1 dm^3 = 1 liter ? (very long)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Regarding Bill Larson's investigation for old uses of the liter:
> Ok, so I've finished grading my 13 tests and dragged out the 
> 1966 CRC manual and a 1965 University Physics text, err, 
> um, inherited from my grandfather? No, I was a child prodigy &…
> OK, when I was a freshman.  Neither mention the "liter" AT ALL!
> After checking current texts, which do.  I conclude that the liter 
> was in some sort of purgatory, possibly because it really was 
> indeed not quite equal to 1000 cm^3.

I'm surprised that neither of these references of yours would *mention*
the liter.  I've checked an assortment of CRC Handbook editions from
multiple years and all of them define the liter and give conversion
factors between liters and cm^3, m^3, etc.  But the earliest edition that
I have access to is the 48th ed 1967-8.  Maybe things were different for
earlier editions? 

This question of the history of the definition of the liter has motivated
me to root around the library looking up various definitions of the liter
in various references.  From what I have found it seems that many authors
have been slow to embrace the revised definition of the liter.  Even the
CRC tables have been nearly a decade late.  Below is an abbreviated
history of the situation as best as I have been able to determine it.
(Much of the info comes from 1991 ed. of the NIST spec. pub. 330 on the 
SI system, available on the NIST web site.)  Bill's conclusion "that
the liter was in some sort of purgatory" seems to be born out with more
investigation.

1.  In the aftermath of the French revolution the metric system is
invented.  (It became impractical and politically incorrrect to define
the standard of length in terms of the king's foot after all the royalty
had been put to the guillotine.)  The original meter is 10^(-7) of the
distance between the North Pole and the Equator on the meridian through
Paris, France.  Using this definition of the meter the original
definition of the kilogram is the mass of 10^(-3) m^3 of pure water.
High precision standardized metrological conditions for definitions of
various units are lacking due to the practical limitations of late 18th
century technology.

2. Throughout the 19th century metrological techniques are continued to
be refined while different countries define their versions of the metric
units (including their own customary weights and measures) a bit
differently from each other.

3. Sometime during this time the obsolete French unit of capacity the
litron is resurrected (or at least etymologically honored) and redubbed
the litre and used to signify the volume of a kg of pure water.
(Apparently the litron was the French version of the Medieval Latin litra,
which itself came from an old Greek unit the litra for a kind of a 12
ounce pound.)

4. The CIPM (Comite International des poids et Mesures) convened the 1st
general conference of the CGPM (Conference Generale des Poids et Mesures)
in 1889 and in an attempt to standardize various national meters and
kilograms the conference sanctioned the construction of a standard
international prototype meter and kilogram to be made of an alloy of
platinum with 10% iridium.  The choice of the actual values of these
prototype artifacts were to be chosen as an appropriate intermediate
value so that the difference between the international standard meter and
the various national meters would differ by no more than 0.01 mm from
each other, and the international standard kilogram, similarly, would
differ from the various national kilograms by no more than 1 mg.  All
future national standards were to be kept within these error bounds of
the international prototype values.

5. At the 3rd CGPM in 1901 the international prototype kilogram is
officially declared the kilogram mass, "mass" and "weight" are officially  
given their modern distinctions (the use of mass units for forces
becomes officially verboten) so that [weight] = [mass]*g, and the
"standard" value for g = 9.80665 m/s^2 is adopted.

Also the liter is officially defined as:
  "the volume occupied by a mass of 1 kilogram of pure water, at its
  maximum density and at standard atmospheric pressure".
(N.B. this definition must implicitly assume that the isotopic
composition of the water in question has normal terrestrial isotopic
ratios, but this definition was adopted before the discovery of the
neutron and before any technology of isotopic separation was invented to
change the isotopic ratios of macroscopic amounts of matter.  Also
experimentally it is found that water's maximum density occurs at
3.98 deg C.)

6.  At the 7th CGPM in 1927 international prototype meter is adopted as
the definition of the meter (as the distance between the axes of the two
central lines marked on the Pt-Ir bar when it is maintained at the
freezing point of water, i.e. 0 deg C, and subjected to standard
atmospheric pressure and supported on two symmetrically placed
cylinders of at least 1 cm in diameter and separated by 571 mm in a
horizontal plane).

7. As a consequence of the actions taken in 5. & 6. above the definition
of the liter became slightly different than the definition of the
cubic decimeter.  This is because the meter and the kilogram were now
defined independently of the density of water, but the definition of the
liter still was in terms of the density of water.  High precision/
accuracy measurements of the density of water using the new prototype
standard kilogram and meter revealed an experimental discrepancy that
ended up being such that 1 liter was 0.001 000 028 m^3.

8. In 1950 the CIPM recommended (without apparently officially changing
the definition) that the liter be *defined* as exactly 0.001 000 028 m^3.
(This was in the interim between the 9th and 10th GCPMs in 1948 and 1954
and apparently no action was taken on this matter at the subsequent
GCPMs in the 50s.)

