Radiocarbon dates for pictographs in Ignatievskaya Cave, Russia: Holocene age for supposed Pleistocene fauna. (Notes & News).
Steelman, K.L. ; Rowe, M.W. ; Shirokov, V.N. 等
Key-words: pictographs, AMS radiocarbon dating, Russia, Bronze/Iron
Age rock art, Holocene, Palaeolithic rock art, Pleistocene fauna
Ignatievskaya Cave is located in the northwestern foothills of the
southern Ural Mountains. It is on the right bank of the Sim River, a
tributary of the Belaya River (FIGURE 1). Foothills there are ~200-700 m
high. Average temperature is 0.1 [+ or -] 1[degrees]C with 500-700 mm of
precipitation per year. The area is a coniferous forest, mixed with
deciduous trees (FIGURE 2). Pine, fir, birch, alder and oak are most
typical. Large grasses, ferns and cereal plants are present. There is
rich, black topsoil over a carbonate (limestone) base.
[FIGURES 1-2 OMITTED]
The largest cave in this karst region, with 600 m of Devonian
limestone passages, Ignatievskaya Cave is ~3 m wide and ~2 m high with a
flat horizontal ceiling, with 4 main chambers (FIGURE 3): Entrance Hall,
Main Corridor, Large and Far Halls--the last two connected by two narrow
tubes. Cave temperature is nearly constant at 5[degrees]C.
[FIGURE 3 OMITTED]
Although Ignatievskaya Cave has long been known by local residents,
ancient red ochre and black charcoal prehistoric images were discovered
by archaeologists V.T. Petrin, S.E. Chairkin & V.N. Shirokov only in
1980. The site was studied on field trips from 1980 to 1986 by Petrin et
al. (1992) and in 1995 by Scelinskij & Shirokov (1999). Over 50
pictographs were found and recorded during those studies.
Paintings are located only in the Large and Far Halls at ~120 m
from the entrance. There are no prehistoric drawings in the Entrance
Hall. This site is a good example of image integration into naturally
occurring rock morphology. In Large Hall, pictographs were placed on
vertical and sloping walls and ceiling, as well as in niches and
depressions. Images are also located on a large pillar. In contrast,
most pictographs in Far Hall are painted on the ceiling, with only a few
on the walls.
Description of pictographic images
Drawings vary from 1.5 cm for symbols to as large as 2.3 m for
animals and anthropomorphs. Lines are 1 to 5 cm wide. Paintings are two
colours: shades of red (iron ochre) and black (charcoal). In Far Hall,
black figures dominate; in Large Hall, red paintings are more prominent.
There are only three black paintings in Large Hall.
Images are animals, symbols, anthropomorphs and indefinite
figurative motifs. Representations of `mammoths' (6 or 7) and
horses (4) constitute a majority of animal images. There are, however,
paintings of an ox, a rhinoceros-like animal, a composite animal with a
camel-like body and a mammoth-like fanciful creature. All animals (20-30
cm long) in Large Hall were sketched as shaded silhouettes, with minimal
features depicted. Some `mammoth' drawings do not show a neck and
only one has tusks. A horse image is sketchily drawn without a mane or
ears (FIGURE 4). Animals have straight legs, and at times only two are
depicted.
[FIGURE 4 OMITTED]
Unlike Palaeolithic rock art of animals in France and Spain, images
here are ambiguous; identification is problematic. Straight legs make
images of black animals rather static. Motion is only suggested in one
`mammoth' image that has bent knee joints. Another `mammoth'
(FIGURE 5) apparently has a characteristic high-domed head, a trunk and
possible tusk(s). But these assignments are not definitive. The
`camel' body of a composite animal is drawn with only three or four
lines. Black animals (0.3 to 1.3 m) are mostly outline drawings. A red
rhinoceros has four legs, roughly sketched, as on other animals. Its
body was drawn in outline with partial shading, and is ~2.3 m long.
[FIGURE 5 OMITTED]
Anthropomorpic images in Far Hall are represented by a black male
figure ~32 cm long and a red female figure (FIGURE 6) ~1.2 m long. These
anthropomorphs form a complex composition with a large figure of a
rhinoceros. There is a black drawing of a `phantom'. A red motif
(20 cm tall) in Large Hall is characterized as a combined human and
aviform. All these figures are outlines.
