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"The discovery of water on the Sun didn't have quite the same impact as the discovery of water on the Moon; even NASA would find it hard to turn it into a call for colonization. But it shows that water finds its way into just about any niche in the Universe that will have it." (p. 111)A dull topic for a book, you'd think. Philip Ball is a fantastic writer and scientist, though, so the dullness is few and far between. After 400 pages a reader becomes a literal expert on the subject. The journey to that point is full of twists and turns and surprising things about water. Who would have ever thought that water was so fascinating?
Contrary to popular belief and common experience, water is an odd molecule. As Ball explains
. . .cold water gets more runny when it is squeezed, whereas most liquids become more viscous under pressure. Water's other peculiarities are chemical. . . (p. 156)Did you know there are different kinds of ice with varying freezing points? Some ice can remain solid even when heated to more than 200° F!
In the latter part of the book Ball turns to curiosities of science, relating to water, that have arisen from time to time. His dissecting of pseudo-science is performed masterfully. He raises the important point that to the scientist the blue "apple tempts--because every scientist dreams of uncovering some new and startling aspect of the world. The risk of a closed mind is a dull and ineffectual career. The risk of gullibility, meanwhile, is a ruined one." (p. 273) He discusses the scientific publishing process from an insider's point of view. And he delves into the significant differences between science and other "Truth" finding methodologies.
Science derives much of its formidable strength from the ability to make--and to live with--mistakes. Many other systems of belief have great problems with mistakes--admission of such in religion and politics is seen to be a mark of weakness. Much of the practice of science, meanwhile, consists of the gradual correction of the mistakes of previous generations. You could say that science progresses by bringing mistakes to light, not by trying to hide them. (p. 276)With this stage set, Ball delves into the history of several dubious claims. Among them are cold fusion, polywater, homeopathy, and "water as fuel." On the latter he, in part, states
I find myself being asked from time to time if I have heard about the water-powered car. I have never been able to track down the source of these rumors, but am struck by their apparent tenacity in the face of chemical good sense. A car fueled by water is like a car fueled by exhaust fumes. Water is not a fuel--at least not a chemical fuel, one that can be burned like gasoline. Rather, it is the exhaust of a fuel: what you're left with when you burn hydrogen. Water is spent fuel. Yet when water was found on the Moon in 1998, you could be forgiven for thinking, on the basis of media reports, that NASA had unearthed a reservoir of rocket fuel. (p. 294)In the Epilogue the resource of water is explored. The environmentalists will cheer. The conservatives (who oxymoronically don't want to conserve the Earth's resources or curb population growth) will moan. It's a good piece to read alongside the dated Desert Solitaire.
The book, as a whole, is great fun to read in conjunction with The Ice Master. Ball's word choice is almost always perfect. He writes concisely, clearly, and seemingly effortlessly. He is a joy to read. I look forward to catching up on his other works and to reading what he produces in the future.
from the publisher:
Life's Matrix
A Biography of Water
By Philip Ball
Published by Farrar, Straus and Giroux
May 2000; $25.00 US/$39.95 CAN; 0-374-18628-6
In this brilliantly written and engrossing biography of one of Earth's most common yet unusual substances, Philip Ball reduces the scientific and philosophical inquiry of over two thousand years to one essential question: What exactly is water?
It is one of the four elements of classical antiquity. It is a geological force that shapes mountains and coastlines, with a might that is unleashed in the destructive fury of hurricanes and floods. Water is the fabric of snow, hail, steam, and ice, and the only substance able to exist on earth in all three of its physical states: solid, liquid, and gas. Water is central to our planetary environment.
Life's Matrix tells of water's origins, its history, and its fascinating pervasiveness: there are, for example, at least fourteen different forms of ice. A provocative exploration of water on other planets highlights the possibilities of life beyond Earth. Life's Matrix reveals the unexpected in the most ordinary places--a drop of dew, a frozen pond, a cup of coffee--and the familiar in unexpected settings. There is water on the sun and the moon, at the heart of molecular biology, at the core of a cell, and there may be enough of it beneath the surface of the Earth to refill the oceans thirty times over. Life's Matrix also surveys the grim realities of our natural resources, and shows how water will become a scarce commodity in the twenty-first century.