9.  Many important unit redefinitions take place (including the
launching of the official SI system in 1960).  Worries about problems
with the liter are finally addressed at the 11th GCPM in 1960 and
Resolution 13 is adopted which *requested* the CIPM to study the problem:
  "The 11th CGPM considering that the cubic decimeter and the liter are
  unequal and differ by about 28 parts in 10^6, that determination of
  physical quantities which involve mesurements of volume are being made
  more and more accurately, thus increasing the risk of confusion between
  the cubic decimeter and the liter, *requests* the CIPM to study the
  problem and submit its conclusions to the 12th GCPM."

10. In 1961 the CIPM, in an attempt to prevent confusion, recommends that
the results of accurate measurements of volume be expressed in the new
official SI units and not in liters.  Apparently, the liter enters
"purgatory" (as suggested by Bill L.) in 1961.

11. At the 12th GCPM in 1964 the CIPM (among other actions) adopts
Resolution 6 which:
  "1. *abrogates* the definition of the liter given in 1901 by the 3rd
  GCPM,
  2. *declares* that the word "liter" may be employed as a special name
  for the cubic decimeter.
  3. *recommends* that the name liter should not be employed to give the
  results of high accuracy volume measurements."

12. At the 16th GCPM in 1979 the CIPM (among other actions) decides to
loosen up the abbreviation for the liter by adopting Resolution 6 saying:
  "The 16th GCPM, *recognizing* the general principles adopted for
  writing unit symbols in Resolution 7 of the 9th GCPM (1948),
  *considering* that the symbol l for the liter was adopted by the CIPM
  in 1879 and confirmed in the same Resolution of 1948, *considering*
  also that, in order to avoid the risk of confusion between the letter
  l and the number 1, several countries have adopted the symbol L instead
  of l for the liter, *considering* that the name liter, although not
  included in the International System of Units, must be admitted for
  general use with the System, *decides*, as an exception, to adopt the
  two symbols l and L as symbols to be used for the unit liter,
  *considering* further that in the future only one of these two symbols
  should be retained, *invites* the CIPM to follow the development of the
  use of these two symbols and to give the 18th CGPM its opinion as to
  the possibility of suppressing on of them."
(N.B. as of 1990 the CIPM thought it is too early to make a final
decision on this matter of the abbreviations l & L.)

So the definition of the liter was officially changed to the cubic
decimeter as of 1964.  However, this does not seem to have had any
impact on the authors of numerous reference books written well after this
time.  For instance, both the 8th (1971) and the 9th (1977) editions of
the _Condensed_Chemical_Dictionary_, ed. Gessner G. Hawley, Van Nostrand
give the old 1901 definition of the liter.  The CRC *Math* Tables,
at least through the 4th ed. (1970), gives a modified version of the
old def.  What I mean by 'modified version of the old def.' is the liter
seems to be defined as 0.001 000 028 m^3 (rather than as the volume
occupied by 1 kg of water under standard conditions which this number
happens agree with to 7 figures).  Condon & Odishaw's Handbook of Physics
(1967) gives the modified old def.  The CRC Handbook of Chemistry and
Physics gives the modified old def. up until the early 70's editions,
after which it changes to the modern 1964 definition of the liter.  But
this change over is internally inconsistent for some of these editions.
The CRC handbooks use the definition of the liter in two places in the
book.  First, in the table entitled: CONVERSION FACTORS there are
conversion factors telling how many liters are in a m^3, cu. in. etc.
Second, just after this table, there is the short section titled:
DEFINED VALUES AND EQUIVALENTS which also gives the definition of the
liter according to CRC. The earliest CRC handbook I could find was the
48th ed, 1967-8 and it used the modified old def. for both of these
tables.  But the 52nd ed, 1971-72, and the 53rd ed, 1972-3 are
inconsistent in that the first table of conversion factors uses the old
def. but the second table uses the modern (1964) def.  Apparently, all
versions (up to the present) of the CRC Handbook after (and including)
the 54th 1973-4 use the modern definition in both sets of tables. Also
the 2nd ed, 1973 CRC Handbook of Tables for Applied Engineering Sciences,
has the same internal inconsistency as the CRC Handbook of Chemistry and
Physics published at the same time. For some reason, the 22nd ed 1973 of
the CRC Standard Math tables, is particularly confused in that in its
table of DEFINED VALUES AND EQUIVALENTS it gives *both* the modified old
def. *and* the new def. as two incompatible definitions of the liter *in
the same table*.  The 1974 edition of the _McGraw-Hill_Dictionary_of_
_Scientific_and_Technical_Terms, gives the modern def. of the liter.

The reason that I thought that the liter was redefined in the
early 70's was that is when I remembered the CRC Handbook switching
definitions.  It never occured to me that this handbook would continue to
use the old definition for nearly a decade after the liter was really
redefined.  I do not know why so many reference works have continued to
use the obsolete definition of the liter for so long after it has been
changed.  Apparently, the process of producing a "new" edition of some
of these works involves massive recopying of the material in previous
editions *without* updating it or checking it for currency at all.  This
is kind of like the common phenomena of new editions of state highway
maps having the same errors in them as previous versions of the map.

David Bowman
dbowman@gtc.georgetown.ky.us