Atomic theory

In chemistry and physics, atomic theory is a scientific theory of the nature of matter, which states that matter is composed of discrete units called atoms. It began as a philosophical concept in ancient Greece and entered the scientific mainstream in the early 19th century when discoveries in the field of chemistry showed that matter did indeed behave as if it were made up of atoms. Through various experiments with electromagnetism and radioactivity, scientists eventually discovered that the so-called "uncuttable atom" was actually a conglomerate of various subatomic particles.

A - F, G - L , M - R , S - Z Opticks (1704) See also, External links
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A - F

 * In 1763 a Croatian Jesuit named Roger Joseph Boscovich (1711 - 1787) identified the ultimate implication of this mechanical atomic theory. One of the crucial aspects of Isaac Newton's laws of motion is their predictive capability. If we know how an object is moving at any instant - how fast, and in which direction - and if, furthermore, we know the forces acting on it, we can calculate its future trajectory exactly. This predictability made it possible for astronomers to use Newton's laws of motion and gravity to calculate, for example, when future solar eclipses would happen. Boscovich realized that if all the world is just atoms in motion and collision, then an all-seeing mind "could, from a continuous arc described in an interval of time, no matter how small, by all points of matter, derive the law [that is, a universal map] of forces itself … Now, if the law of forces were known, and the position, velocity and direction of all the points at any given instant, it would be possible for a mind of this type to foresee all the necessary subsequent motions and states, and to predict all the phenomena that necessarily followed from them."
 * Philip Ball, Critical Mass: How One Thing Leads to Another (2004)


 * We have come a long way from the classical ideal of objective descriptions. In quantum mechanics the departure from this ideal has been even more radical. We can still use the objectifying language of classical physics to make statements about observable facts. For instance, we can say that a photographic plate has been blackened, or that cloud droplets have formed. But we can say nothing about the atoms themselves.
 * Niels Bohr, remarks after the Solvay Conference (1927) as quoted by Werner Heisenberg, Physics and Beyond (1971)


 * Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic!
 * Ludwig Boltzmann, "Lectures on Gas Theory", translated by Stephen George Brush (1971), p. 26


 * It seems not absurd to conceive that at the first Production of mixt Bodies, the Universal Matter whereof they among other Parts of the Universe consisted, was actually divided into little Particles of several sizes and shapes variously mov'd.
 * Robert Boyle, The Sceptical Chymist (1661) Proposition I.


 * Neither is it impossible that of these minute Particles divers of the smallest and neighbouring ones were here and there associated into minute Masses or Clusters, and did by their Coalitions constitute great store of such little primary Concretions or Masses as were not easily dissipable into such Particles as compos'd them.
 * Robert Boyle, The Sceptical Chymist (1661) Proposition II.


 * I shall not peremptorily deny, that from most of such mixt Bodies as partake either of Animal or Vegetable Nature, there may by the Help of the Fire, be actually obtain'd a determinate number (whether Three, Four or Five, or fewer or more) of Substances, worthy of differing Denominations.
 * Robert Boyle, The Sceptical Chymist (1661) Proposition III.


 * It may likewise be granted, that those distinct Substances, which Concretes generally either afford or are made up of, may without very much Inconvenience be call'd the Elements or Principles of them.
 * Robert Boyle, The Sceptical Chymist (1661) Proposition IV.


 * And, to prevent mistakes, I must advertize You, that I now mean by Elements, as those Chymists that speak plainest do by their Principles, certain Primitive and Simple, or perfectly unmingled bodies; which not being made of any other bodies, or of one another, are the Ingredients of which all those call'd perfectly mixt Bodies are immediately compounded, and into which they are ultimately resolved: now whether there be any one such body to be constantly met with in all, and each, of those that are said to be Elemented bodies, is the thing I now question.
 * Robert Boyle, The Sceptical Chymist (1661)


 * Fraunhofer's publication of 1814 did not receive prompt recognition, nor did his papers of 1821 and 1823. Physicists were fighting over the emission and wave theories of light. The attention of chemists was concentrated upon Dalton's atomic theory and the Berthollet-Proust controversy over the law of definite proportions. The full explanation of the new fact brought forth by Fraunhofer was not given for nearly forty years. He himself had failed to find the key to the hieroglyphics of the solar lines, the "Fraunhofer lines," nor had he clearly defined the role which the spectral lines were destined to play in chemical analysis.
 * Florian Cajori, A History of Physics in its Elementary Branches (1917)