Ball's lively and intelligent book takes us on a journey through the history of science, folklore, the wilder fringes of the scientific world, cutting-edge chemistry, physics, cell biology, and ecology to give a startling new perspective on life and the substance that sustains it. Life's Matrix offers an exhilarating exploration of one of the oldest, most idiosyncratic substances known to mankind, and ensures that we will never think about water in the same way again.
Author
Philip Ball majored in chemistry at the University of Oxford and received a
Ph.D. in physics from the University of Bristol. He worked for ten years
as an editor at Nature, where he is now a writer and consulting editor.
Ball is the author of Designing the Molecular World: Chemistry at the
Frontier, Made to Measure: New Materials for the 21st Century, and
The Self-Made Tapestry: Pattern Formation in Nature. He lives in
London.
Reviews
"Marvellous...compelling...This is one of the
best science books of the year. By dint of a lot of flair and eclectic
learning, Ball makes us look afresh at the most commonplace substance
imaginable. Somehow, he has made water exciting."
--Graham Farmelo, New Scientist
"There can be no other substance for which one could
write such an engaging account of the profound historical influence exerted on
this wide range of subjects. The author's panoramic knowledge, conveyed through
a clear and often delightful writing style, makes attractive reading."
--Frank H. Stillinger, Nature
"Philip Ball is a brilliant science writer and
risk-taker...He has handled his incredibly complex scientific brief more
skillfully and more entertainingly than anybody else could have done."
--Anna Paterson, Sunday Herald (Glasgow)
"A science book to recommend highly...Philip Ball writes
clearly, humorously and with an enviable range of literary allusions about a
subject which would tie others in knots."
--Charles Clover, The Daily Telegraph
Excerpt
The following is an excerpt from the book Life's Matrix: A Biography of Water
by Philip Ball
Published by Farrar, Straus and Giroux;
May 2000;
$25.00US/$39.95CAN; 0-374-18628-6;
Copyright © 2000 Philip Ball
THE FIRST FLOOD
WATER'S ORIGINS
Surely this is a great part of our dignity ... that we can know, and that
through us matter can know itself; that beginning with protons and electrons,
out of the womb of time and the vastness of space, we can begin to understand;
that organized as in us, the hydrogen, the carbon, the nitrogen, the oxygen,
those 16 to 21 elements, the water, the sunlight--all, having become us, can
begin to understand what they are, and how they came to be.
George Wald, Nobel laureate in medicine
Those stars are the fleshed forebears
Of these dark hills, bowed like labourers,
And of my blood.
Ted Hughes, "Fire Eater"
In the beginning there was water. While the earth was formless and empty, the
Hebrew God was "hovering over the waters." There was no sky, no dry
land, until God separated "the water under the expanse from the water above
it" and commanded that "the water under the sky be gathered to one
place."' Then the world emerged--from an infinite primeval ocean.
This is echoed in similar myths throughout the world. In central and northern Asia, North America, India, and Russia, a recurring motif is that of the Earth Diver: an animal or a god who plunges to the bottom of a primordial ocean to bring up a seed of earth. The Polynesian cosmogeny reproduces that of the Old Testament in extraordinary detail: the supreme being, Io, says, "Let the waters be separated, let the heavens be formed, let the earth be!" For the Omaha Native Americans, all creatures once floated disconsolately on a wholly submerged Earth until a great boulder rose from the deep. In Hindu mythology, the sound that embodied Brahma became first water and wind, from which was woven the web of the world. "Darkness was there, all wrapped around by darkness, and all was Water indiscriminate" says the beautiful creation hymn of the Rig Veda (3700 B.C.) For the Maya of Central America also, the deity Hurakan called forth the land from a universe of darkness and water.
Why does this idea of a watery beginning resonate throughout disparate cultures, without heed to the local particulars of geography or religious tradition? Ultimately its origin may be psychological: the land was knowable for ancient peoples, but the sea was a symbol of the unconscious--something mysterious, pristine, unfathomable. I know of no creation myths where the land came first and the seas followed in a subsequent deluge.
Yet land and sea are contemporaneous and complementary in some traditions. The Judeo-Christian distinction between flesh and blood is a distinction between the earthy and watery aspects of the corpus of the world. In Norse mythology, the land is the flesh and bones of Ymir, the first giant, slain by Odin. His salty blood, gushing from the spear wound in his heart, became the oceans. So too in Chinese myth are land and sea coeval aspects of a primal being, Pan-Ku the sculptor, whose medium was his own body.