[FIGURE 6 OMITTED]
Numerous signs include: single lines and groups, dots, meanders,
arrow-shaped forms, tridents, triangles, extended parallelograms, cross-
and anchor- shaped motifs, as well as patches of colour. One ring-shaped
motif looks like a rhinoceros footprint. Signs outnumber human and
animal figures threefold, varying from 1.5 cm to >1 m.
Previous investigations at Ignatievskaya Cave
Archaeological excavation undertaken in the cave uncovered an Upper
Palaeolithic level. Its sediments contained fragments of torches,
charcoal, stone and bone artefacts, as well as pieces of ochre,
ornaments and animal bones. More than 1300 stone tools were unearthed,
mostly near the cave entrance. They were made from different types of
stone: jasper, flint, quartzite, sandstone, limestone, etc. Scrapers,
retouched flakes, burins, scaled pieces and notched denticulate forms
dominate artefacts. There are blades with blunted edges, including some
worked at the ends. These could have formed part of a composite tool
with a bone, horn or wooden shaft. Two pendants were made from the
canine of a polar fox and a tooth of an ox or bison. Two tiny round flat
beads were made from bone or tusk.
Three radiocarbon dates obtained from charcoal from Large Hall
place human activity in Ignatievskaya Cave at Late Pleistocene: 14,240
[+ or -] 150 BP (Laboratory of Siberian Branch of Russian Academy of
Sciences (LSBRAS), 2209); 13,335 [+ or -] 195 BP (Institute of
Evolutional Morphology and Ecology of Animals, 365); 10,400 [+ or -] 465
BP (LSBRAS, 2468). One of us (VNS) assumed that some images were of
Pleistocene age. Aside from depiction of `mammoths' and
`camels', there is no direct evidence to connect painted images
with Pleistocene occupation of the site. Paintings could be contemporary
with more recent archaeological finds within or outside the cave.
Although Upper Palaeolithic finds occur near the cave entrance, there
were few artefacts from the Bronze (early 2nd to mid 1st millennia BC)
and Iron (mid 1st millennium BC to late 1st millennium AD) Ages here,
and no ancient drawings.
Experimental procedure
Sample collection
During August 1998, we removed small samples of charcoal pigment
from three pictographs and a red iron oxide pigment from a fourth with
scalpels while wearing rubber gloves. Samples, including underlying rock
and accretionary mineral matter, were placed on aluminium foil, wrapped
and stored in plastic bags. Backgrounds, adjacent rock with no pigment,
were collected and analysed. These went to Texas A&M University
(hereafter TAMU). Each sample was examined with an optical microscope to
ensure that no extraneous material was included in the sample. None was
found.
Chemical pretreatment
Again, rubber gloves were worn to avoid contamination during all
sample handling. Procedures for chemically pretreating archaeological
charcoal vary slightly from laboratory to laboratory; all involve
treatment with acid-base-acid (e.g. Bowman 1990; Taylor 1987). We
routinely eliminate both acid washes as we have shown them to be
unnecessary with plasma-chemical extraction (Pace et al. 2000).
Carbonate and oxalate carbon are not extracted by plasma; only organic
material was removed to be analysed by radiocarbon measurements (e.g.
Russ et al. 1992; Chaffee et al. 1994).
To remove potential humic acid contamination, we immersed each
sample in ~5 ml of 1 M NaOH and placed them in an ultrasound bath for an
hour at 50 [+ or -] 5[degrees] C. After NaOH wash/ ultrasonication
treatments, when the resulting supernatant was coloured, subsequent NaOH
washes were necessary because humic acids appear brownish-yellow in
NaOH. After supernatant was colourless, one additional treatment with
NaOH was done to ensure humic acid removal. Adsorbed C[O.sub.2] and
water from air are removed by vacuum and plasma treatments. Plasma
extraction was performed on dried filtrate.