 * To try to make a model of an atom by studying its spectrum is like trying to make a model of a grand piano by listening to the noise it makes when thrown downstairs.
 * W. K. Clifford, as quoted by The British Journal of Radiology: The Journal of the Röntgen Society. Röntgen Society section, Volumes 20-21 (1924)


 * In 1738 Daniel Bernoulli correctly derived Boyle's law by assuming gases consisted of collections of particles that continuously collided with the container walls.
 * Cathy Cobb & Harold Goldwhite, Creations of Fire: Chemistry's Lively History from Alchemy to the Atomic Age (1995)


 * Dalton did not propose atoms as an abstraction or mathematical device; Dalton's atoms were physical. ...Despite its foundation in dubious hypothesis and its erroneous initial results, Dalton's theory was just the breakthrough that was needed. For the first time it allowed chemists to interpret mass relationships rationally.
 * Cathy Cobb & Harold Goldwhite, Creations of Fire: Chemistry's Lively History from Alchemy to the Atomic Age (1995)

If I venture to say that... elements are not simple and primordial... but have evolved from simpler matters—or... one sole kind of matter—I... give formal utterance to an idea... for some time "in the air" of science. Chemists, physicists, philosophers of the highest merit declare explicitly their belief that the seventy... elements of our text-books are not the which we must never hope to pass.
 * I have raised a question which may be regarded as heretical. At the time when our modern conception of chemistry first dawned... the average chemist... accepted the elements as ultimate facts... absolutely simple, incapable of transmutation or decomposition, each a kind of barrier behind which we could not penetrate. ...[H]e said they were self-existent from all eternity ...But in our times... we cannot help asking what are the elements, whence do they come, what is their signification? ...These elements perplex us in our researches, baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us—mocking, mystifying and murmuring strange revelations and possibilities.
 * William Crookes, "Genesis of the Elements" (Feb 25, 1887) The Chemical News Vol. LV, No 1422.


 * Sweet exists by convention, bitter by convention, colour by convention; atoms and Void (alone) exist in reality.
 * Democritus (5th century BCE) Tetralogies of Thrasyllus 9. sext. adv. math. VII 135, Tr. Kathleen Freeman, Ancilla to the Pre-Socratic Philosophers: A Complete Translation of the Fragments in Diels (1948)


 * By convention (νόμω) sweet is sweet, by convention bitter is bitter, by convention hot is hot, by convention cold is cold, by convention color is color. But in reality there are atoms and the void. That is, the objects of sense are supposed to be real and it is customary to regard them as such, but in truth they are not. Only the atoms and the void are real
 * Democritus (5th century BCE) Tetralogies of Thrasyllus 9. sext. adv. math. VII 135, Tr. Charles Montague Bakewell, Sourcebook in Ancient Philosophy (1907) Fragment 0, p. 60


 * There cannot exist any atoms or parts of matter that are of their own nature indivisible. For however small we suppose these parts to be, yet because they are necessarily extended, we are always able in thought to divide any one of them into two or more smaller parts, and may accordingly admit their divisibility. ...and although we should even suppose that God had reduced any particle of matter to a smallness so extreme that it did not admit of being further divided, it would nevertheless be improperly styled indivisible, for though God had rendered the particle so small that it was not in the power of any creature to divide it, he could not however deprive himself of the ability to do so... Wherefore, absolutely speaking, the smallest extended particle is always divisible...
 * René Descartes, A Discourse on Method (1637) Principles of Philosophy-II. Of the Principles of Material Things Tr. John Veitch (1916)


 * If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz.
 * Albert Einstein, "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality" in Essays in Science (1934)


 * If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis... that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.
 * Richard Feynman, The Feynman Lectures on Physics (1964) Vol. I; Lecture 1, "Atoms in Motion"; section 1-2, "Matter is made of atoms"; p. 1-2


 * The atomic theory was not generally accepted in the time of Democritus, largely because of its deterministic character, for it allows no chance, choice, or free will.
 * John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012) p. 287

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Einstein disagreed, and argued the case for atoms with his friends. He became obsessed with the idea, and determined that if no one else could prove that atoms were real, he would do it himself.
 * The problem was that although ideas like statistical mechanics and the kinetic theory worked at the practical level to provide a mathematical description of what was going on, nobody had seen atoms—more to the point, given the technology of the time it was physically impossible to see atoms. This left the door open to for philosophers such as Ernst Mach to argue that the atomic hypothesis was no more than a hypothesis, what is known as a heuristic device, meaning just because things in the macroscopic world behave as if they were made of atoms that doesn't prove that they are... Mach regarded atoms as no more than a convenient fiction, which provided a basis for physicists to make calculations; anything that could not be detected by the human senses, he argued, was not the proper subject of scientific debate.
 * John Gribbin and Mary Gribbin, Annus Mirabilis: 1905, Albert Einstein, and the Theory of Relativity (2005)