But is there any truth of a more material nature in these myths--was the world
once covered with water? And where has the water come from?
IN THE BEGINNING
In myth, the origin of the Universe is seldom differentiated from the origin of the Earth. To look beyond the beginning of our world is to ponder the eternal: the Chaos of the Greeks, the abyss of fire and ice called Ginnungagap by the Norse, or the supreme deity Akshara-Brahma in Hindu tradition. Today, Earth's beginning is merely a local question, a moment of parochial interest in an already mature universe. The real moment of creation goes back at least six billion years beyond that, and it is as fantastic as any myth.
Origins are seldom uncontentious. Current fashion sometimes has it that the idea of a cosmic Big Bang is best regarded as our latest cultural myth, as much a social construct as the slaying of Ymir. On the one hand, it can only be arrogant to suggest otherwise; on the other, it's this particular kind of confidence that makes science possible. From a scientific perspective, the Big Bang is beyond question still the best model we have for the birth of the Universe, and rests on some formidable pillars. To address the question of why water is what it is, modern cosmology provides a consistent and explanatory framework in a way that Odin's murder of Ymir does not.
Imagine watching a movie of an explosion moments after it has happened. You see many fragments, rushing away from one another within a "bubble" of expanding size. When, in 1929, the astronomer Edwin Hubble saw the galaxies of the Universe behaving in the same way, he was forced to the same conclusion as the one we would reach from the movie: this is the aftermath of an explosion. But Hubble was seeing it from the inside--we are riding on one of those fragments, the Milky Way galaxy. The Universe is getting bigger as all the galaxies rush away from one another. The natural inference is that all the matter in the Universe was once focused into a much smaller volume, which went Bang! Albert Einstein had deduced as much in 1917: when he applied his theory of general relativity to the Universe as a whole, he found the equations predicting that it had to be either expanding or contracting. That seemed to him then to be a crazy notion, and so he added a "fudge factor" to remove the expansion. But Hubble's discovery persuaded him in 1931 that no fudging was needed after all.
After just one-millionth of a billionth of a second, when according to some
theories the Universe might have been just a few feet across, the temperature
would have been in the region of a billion billion degrees. In such extremes,
there can be no atoms and molecules, no matter as we currently know it.
But as it expanded, the temperature of the Universe dropped rapidly. At the end
of the first day of creation, it would have been about twenty million
degrees--about as hot as the center of a star. The Universe today, with all its
stars and supernovae and quasars, is but a dim, cool remnant of this cosmic
fireball. In 1965 Arno Penzias and Robert Wilson at Bell Telephone Laboratories
detected the faint afterglow that pervades the sky: a uniform background
radiation of microwaves coming from all directions, indicating an average
temperature of about five degrees Fahrenheit above absolute zero. This cosmic
microwave background is all that is left of the Big Bang's fury.
THE FABRIC OF WATER
George Wald's view, quoted at the beginning of this chapter, is mine:
understanding what we are composed of, and where that stuff came from, is part
of our dignity. It demands, too, a greater humility to read the lives of stars,
rather than divine providence, in our bones and blood. But bones and blood must
come later; for now, I want to follow only the gestation of those protons and
electrons, and from them the hydrogen, the oxygen--and the water.
For this is what we're after, these two elements: the H and the 0, which unite
so readily to create our subject. Water is H20, the only chemical formula that
everyone learns: two atoms of hydrogen welded to one of oxygen. Their union is a
molecule--a cluster of atoms. Chop up a block of ice, and keep chopping--and your
finest blade, finer than the keenest surgical scalpel, will eventually reduce
the fragments to these individual three-atom clusters. If you chop beyond that,
you no longer have water. The H20 molecule is the smallest piece of water you
can obtain, the basic unit of water.
So here is a central aspect of water's character: it is a compound, an
association of atoms, divisible into atoms of different natures. Yet water is so
fundamental to the world that for millennia it was mistaken, naturally enough,
for an element, something indivisible. Hydrogen and oxygen are elements, because
they each contain only one kind of atom. But there is no "water
atom"--only a water molecule, made up of two different types of atom.
Before making bread, one must make flour; and before water could come into the
Universe, there had to be hydrogen and oxygen atoms. But before flour comes
wheat--and atoms too have more fundamental constituents, Wald's protons and
electrons.