Plasma-chemical treatment
The plasma-chemical method used to extract organic carbon from
these pictographs was described elsewhere (e.g. Russ et al. 1990; Hyman
& Rowe 1997). Ultra-high purity bottled argon and oxygen (99.999%)
were used for plasmas. Rotary pumps are sufficient to maintain vacuum
([~10.sup.-4] torr). First, a low-temperature ([less than or equal to]
150[degrees]C), low-pressure (~1 torr) oxygen plasma was used to
preclean the reaction chamber; this was repeated until [less than or
equal to] 0.001 mg carbon, as C[O.sub.2], was released. Once the chamber
was clean, samples were introduced via a copper-gasketed stainless steel
flange port under a flow of argon to prevent atmospheric C[O.sub.2],
aerosols or organic particles from entering the system. After the
chamber was resealed and the sample degassed under vacuum and heat,
low-temperature argon plasmas were used to desorb C[O.sub.2] molecules
from the sample and chamber walls by inelastic collisions of the
nonreactive, but energetic, argon species. Adsorbed C[O.sub.2] on the
samples was reduced to [less than or equal to] 0.001 mg of carbon by
vacuum pumping.
Next, an oxygen plasma oxidized charcoal in black pigment samples
and unknown organic material in the iron oxide pigment to C[O.sub.2].
Decomposition of inorganic carbon present (limestone and calcium
oxalate) was prevented by plasma conditions. Oxidising plasmas react
only with organic carbon in the samples, leaving substrate rock and
accretionary carbonates and oxalates intact (Russ et al. 1992; Chaffee
et al. 1994). Carbon dioxide from samples was flame-sealed into glass
tubes cooled to liquid nitrogen temperature (-194[degrees]C) after water
was frozen out with a dry-ice/ethanol slurry (-58[degrees]C), and
finally sent for radiocarbon analysis to the Center for Accelerator Mass
Spectrometry at the Lawrence Livermore National Laboratory (CAMS).
Results
TABLE 1 shows results of plasma extraction for four Ignatievskaya
Cave samples and the three radiocarbon dates obtained. Carbon extracted
from the red woman pictograph was insufficient to obtain a radiocarbon
date. Since the relationship between radiocarbon years and calendar
years is not linear, calibration is necessary in order to assess the
actual calendar date of any archaeological sample. Therefore, the
2[sigma] (95.4% confidence level) calibrated range using the OxCal
Program, version 3.5, calibration is included with uncalibrated ages
(Ramsey 2000; Stuiver et al. 1998). The calibration curve for sample
4RU292 is shown in FIGURE 7.
[FIGURE 7 OMITTED]
Discussion
These [sup.14]C dates for pictographs at Ignatievskaya Cave are
more recent than was generally supposed by Russian archaeologists
(Petrin & Shirokov 1990; Petrin 1992; Scelinskij & Shirokov
1999). Excavations and depictions of extinct animals such as those
interpreted as mammoths suggested Palaeolithic antiquity. Although other
evidence at this site must be considered, these pictograph dates cannot
be ignored, especially because of previous doubts about Palaeolithic
antiquity for drawings at Ignatievskaya Cave (Formozov 1999; 2000).
Absence of contamination
Dates obtained for the drawings are more recent than was expected
for `mammoth' images. Could soot, containing modern carbon, have
contaminated the samples? Ignatievskaya Cave was named after Ignatij, a
hermit, who lived there in the late 18th and early 19th centuries. After
his death, religious processions took place there every year until the
1930s. Inside the cave, people used torches and burned other objects
such as tyres. Due to its accessibility, numerous tourists, also using
torches, visited it. Some walls and the ceiling appear to be covered by
soot. In our (KLS & MWR) experience, what appears to be soot is
often a black mineral deposit (sometimes calcium oxalate). Similarly,
potential presence of lichen, fungi, bacteria and general wind-blown
organic matter, if present in significant amounts, could cause a falsely
young age. We saw no indication of lichen or fungi contamination with
microscopic examination.
To assess potential contaminations, especially bacterial and
wind-blown materials, we routinely take background samples from
unpainted rock adjacent to pigment samples. That process takes on an
important role here because resultant dates were much younger than
expected, at least for the representation of a `mammoth'. The
amount of carbon extracted from a background is used to estimate
contamination in unpainted rock, and hence of sample containing pigment.
Relative sizes of a pigment-containing sample and its background are
considered when necessary. Without a background, potentially devastating
contamination in a sample may not be taken into account, rendering a
radiocarbon date untrustworthy.