 * In the Brownian motion paper, Einstein... calculations involved the relationship between osmotic pressure, viscosity, and the way individual particles suspended in the liquid diffuse... He realized that the kick produced by a single molecule hitting a particle as large as a pollen grain could not produce a measurable shift... But the large particle is constantly being bombarded... if you take a very small time interval, then just by chance at that instant the particle will be receiving more kicks on one side. The combined effect will shift the particle by a minute amount... Einstein discovered that it gradually moved farther from its starting point... as a random walk. He showed the distance ... depends on the square root of the time... This is called "root mean square" displacement and the equation Einstein worked out for displacement involves the temperature of the liquid, its viscosity, the radius of the particle and Avogadro's number. ...He also realized that if the predicted displacement could be measured... the same equation... could be used to give a value of Avogadro's number. ...It was extremely difficult to make the observations... but in 1908... Jean-Baptiste Perrin finally succeeded. ...Perrin's results exactly matched the predictions from Einstein's theory. ...The whole package finally established the reality of atoms and molecules, and the validity of the kinetic theory...
 * John Gribbin and Mary Gribbin, Annus Mirabilis: 1905, Albert Einstein, and the Theory of Relativity (2005)


 * Light and matter are both single entities, and the apparent duality arises in the limitations of our language. It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme — the quantum theory — which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies — the wave picture and the corpuscular picture.
 * Werner Heisenberg, "Introductory" in The Physical Principles of the Quantum Theory (1930) as translated by Carl Eckhart and Frank C. Hoyt, p. 10.


 * The thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of Science.
 * Werner Heisenberg, The Development of Quantum Mechanics (11 December 1933) Nobel lecture


 * There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality.
 * Werner Heisenberg, as quoted in Physics from Wholeness : Dynamical Totality as a Conceptual Foundation for Physical Theories (2005) by Barbara Piechocinska.


 * It was the quantitative relationship between electrochemical change and current which interested Faraday... It was not until after Faraday's death that the significance of his laws of electrolysis for atomic theory was realized. In 1881 von Helmholtz pointed out that if elementary substances are composed of atoms, it follows from Faraday's laws of electrolysis that electricity also is composed of elementary portions which behave like atoms of electricity. Investigations on the conduction of electricity by gases led to the identification of the electron as the fundamental unit of electricity at the end of the century. Faraday's positive and negative ions are therefore atoms (or groups of atoms or radicals) with a deficiency or an excess of an integral number of electrons, where the integral number is the valency of the atom. The ions move in opposite directions through the solution to the electrodes where their charges are neutralised, causing them to be discharged to neutral atoms or radicals. These are the primary electrode reactions, of which the deposition of silver on a platinum cathode in the silver coulometer is a typical example.
 * A. Horsfield, "The Faraday and Its Significance in Determining the Fundamental Constants," in Precision Measurement and Fundamental Constants; Proceedings (1971) Issue 343, U.S. National Bureau of Standards


 * I adopt Mr. Darwin's hypothesis, therefore, subject to the production of proof that physiological species may be produced by selective breeding; just as a physical philosopher may accept the undulatory theory of light, subject to the proof of the existence of the hypothetical ether; or as the chemist adopts the atomic theory, subject to the proof of the existence of atoms; and for exactly the same reasons, namely, that it has an immense amount of primâ facie probability: that it is the only means at present within reach of reducing the chaos of observed facts to order; and lastly, that it is the most powerful instrument of investigation which has been presented to naturalists since the invention of the natural system of classification and the commencement of the systematic study of embryology.
 * Thomas Henry Huxley, Evidence as to Man's Place in Nature (1863) Ch.2, p. 128.