As far as atoms are concerned, protons and electrons are like knives and
forks at the dinner table: no matter how big the table, there are equal numbers
of each. The difference between atoms of different elements--between an atom of
oxygen and one of carbon, say--is simply that they contain different numbers of
protons. In this regard, the underlying pattern of atoms is numerical, as Jacob
Bronowski says in The Ascent of Man. An atom with one proton (and one
electron) is hydrogen; an atom with eight of each is oxygen. At one level,
chemistry is as simple as counting.
At another level, it is clearly not. For mere proton bookkeeping offers no clue as to why hydrogen atoms join with oxygen atoms in the ratio of 2:1, or why sodium (eleven protons) is a soft reactive metal, chlorine (seventeen protons) a corrosive gas, silicon (fourteen protons) an inert gray solid. To understand any of this, we need to consider how the electrons are deployed: for there are deeper patterns in the arrangement of the electrons that determine the element's chemical properties.
Protons and electrons are not, as British physicist J. J. Thomson believed at the turn of the century, lumped together inside the atom as a heterogeneous blob. Rather, they bear to one another something like the relationship of the planets to the Sun, with the electrons orbiting a central, dense nucleus where the protons are. In this "solar system" model of the atom, proposed by Thomson's protégé, New Zealander Ernest Rutherford, if the nucleus of an atom were scaled up to the size of the Sun, then the electrons would be more distant than Neptune's orbit by a factor of about ten. Yet we shouldn't take the model too seriously: electrons can't be pinpointed like planets, and do not follow well-defined elliptical paths, but instead occupy regions of space called orbitals. These regions, which have the shapes of spheres, lobes, and rings centered on the nucleus, are best regarded as hazy "electron clouds," rather like swarms of bees around a hive. From the manner in which an atom's electrons are distributed among the various available orbitals flows the whole of chemistry.
Moreover, atomic nuclei grasp their electrons not by the force of gravity but by electrical attraction: an electron is negatively charged, and a proton has a positive charge of equal magnitude. An atom, with equal numbers of both particles, is electrically neutral. Electrons, however, can be stripped away from atoms, rather as a passing star could pull a planet from a nearby solar system. The depleted atom then has an excess of protons over electrons, and so is positively charged. Atoms can also gain an excess of of electrons over protons, and so become negatively charged. These charged atoms are called ions. This is why, even though protons and electrons are equally represented in a neutral atom, it is the number of protons that is the fundamental characteristic of an element. To pull a proton out of an atom, you have to dig it from the dense mass of the nucleus. That takes huge amount of energy, and converts the atom into a different element entirely.
Although hydrogen atoms have one proton and oxygen atoms have eight, oxygen is about sixteen times heavier than hydrogen. There is a third ingredient to the atom--a particle called the neutron, which has virtually the same mass as a proton but is electrically neutral. All atoms bar hydrogen have neutrons as well as protons in their nuclei, and generally speaking the nuclei contain equal numbers of each. The vagueness in this statement is, I fear unavoidable, for two reasons. First, the number of neutrons tends increasingly to exceed the number of protons for heavier atoms: the proportions are pretty much fifty-fifty for light atoms like carbon, oxygen, and nitrogen, whereas lead atoms have around 40 percent more neutrons than protons. Second, even atoms of the same element can possess different numbers of neutrons. Oxygen atoms can contain seven, eight, nine, or ten neutrons to accompany their eight protons, while hydrogen atoms can contain no, one, or two neutrons. These different forms of atoms of the same element are called isotopes. Most hydrogen atoms have no neutrons; but 0.000015 percent of all of those in nature have one neutron. This heavier isotope is called heavy hydrogen, hydrogen-2, or deuterium.
This is, I appreciate, the stuff of dry chemistry textbooks, and I regret
forcing it on you so soon. I hope it is of some consolation to learn that this
is all you will need to know about atoms for the rest of the book. But they are
the alphabet of chemistry, so we need to be at least on familiar terms with
them. Besides, if we are to consider how the Universe cooked up water, we need
to know which ingredients must go into the pot.
THE SOUP GOES COLD
Water is but a simple dish: the recipe tells us to mix hydrogen and oxygen. The
first ingredient is the easy one: it dropped right out of the Big Bang, once
things got cool enough. That's to say, protons--the nuclei of hydrogen
atoms--condensed out of the fireball about a millionth of a second after time and
space were born.