Less than 0.002 mg of carbon was extracted from Ignatievskaya Cave
background samples for the dated images, indicating that contamination
is negligible. We calculate here the percentage modern (1950)
contamination that would be necessary to skew expected ages (according
to an assumed mammoth extinction time for the area of 12,000 years ago)
at Ignatievskaya Cave to the radiocarbon ages measured. We used activity
half-life and contamination equations from Bowman (1990:27-28): A =
[A.sub.0][e.sup.-t/8033] and [A.sub.m] = f[A.sub.x] + (1-f)[A.sub.s],
where A = [sup.14]C activity at time t, [A.sub.0] = modern [sup.14]C
activity, f = fraction of contamination, [A.sub.m] = measured [sup.14]C
activity, [A.sub.x] = contaminant [sup.14]C activity, and [A.sub.s] =
`true' sample [sup.14]C activity.
Results of these calculations are summarized in TABLE 2. For the
`mammoth' pictograph, 23% contamination with modern (1950) carbon
is required to obtain a `true' age of 12,000 years BP. This level
of contamination was not observed in backgrounds of these samples. In
addition, this level of contamination from lichen or fungi would have
been visible during microscopic examination. Thus, the potential
problems listed above are not the cause of the unexpectedly recent dates
obtained, unless bacterial growth occurred preferentially in the paint.
Bacterial growth associated with organic material added during paint
manufacture would be expected to approximate the age of the painting
itself.
Evidence for Palaeolithic antiquity
The strongest evidence for a Palaeolithic age of Ignatievskaya
images is the depiction of supposed Pleistocene animals. `Mammoths'
and other Palaeolithic fauna predominate over depictions of other
animals in both halls. Other Ice Age creatures, namely horses, a
rhinoceros-like animal and ancient oxen, are also depicted in
Ignatievskaya Cave. The image of a composite animal with a `camel'
body is interesting, especially when one realizes that bones of camels
are known from Pleistocene deposits in the Ural Mountain region. This
set of extinct species differs from animals represented at open-air
rock-art sites in this region. Such sites contain reproductions of elk,
deer, roe, water-birds, occasional drawings of bear and undetermined
figures of small animals. One of us (VNS) surveyed and studied all ~70
known rock and cave-wall art sites of the Ural Mountains.
In support of Palaeolithic ages, mammoths apparently disappeared in
the southern Ural Mountains by the Late Pleistocene. Radiocarbon dates
from remains of mammoths indicate these animals were extinct 12-14,000
years BP (Sulergitsky 1995). In Large Hall, in the area of drawings,
only Upper Palaeolithic artefacts have been found. Therefore, the
repertoire of images from Ignatievskaya Cave was thought to represent an
Upper Palaeolithic age (Kosintcev 1990: 171-8). However, there is little
stratigraphic evidence of relative contemporaneity of mammoth remains
with Upper Palaeolithic drawings of Ignatievskaya Cave. During
excavation of friable deposits close to a red horse panel (group 23 in
Petrin 1992), there is a tiny seam of a white earthy incrustation of
unknown mineralogy. Numerous pieces of charcoal and ochre, as well as
stone tools and a pendant made from a polar fox canine, were unearthed
beneath it. Polar fox, as a species, inhabited the South Ural Mountains
only in the Pleistocene (Kosintcev 1999). Since white incrustation
covers some art motifs located on the cave walls, it seems plausible
that some images in Ignatievskaya Cave are at least 10,000 years old
(Kosintcev 1990: 171-8; Petrin & Shirokov 1990; Petrin 1992;
Scelinskij & Shirokov 1999).
Evidence for Bronze Age images
Formozov (2000) stated that although some images at Ignatievskaya
Cave might be Palaeolithic depictions, others belong to later time
periods. Formozov supports a later date for paintings at Ignatievskaya
Cave from artefacts of the Bronze Age (level B of Formozov 1998; 2000)
and Iron Age (level C) that were found at the site in addition to those
of the Upper Palaeolithic (level A).
The repertoire of images and symbols in Ignatievskaya Cave and
open-air rock-art sites of the post-Palaeolithic period are very
different. Among known anthropomorphic drawings of rock art in the open
air, there are no images with female features like the red female figure
in Ignatievskaya Cave. In general, most open-air rock-art sites were
created from the Late Neolithic to Bronze Age periods, with some even
dating to the Iron Age (Chernetsov 1964; Formozov 1969; Shirokov et al.
2000). However, direct dating methods should be applied to have reliable
dates for these open-air sites.