 * With respect to the ultimate constitution of... masses, the same two antagonistic opinions which had existed since the time of Democritus and of Aristotle were still face to face. According to the one, matter was discontinuous and consisted of minute indivisible particles or atoms, separated by a universal vacuum; according to the other, it was continuous, and the finest distinguishable, or imaginable, particles were scattered through the attenuated general substance of the plenum. A rough analogy to the latter case would be afforded by granules of ice diffused through water; to the former, such granules diffused through absolutely empty space.
 * Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)


 * In the latter part of the eighteenth century, the chemists had arrived at several very important generalisations... However plainly ponderable matter seemed to be originated and destroyed in their operations, they proved that, as mass or body, it remained indestructible and ingenerable... a certain number of the chemically separable kinds of matter were unalterable by any known means (except in so far as they might be made to change their state from solid to fluid, or vice versâ)... and that the properties of these several kinds of matter were always the same, whatever their origin. All other bodies were found to consist of two or more of these, which thus took the place of the four 'elements' of the ancient philosophers. Further, it was proved that, in forming chemical compounds, bodies always unite in a definite proportion by weight, or in simple multiples of that proportion, and that, if any one body were taken as a standard, every other could have a number assigned to it as its proportional combining weight. It was on this foundation of fact that Dalton based his re-establishment of the old atomic hypothesis on a new empirical foundation.
 * Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)


 * The gradual reception of the undulatory theory of light necessitated the assumption of the existence of an 'ether' filling all space. But whether this ether was to be regarded as a strictly material and continuous substance was an undecided point, and hence the revived atomism escaped strangling in its birth. For it is clear, that if the ether is admitted to be a continuous material substance, Democritic atomism is at an end and Cartesian continuity takes its place.
 * Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)


 * The real value of the new atomic hypothesis... did not lie in the two points which Democritus and his followers would have considered essential—namely, the indivisibility of the 'atoms' and the presence of an interatomic vacuum—but in the assumption that, to the extent to which our means of analysis take us, material bodies consist of definite minute masses, each of which, so far as physical and chemical processes of division go, may be regarded as a unit—having a practically permanent individuality. ...that smallest material particle which under any given circumstances acts as a whole.
 * Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)


 * At times the success of a concept in one area of science may have a retarding effect upon progress in other areas. ..."the Law of Definite Proportions," was established... only after a long battle between Berthollet and Proust. The success of the Proust position was so decisive that the matter received little critical study during the decades which followed. Possibly this was for the best as far as the progress of chemistry was concerned. Had chemists concerned themselves with the composition of solutions, glasses, and alloys the establishment of atomic theory might have been even slower than it was.
 * Aaron J. Ihde, "On the Papers of Cyril Stanley Smith and Marie Boas," in Critical Problems in the History of Science (1959) ed. Marshall Clagett

It is in solid state chemistry that the Law of Definite Proportions has been found wanting. Not only in the case of metallic compounds are peculiar atomic ratios of the component elements to be found, but even in such solids as metallic oxides and sulfides. Ferrous oxide (FeO) presents a particularly fine example... Although the compound is frequently mentioned in freshman chemistry courses to illustrate the Law of Definite Proportions... on accurate analysis... the ratio is somewhat between the range of 0.84 to 0.95 atoms of iron per atom of oxygen. ...The existence of a considerable number of such compounds has led to the proposal that compounds be classified as Berthollides and Daltonides; the term Berthollide referring to such compounds as cuprous sulfide with a somewhat variable domposition, and Daltonide referring to those with precisely fixed atomic ratios.
 * Anyone who had studied the vicissitudes of atomic theory during the period between 1810 and 1860 recognizes the tremendous problems which faced chemists of that day in connection with atomic weights, equivalent weights, reliable formulas, and matters of that sort. The Law of Definite Proportions was a useful concept in helping bring order out of chaos. ...Had chemists had to face the fact of variable composition in some of their common compounds it is doubtful if atomic theory might have been established as soon as it was.
 * Aaron J. Ihde, "On the Papers of Cyril Stanley Smith and Marie Boas," in Critical Problems in the History of Science (1959) ed. Marshall Clagett


 * It is sometimes desirable to have experimental data which is not completely precise. Had Berthollet been successful in convincing the chemical world that compounds do not have fixed proportions, the development of the atomic theory would have been greatly hindered. The fact that the Proust position became the accepted one in view of the work of Dalton, meant that the trials and errors toward a successful formulation of chemical compounds would ultimately succeed on the basis of an atomic philosophy. Once the atomic philosophy was clearly developed, the existence of the Berthollides could still be incorporated into chemical philosophy on the basis of studies of solid state physics. This illustrates clearly... the fact that science progresses from one state of approximation to another, and that progress may well be hindered when so much precise information is available that broad and useful concepts are overlooked.
 * Aaron J. Ihde, "On the Papers of Cyril Stanley Smith and Marie Boas," in Critical Problems in the History of Science (1959) ed. Marshall Clagett