But at this point the temperature would have been around a trillion degrees, which is too hot for protons to hold on to electrons. The Universe was then a soup of protons and electrons, seasoned with neutrons and other subatomic particles such as neutrinos, all swimming in a seething broth of X-rays. And for a good few minutes, that's how things stayed; the Universe was too hot to be interesting.
Although protons could not yet combine with electrons, they could at least team up with each other and with neutrons--for the force that binds protons and neutrons together in the nucleus, called the nuclear strong force, is many, many times stronger than the electrical force of attraction between protons and electrons. Just one hundred seconds into the Big Bang, with temperatures close to six billion degrees, protons and neutrons began to combine to form the nuclei of heavier elements--a process called nucleosynthesis. Fusion of these particles led to the formation of the nuclei of several light elements: helium-4 (an amalgam of two protons and two neutrons), lithium (three protons and three or four neutrons), and boron-11 (five protons, six neutrons). About a quarter of the mass in the Universe is helium-4, formed by nucleosynthesis in the early days of the Big Bang.
The proportion of the Universe's total mass that comes from all other
elements is tiny, however: about 1 to 2 percent in all. In other words, around
three-quarters of the Universe's mass is hydrogen, and the rest is mostly
helium. Once the temperature had dropped to around 7200º F, nuclei became able
to grasp and retain electrons. Protons teamed up with electrons, and hydrogen
atoms were born.
ATOMCRAFT
If chemistry had relied solely on the Big Bang, the periodic table would be but
a short, formless list of half a dozen elements--easier to grasp, perhaps, except
that you wouldn't exist to appreciate it. By the time it had fashioned boron,
the Big Bang had exhausted its atom-making vigor.
Fortunately for us, gravity came to the rescue. Within the diffuse clouds of
matter synthesized in the Big Bang, gravity began the slow but inexorable task
of galaxy-building. Where the gas was ever so slightly denser, the inward tug of
gravity was that bit stronger. And so, almost imperceptible variations in
density gradually became accentuated, condensing into ever more compact blobs,
like a sheet of rainwater on a wind-shield breaking up into a network of
droplets. These amorphous clumps became the precursors of vast galaxy clusters,
within which smaller clumps condensed into separate galaxies--a hierarchical
fragmentation tight down to the scale of the nebulae that would ultimately
become stars.
As the pull of gravity made matter collapse in on itself, the stuff heated up.
Stars ignited and began blazing. One by one, the lights came on again throughout
the Universe. The stars are more than mere fireballs--they are engines of
creation, and out of their fiery hearts come the elements needed to make worlds.
TRANSMUTATION MADE REAL
Astronomy is an indispensable art; it should be rightly held in high esteem,
and studied earnestly and thoroughly.
So said the itinerant physician and alchemist Paracelsus in the sixteenth century, unsuspecting all along that the stars possessed the art he himself sought: the ability to convert one element to another. Stars are the alchemists of the Universe.
In the interiors of stars, hydrogen nuclei are fused together to generate heavier elements; this is the process of nuclear fusion, and it is how stars conduct nucleosynthesis. Young stars are made mostly of hydrogen, which fuses in three steps to generate helium-4 and a great deal of energy. Over its lifetime, a typical star burns about 12 percent of its hydrogen to helium in this way.
One often hears that this transmutation of elements is a thoroughly modern idea, unrelated in more than a coincidental sense with the alchemists' belief that elements can be interconverted. But on the contrary, it is possible to follow a continuous thread of logic and supposition from Paracelsian metaphysics to Enrico Fermi's first atomic pile in Chicago in the 1940s.
In 1815 the British chemist William Prout proposed that atoms of the heavier elements were formed by the clustering together of hydrogen atoms, making hydrogen the "first matter," or prote hyle, from which Aristotle had suggested all matter is composed. Tempting though it is to suggest that in this way Prout anticipated the twentieth-century discoveries of nuclear fusion and the structure of the atom, the reason Prout's idea wasn't laughed out of court (although it was by no means uncontroversial) was in fact because the legacy of alchemy was still in the air. Indeed, no less a figure than the eminent British chemist and physicist Michael Faraday remained convinced of the doctrine of elemental transmutation throughout his life.
