecked article
04/13/2009: fix very minor typos and clarified a couple of details
09/13/2009: Correct typo in ...OK.... pay attention here!:::
area, where I had 19.5 mm instead of
proper 10.5 mm.
05/17/2011: slight cleanup. Still a very messy article!
09/19/2012: Add QR code and update google code and fix a couple of unimportant spelling typos
04/30/2013: Complete re-do of the article. Add two bulletins, remove one, re-arrange article,
clarify certain details, etc.
05/13/2013: Add the Bing 1984 original bulletin bing-tech-bulletin-1984.pdf
05/14/2013: Clear up a minor confusing point.
02/08/2014: Revise in several areas, to avoid some confusion with statements about the bowls; clear up typos;
remove information on the bowl gasket that could cause confusion, etc.
09/12/2015: Clean up article
01/08/2016: Meta-codes; left formatting; horizontal separators; narrow the article. minor clarification 01/11
Copyright, 2014, R. Fleischer
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