Conclusions
Although there was evidence that some paintings in Ignetievskaya
Cave were of Palaeolithic age, in particular depictions of megafauna such as mammoths, three radiocarbon dates (~6000 to ~8000 BP) place
images into the early Holocene. We have no reason to suspect the
pictograph radiocarbon dates presented here. We have shown that modern
backgrounds are far too low to cause movement of a true age of 12,000 BP
to appear as young as 7370 BP. To bring our ages from the 6000-8000
range up to 12,000 BP would require almost 25% contamination by modern
(1950) carbon. That is larger by two orders of magnitude than we have
seen here. Analysis of unpainted rock as background eliminates soot from
torches as significant contributing factors, as well as other potential
contaminants discussed above. Humic acids were removed with NaOH washes
as is routine in radiocarbon dating of charcoal. It is nonetheless
surprising that the `mammoth' image produced such a recent date
(7370 [+ or -] 50 BP). Two commonplace effects that must always be
considered for radiocarbon dates on charcoal, `old wood' and
`fossil charcoal', if important here, would move the dates in the
opposite direction to that observed in this work (Schiffer 1986;
Bednarik 1994). That is, the age determined would appear older than
expected, not younger as observed.
These radiocarbon dates indicate that either: 1 the `mammoth'
image (FIGURE 5) may not actually be of a mammoth;
2 mammoth existence extended into the Holocene in the area,
although there is no dating evidence for that;
3 the depiction was not based on a live mammoth; or
4 there was repainting of an older image, such that younger
overpainting and original painting charcoal combines to give a
meaningless radiocarbon age, more recent than the initial painting
event.
Acknowledgements. This research was funded in part by the Office of
the Vice-President for Research and Associate Provost for Graduate
Studies with a Regents Fellowship and with a travel grant from the
International Research Travel Assistance Grant, both from Texas A&M
University. Lawrence Livermore National Laboratory is funded by the US
Department of Energy under contract W-7405-Eng-48. VNS' text was
translated from Russian into English by S. Sharapova. Elena Miklashevich
and Paul Bahn also helped with translation and information of various
kinds; this manuscript was significantly improved through their efforts.
Jason Ott and Ruth Ann Armitage assisted in plasma measurements.
Photographs of pictographs were enhanced with Adobe Photoshop by Robert
Mark, Rupestrian Cyber Services.
TABLE 1. Results of plasma oxidation and the radiocarbon dates
obtained for Ignetievskaya Cave samples. The `mammoth' dated is
shown in FIGURE 5.
motif colour TAMU# carbon CAMS #
`Mammoth' black 4RU292 0.10 mg 56586
radiating lines black 4RU291 0.21 mg 56271
lines black 4RU318 0.07 mg 67688
woman red 4RU330 <0.01 mg --
motif [sup.14]C age 2[sigma] age
(BP) range (cal BC)
`Mammoth' 7370 [+ or -] 50 6390-6080
radiating lines 7920 [+ or -] 60 7040-6640
lines 6030 [+ or -] 100 5300-4650
woman -- --
TABLE 2. Calculations showing the percent contamination of modern
carbon required to alter these measured radiocarbon dates to the
archaeologically expected ages.
observed expected [A.sub.m] [A.sub.s] [A.sub.x] %
date date contamination
7370 12,000 0.3995 0.2245 1 23
7920 12,000 0.3731 0.2245 1 19
6030 12,000 0.4721 0.2245 1 32
References
BEDNARIK, R.G. 1994. Conceptual pitfalls in dating of Palaeolithic
rock art, Prehistoire Anthropologie Mediterraneennes 3: 95-102.
BOWMAN, S. 1990. Interpreting the past: radiocarbon dating. Los
Angeles (CA): University of California Press.
CHAFFEE, S.D., M. HYMAN & M.W. ROWE. 1994. Radiocarbon dating
of rock paintings, in D. Whitley & L.L. Loendorf (ed.), Newlight on
old art: recent advances in hunter-gatherer rock art: 9-12. Berkeley/Los
Angeles (CA): University of California Press.
CHERNETSOV, V.N. 1964. Naskalnye Izobrajenia Urala. Chast' 1.
M.: On je, chast 2, 1971, Moscow.
FORMOZOV, A.A. 1969. Ocherki po pervobytnomu iskusstvu. Moscow.
1998. O svyatilistche v Ignatievskoy pestchere na Urale //
Politropon. K cemidesyatyletiu Vladimira Nickolaenicha Toporova. M., pp.