 * Now his principal doctrines were these. That atoms and the vacuum were the beginning of the universe; and that everything else existed only in opinion.
 * Diogenes Laërtius (fl. c. 3rd century CE) The Lives and Opinions of Eminent Philosophers, Democritus, Vol. IX, 44 Tr. Charles Duke Yonge (1853)


 * His opinions are these. The first principles of the universe are atoms and empty space; everything else is merely thought to exist. The worlds are unlimited; they come into being and perish. Nothing can come into being from that which is not nor pass away into that which is not. Further, the atoms are unlimited in size and number, and they are borne along in the whole universe in a vortex, and therby generate all composite things – fire, water, air, earth; for even these are conglomerations of given atoms. And it is because of their solidity that these atoms are impassive and unalterable. The sun and the moon have been composed of such smooth and spherical masses [i.e. atoms], and so also the soul, which is identical with reason. We see by virtue of the impact of images upon our eyes.
 * Diogenes Laërtius (fl. c. 3rd century CE) The Lives and Opinions of Eminent Philosophers, Democritus, Vol. IX, 44 The Lives and Opinions of Eminent Philosophers Tr. Robert Drew Hicks (1925)


 * All those who maintain a vacuum are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms; but reason brought me into the right way. ...The least corpuscle is actually subdivided in infinitum, and contains a world of other creatures, which would be wanting in the universe, if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature, is ascribing to God a very imperfect work... space is only an order of things as time also is, and not at all an absolute being. ...Now, let us fancy a space wholly empty. God could have placed some matter in it, without derogating in any respect from all other things: therefore he hath actually placed some matter in that space: therefore, there is no space wholly empty: therefore all is full. The same argument proves that there is no corpuscle, but what is subdivided. ...there must be no vacuum at all; for the perfection of matter is to that of a vacuum, as something to nothing. And the case is the same with atoms: What reason can any one assign for confining nature in the progression of subdivision? These are fictions merely arbitrary, and unworthy of true philosophy. The reasons alleged for a vacuum, are mere sophisms.
 * Gottfried Wilhelm Leibniz, Five Letters to Samuel Clarke (1716) Postscript, Mr. Leibniz's Fourth Paper; Being a Reply to Dr. Clarke's Third Reply in The Philosophical Works of Leibnitz (1908)


 * Loschmidt reasoned that in a liquid, the atoms or molecules would be more or less squeezed up against each other, so the volume of a liquid would be straightforwardly the volume of an individual molecule multiplied by the number of them. ...The diameter he came up with was a little less than one millionth of a millimeter—by modern standards a pretty fair answer. ...To critics... Loschschmidt's analysis still didn't prove anything. ...in the absence of tangible evidence that atoms existed, it was mere mathematics, empty theorizing. Loschmidt had shown that if atoms existed, they must have a certain size—but that first "if" had not been overcome.
 * David Lindley, Boltzmann's Atom: The Great Debate that Launched a Revolution in Physics (2001)

...As well as having a hand in kinetic theory, ...In 1864, ...Maxwell's theory introduced a new idea, the electromagnetic field. Over atoms and electromagnetic fields, the same question arose: real or imaginary?
 * Traditionally, [physics] had concerned itself with searching out quantitative relationships between measurable phenomena... To go beyond this, to explain observable facts in terms of unobservable but alledgedly "real" entities such as atoms, was to go beyond what many physicists regarded as the limits of their discipline. What was happening in the second half of the 19th century, was the birth of the subject we now call theoretical physics... a puzzling innovation.
 * David Lindley, Boltzmann's Atom: The Great Debate that Launched a Revolution in Physics (2001)


 * The last thirty years have seen the beginning and development of a new period in physics and chemistry, namely the atomic period. In contrast to the period preceding it where nature's processes were described in terms of continua, recent developments have emphasized the discrete structure of the submicroscopic universe. Thus, today one hears of the atoms of matter, the atoms of electricity, and even the atoms of energy, the quanta. ...[T]he atomic theory of matter is the oldest and perhaps the most complete. ...[B]ecause of its relative simplicity the problem of the atomic theory of gases, in the form of the kinetic theory of gases, has attained the highest degree of perfection in this field. Its admirable methods of analysis are therefore indispensable...
 * , The Kinetic Theory of Gases (1927) Preface to the 1st edition.