Prout's theory was elaborated on by the French chemist Jean Baptiste Dumas in the 1840s. Dumas noted that the atomic weights of some elements, which by then were known with impressive accuracy, were certainly not whole multiples of the atomic weight of hydrogen, and therefore these elements could not be made of clusters of hydrogen atoms. Dumas proposed that the fundamental unit of matter might instead be some subdivision of the hydrogen atom, perhaps a quarter or a half. Unknown to Dumas, the discrepancies are actually a consequence of the fact that elements exist in nature as a mixture of isotopes, so that their average mass does not correspond to a whole number of protons. The link between these ideas and the chemistry of the extraterrestrial Universe was made by Norman Lockyer in the 1870s. During this and the preceding decade, astronomers detected the fingerprints of many earthly elements in the light emitted by the Sun and other stars. Lockyer, in parallel with the Frenchman Pierre Janssen, discovered a new element in 1868 purely from its distinctive imprint on the spectrum of sunlight--a series of dark bands where the element absorbs light of certain colors. Lockyer called the element helium (after helios, Greek for the Sun), and it was not found on Earth until twenty-seven years later.
Lockyer developed a theory of the "evolution of stars and chemical elements" which drew explicitly on Dumas's elaboration of Prout's hypothesis. He proposed that heavy elements were made from lighter ones inside stars as the stars cooled from a blue-white brightness to a red dimness--a progression inferred from the observed colors of different stars. The British chemist William Crookes developed a similar hypothesis in the 1880s, based on the observation that gases subjected to high voltages could be decomposed into a plasma, a mixture of ions and electrons. Crookes considered plasmas to be a "fourth state of matter" consisting of subatomic particles akin to those postulated by Prout and Dumas. He constructed an exotic scheme for the evolution and transmutation of elements from this plasma, which he assumed to be the stuff of stars.
ENTER OXYGEN
In 1919 the British physicist Francis Aston, working at the Cavendish Laboratory
of Cambridge University, developed a device that enabled him to measure the
relative masses of atomic nuclei with great precision: the "mass
spectrograph," which we would now call a mass spectrometer. He found that
even the nuclear masses of individual isotopes are generally not exactly whole
multiples of hydrogen's; they are somewhat lighter, although typically by a
margin of only a fraction of 1 percent. The tiny difference in mass reflects the
fact that a huge amount of energy is released when protons and neutrons combine
to form heavier nuclei: the energy accounts for the "missing mass" and
is calculated according to Einstein's famous formulation E=mc2. For the first
time, Aston realized the vast energy lurking within the nuclei of atoms. When
Ernest Rutherford, the director of the Cavendish, demonstrated in 1919 that a
nuclear transmutation process could be induced by artificial means, scientists
realized that it might be possible to extract this energy technologically--for
better or worse. French physicist Jean Perrin proposed in the same year that the
Sun and other stars might derive their energy from the fusion of hydrogen to
heavier elements. In other words, nuclear fusion might not be just a consequence
of the furious solar environment, as Lockyer had supposed, but the cause
of it. Arthur Eddington added his approval in 1920: "What is possible in
the Cavendish Laboratory may not be too difficult in the Sun."
In the mid-1930s the Russian physicist George Gamow put Perrin's idea on firmer footing, suggesting that hydrogen was transformed to heavier elements by capturing a succession of protons or neutrons. The German physicist Hans Bethe showed in 1939 that a tiny dose of carbon is needed to stimulate this process. A newly formed star condensing from a gaseous nebula typically contains about 1 percent carbon, primarily in the form of the isotope carbon-12. This can provide the seed for the six-step sequence of nuclear reactions that converts hydrogens to helium-4. The carbon-12 is recycled: consumed at the beginning of the sequence, but regurgitated at the end. By definition, it acts as a catalyst. This means that a tiny amount of carbon can facilitate the fusion of a lot of hydrogen.
At first glance, this cycle doesn't seem to get us very much further, since its net result is to transform hydrogen to helium--and we've seen that this can happen anyway, without the help of carbon. But in the intermediate steps of the cycle, other elements are formed: three different isotopes of nitrogen, and one of oxygen (the rare isotope oxygen-15). In Bethe's so-called C-N-O cycle, oxygen makes its entrance onto the cosmic stage.
All Endnotes have been omitted.
Copyright © 2000 Philip Ball
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