871-874.
2000. O datirovke rospicey v Ignatievskoy pestchere na Ugnom Urale
// Rossiyskaya arheologia, No. 1: .215-217.
HYMAN, M. & M.W. ROWE. 1997. Plasma-chemical extraction and AMS
radiocarbon dating of rock paintings, in S.M. Freers (ed.), American
Indian Rock Art 23: 1-9. San Miguel (CA): American Rock Art Research
Association.
KOSINTCEV, P.A. 1990. Istoria razvitia fauny krupnyh
mlekopitaustchih // Istroricheskaya ekologia givotnyh gor Ugnogo Urala.
Cverdlovsk, Russia.
1999. Formation and evolution of the Holocene fauna of megamammals
in the Urals and West Siberia, in N. Benecke (ed.), Archaologie in
Eurasia 6: 133-9.
PACE, M.F.N., M. HYMAN, M.W. ROWE & J.R. SOUTHON. 2000.
Chemical pretreatment on plasma-chemical extraction for [sup.14]C dating
of Pecos River genre rock paintings, in F.G. Bock (ed.), American Indian
Rock Art 24: 95-102. San Miguel (CA): American Rock Art Research
Association.
PETRIN, V.T. 1992. Paleoliticheskoe svyatilistche v Ignatievskoy
pestchere na Ujnom Urale. Novosibirsk.
PETRIN, V.T. & V.N. SHIROKOV. 1990. Naskalnye izobragenia
Ugnouralskogo regiona (itogy i perspektivy issledovany). Problemy
izuchenia naskalnyh izobrageny v SSSR. M.: 73-8.
RAMSEY, C.B. 2000. Manual for OxCal Program Version 3.5, University
of Oxford Radiocarbon Accelerator Unit. www.rlaha.ox.ac.uk/oxcal/
Russ, J., M. HYMAN & M.W. ROWE. 1992. Direct radiocarbon dating
of rock art, Radiocarbon 34: 867-72.
Russ, J., M. HYMAN, H.J. SHAFER & M.W. ROWE. 1990. Radiocarbon
dating of prehistoric rock paintings by selective oxidation of organic
carbon, Nature 348: 710-11.
SCELINSKIJ, V.E. & V.N. SHIROKOV. 1999. Hohlenmalerei im Ural.
Kapova und Ignatievka. Die altsteineitlichen Bilderhohlen im sudlichen
Ural. Thorbecke, Germany.
SCHIFFER, M.B. 1986. Radiocarbon dating and the `old wood'
problem: the case of the Hohokam chronology, Journal of Archaeological
Science 13: 13-30.
SHIROKOV, V.N., S.E. CHAIRKIN & U.P. CHEMIAKIN. 2000. Uralskie
pisanitsy. Reka Nejva. Ekaterinburg, Russia.
STUIVER, M., P.J. REIMER, E. BARD, J. W. BECK, G. S. BURR, K.A.
HUGHEN, B. KROMER, G. MCCORMAC, J. VAN DER PLICHT & M. SPURK. 1998.
INTCAL98 radiocarbon age calibration 24000-0 cal BP, Radiocarbon 40:
1041-83.
SULERGITSKY, L.D. 1995. Cherty radiouglerodnoy hronologii mamontov
(mammuthus primigenius) Cybiri i Cevera Vostochnoy Evropy //
Issledovania po Pleistotsenovym i Sovremennym Mlekopitaustchim.
SPb.,1995, T. 263; pp.163-183.
TAYLOR, R.E. 1987. Radiocarbon dating: an archaeological
perspective. New York (NY): Academic Press.
K.L. STEELMAN, M.W. ROWE, V.N. SHIROKOV & J.R. SOUTHON *
* Steelman & Rowe, Department of Chemistry, Texas A&M
University, PO Box 300012, College Station TX 77842-3012, USA.
steelman@mail.chem.tamu.edu rowe@mail.chem.tamu.edu Shirokov, Institute
of History & Archaeology, Urals Branch of Russian Academy of
Sciences, 56 Luxemburg Street, Ekaterinburg 620026, Russia.
istor@uran.ru Southon, Center for Accelerator Mass Spectrometry,
Lawrence Livermore National Laboratory, Livermore CA 94551-9900, USA.
Southon1@llnl.gov
Received 22 March 2001, accepted 5 November 2001, revised 6
November 2001