The Atomists. From this springs naturally the atomistic theory of Leucippus and Democritus. This theory is an endeavour to give a sort of solidity and reality to the mutability of Heraclitus, whilst retaining his controversial advantages in the denial of an all-embracing One. The veritable original of things is taken by these Atomists to be, not one, but innumerable, indefinitely minute, homogeneous atoms, the mere mechanical combination of which makes up the variety of nature.
 * Heraclitus. ...change and incessant movement is the basis, and the only basis, of all things and that what is illusory is the idea of a central, or indeed of any other, unity: the Universe is a stream of incessant and infinitely minute changes.
 * Richard Lowndes, Introduction, Rene Descartes : His Life and Meditations (1878)

M - R

 * However well fitted atomic theories may be to reproduce certain groups of facts, the physical inquirer who has laid to heart Newton's rules will only admit those theories as provisional helps. and will strive to attain, in some more natural way, a satisfactory substitute.
 * Ernst Mach, The Science of Mechanics (1893)


 * The atomic theory plays a part in physics similar to that of certain auxilliary concepts in mathematics; it is a mathematical model for facilitating the mental reproduction of facts. Although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of times, etc., no one will fancy that vibrations in themselves have anything to do with the circular functions, or the motions of falling bodies with squares. It has simply been observed that the relations between the quantities investigated were similar to certain relations obtaining between familiar mathematical functions, and these more familiar ideas are employed as an easy means of supplementing experience. Natural phenomena whose relations are not similar to those functions with which we are familiar, are at present very difficult to reconstruct. But the progress of mathematics may facilitate the matter.
 * Ernst Mach, The Science of Mechanics (1893)


 * Avogadro... suggested in 1811 that the same volumes of different gases contain the same number of particles under the same conditions of temperature and pressure. ...Avogadro's hypothesis raised the difficulty that when one volume of hydrogen combined with one volume of chlorine, two volumes of hydrogen chloride were produced, implying that the atoms of hydrogen and chlorine were split into halves during the process of combination. Avogadro overcame this difficulty by supposing that the fundamental particles of hydrogen, chlorine, and other gases, were molecules containing two atoms of the element, and that chemical combination between two gases resulted in the splitting up of the elementary molecules and the formation of compound molecules in which there was one atom of each element... Avogadro's hypothesis... was not accepted until the 1860's, as it demanded that the atoms of the same element should combine together to form molecules. Dalton and others rejected such a conception, for they held that like atoms must repel one another and could not combine. Moreover, Dalton... thought that the various species of atoms differed not only in their atomic weights, but also in their sizes, and the number per unit volume in the gaseous state.
 * Stephen F. Mason, A History of the Sciences (1956)


 * In studying the constitution of bodies we are forced from the very beginning to deal with particles which we cannot observe. For whatever may be our ultimate conclusions as to molecules and atoms, we have experimental proof that bodies may be divided into parts so small that we cannot perceive them. Hence, if we are careful to remember that the word particle means a small part of a body, and that it does not involve any hypothesis as to the ultimate divisibility of matter, we may consider a body as made up of particles, and we may also assert that in bodies or parts of bodies of measurable dimensions, the number of particles is very great indeed.
 * James Clerk Maxwell, On the Dynamical Evidence of the Molecular Constitution of Bodies (1875) Nature Vol. XI as quoted in The Scientific Papers of James Clerk Maxwell (1890)


 * The ancient Greek philosopher, Democritus, propounded an hypothesis of the constitution of matter, and gave the name of atoms to the ultimate unalterable parts of which he imagined all bodies to be constructed. In the 17th century, Gassendi revived this hypothesis, and attempted to develope it, while Newton used it with marked success in his reasonings on physical phenomena; but the first who formed a body of doctrine which would embrace all known facts in the constitution of matter, was Roger Joseph Boscovich, of Italy, who published at Vienna, in 1759, a most important and ingenious work, styled Theoria Philosophiæ Naturalis ad unicam legem virium, in Natura existentium redacta. This is one of the most profound contributions ever made to science; filled with curious and important information, and is well worthy of the attentive perusal of the modern student. In more recent days, the theory of Boscovich has received further confirmation and extension in the researches of Dalton, Joule, Thomson, Faraday, Tyndall, and others.
 * Alfred Marshall Mayer, Lecture-notes on Physics (1868) Part 1


 * The atomic theory may be regarded in two distinct ways, ...The older and vague atomic theory professed to be a theory of the constitution of bodies and to afford the basis for a physical explanation of physical phenomena; in order to do this, forces of attraction and repulsion between the particles of matter had to be assumed, and elaborate calculations as to the integral or resultant effect of these elementary forces had to be instituted, or at least formulated. ...ingenious as those theories were, they led to no results in the direction of the calculation of the molar and molecular properties of bodies, or if they did, they yielded none which could not be gained by the opposite view which regarded matter as continuous. The atomic theory, however, did good service from another point of view, when through Richter, Dalton, Proust, and Berzelius the fact that bodies combine only in definite proportions of weight, or their simple multiples, became firmly established. The authors of this discovery were driven to the atomic view of matter as the most convenient method of expressing the formulæ of chemical compounds.
 * John Theodore Merz, A History of European Thought in the Nineteenth Century (1903) Vol.1 Chapter V. The Atomic View of Nature


 * There is here a whole new branch of spectroscopy, which is sure to tell one much about the nature of an atom.
 * Henry Moseley as quoted by J. L. Heilbron H. G. J. Moseley: The Life and Letters of an English Physicist, 1887-1915 (1974) p. 205


 * In... A New System of Chemical Philosophy published in 1808, John Dalton laid the foundations of the atomic theory: he assumed chemical action to be an action between very minute particles of elements and compounds, and all the minute particles of the same element, or compound, to be exactly the same size and weight. ...his hypothesis assumed the accuracy and universal applicability of those generalisations which are now called the laws of chemical combination.
 * Matthew Moncrieff Pattison Muir, The Elements of Chemistry (1904)


 * Now, if the molecules possess anything which is ever so distantly related to sensation, and we cannot doubt it, since each one feels the presence, the certain condition, the peculiar forces of the other, and, accordingly, has the inclination to move, and under circumstances really begins to move—becomes alive as it were; moreover, since such molecules are the elements which cause pleasure and pain; if, therefore, the molecules feel something that is related to sensation, then this must be pleasure, if they can respond to attraction and repulsion, i.e. follow their inclination or disinclination; it must be displeasure if they are forced to execute some opposite movement, and it must be neither pleasure nor displeasure if they remain at rest.
 * Carl Wilhelm von Nägeli address to the Munich meeting of the German Association (1877) as quoted by Lewis Campbell, William Garnett, The Life of James Clerk Maxwell (1882)


 * If a fluid be composed of particles mutually flying [fleeing from] each other, and the density be as the compression, the centrifugal forces [repulsion] of the particles will be reciprocally proportional to the distances of their centres. And, vice versa, particles flying each other with forces that are reciprocally proportional to the distances of their centres, compose an elastic  [liquid or gas], whose density is as the compression.
 * Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1687) Book II, Proposition XXIII, Theorem XVIII, as quoted in The Mathematical Principles of Natural Philosophy (1803) Tr. Andrew Motte, Vol. 2, p. 60. This is described as an attempt to explain Boyle's law in terms of inter-atomic repulsions by, , The Architecture of Matter (1962) p. 191.


 * Dalton, the mathematical tutor, following up the lead of Newton, combined the whole of the results of quantitative measurement which had accumulated up to his time, in a comprehensive theory, based on the concept of the chemical atom.
 * J. R. Partington, Higher Mathematics for Chemical Students (1911) Introduction


 * The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions, such as fire-stuff, or phlogiston, destroyed; and at the same time we perceive definite measurable quantities such as fixed air, or oxygen, taking their place. In the second direction we notice the establishment of generalizations, laws, or theories, in which a mass of quantitative data is reduced to order and made intelligible. Such are the law of conservation of matter, the laws of chemical combination, and the atomic theory.
 * J. R. Partington, Higher Mathematics for Chemical Students (1911) Introduction


 * The Atomic Theory and the Periodic Law have been given prominence, since their neglect unfailingly leads to obscurity and triviality.
 * J. R. Partington, A Text-Book of Inorganic Chemistry (1921)


 * The old mechanical and atomic hypotheses have, during recent years, become so plausible that they have ceased to seem like hypotheses; atoms are no longer just a convenient fiction. It seems almost as if we could see them, now that we know how to count them. ...The kinetic theory of gases has thus received unexpected corroboration. ...The remarkable counting of the number of atoms by Perrin completed the triumph of the atomic theory. ...In the processes used with the Brownian phenomenon, or in those used for the law of radiation, we do not deal directly with the number of atoms, but with their degrees of freedom of movement. In that process where we consider the blue of the sky, the mechanical properties of the atoms come into play; the atoms are looked upon as producing an optical discontinuity. ...The atom of the chemist is now a reality. But that does not mean that we have reached the ultimate limit of the divisibility of matter. When Democritus invented the atom he considered it as the absolutely indivisible element within which there would be nothing further to distinguish. That is what the word meant in Greek. ... the atom of the chemist would not have satisfied him since that is not indivisible; it is not a true element; it is not free from mystery, from secrets. The chemist's atom is a universe. Democritus would have considered, even after so much trouble in finding it, that we were still only at the beginning of our search—these philosophers are never satisfied. ...This atom disintegrates into yet smaller atoms. What we call radioactivity is the perpetual breaking up of atoms. ...Each atom is like a sort of solar system where the small negative electrons play the role of planets revolving around the great... sun. ...the atom of a radioactive body is a universe within itself and a world subject to chance.
 * Henri Poincaré, "The Connection Between Ether and Matter," Annual Report of the Board of Regents of the Smithsonian Institution (1912) p.199


 * The study of the radio-active substances and of the discharge of electricity through gases has supplied very strong experimental evidence in support of the fundamental ideas of the existing atomic theory. It has also indicated that the atom itself is not the smallest unit of matter but is a complicated structure made up of a number of smaller bodies.
 * Ernest Rutherford, Radio-activity (1904)

S - Z

 * What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
 * Arnold Sommerfeld in: Wolfgang Pauli Writings on Physics and Philosophy, Springer Science & Business Media, 27 September 1994


 * The atomistic theory of matter appears in well established and elaborated form in various systems of Hindu philosophy... The oldest of these systems... appears to be that of the Vaiseshika, attributed to Kanada... Whether or no the... theory antedated Democritus... is... uncertain. Professor Garbe's opinion is that beyond a doubt the Indian theory is a long time after the theory of Leucippus and Democritus. L. Mabilleau, on the other hand, considers the Vaiseshika system as several centuries earlier than Democritus. ...This theory recognizes nine distinct entities constituting the universe. These are earth, water, fire, air (or wind), ether (akasa), time, space, soul, and "manas." ...Time, space, and soul are not material, though existent. The "manas" is the medium through which impressions of sense are conveyed to the soul. The first four, therefore, correspond to the four elements of Empedocles; the fifth, ether, can be compared with little similarity to the ether of Aristotle. The first four elements are composed of atoms which are eternal, never created nor destroyed. Each of these four elements exists as atoms and also as aggregates of atoms. As atoms, they are imperishable. The elements which we see or feel are aggregates of atoms and as such are subject to change, but the atoms, which are invisible, do not change. ...Akasa, or ether, is assumed not to consist of atoms, but is infinite in extent, continuous and eternal. It cannot be apprehended by the senses, but is the carrier of sound. It is also described... as all-pervasive, occupying the same space that is occupied by the various forms of matter, and therefore devoid of the property of impenetrability, characterizing the atoms of other elements.
 * John Maxson Stillman, The Story of Alchemy and Early Chemistry (1924)


 * Boyle entertains the hypothesis of a universal matter, the concept of atoms of different shapes and sizes, and the possibility of existence of substances that might properly be called elements... The atomic theory as originally conceived by Democritus and Epicurus, developed by Lucretius, and resurrected by Gassendi from about 1647 on, was doubtless the source from which Boyle derived his ideas, ...as he cites both Epicurus and Gassendi. Boyle, however... avoids any dogmatic assertion of these hypotheses. It is plain, however, that these atoms or "corpuscles" as he calls them are a constant element of his thought.
 * John Maxson Stillman, The Story of Alchemy and Early Chemistry (1924)


 * The final step... came in the late 1850s. Up to that time [evidence supporting] the atomic theory had been entirely... chemical... Within... physics, however, the theory had made little progress beyond the brilliant guesswork of Newton's Optics. As a result of Clausius' and Maxwell's new theory of heat and gases, physics at last caught up with chemistry. ...This theory was not entirely new. In outline its mathematical foundations had been worked out [as early as the 1730s] by Daniel Bernoulli... [who] demonstrated that random agitation of the atoms of air would explain Boyle's Law just as well as Newton's theory of repulsive forces; but although ... extended this explanation into a dynamical theory of heat it remained a minority view... overshadowed by Boerhaave's and Lavoisier's [heat as a] material theory. Around 1800... a few... were positively sceptical about caloric... Benjamin Thompson... observed that friction would generate unlimited quantities of heat... though... the material theory retained the allegiance of leading scientists for another half-century.
 * ,, The Architecture of Matter (1962)


 * Between Bernoulli and Maxwell... Euler, d'Alembert, Lagrange and Hamilton expounded [ Newton's dynamics] in more and more general forms, until at last all [mechanical] processes... were seen as conforming to... the Principle of the Conservation of Energy, and the Principle of Least Action. This mathematical drive... continued, overflowing beyond... mechanics... [and into] processes involving nonmechanical factors: heat, electricity, vitality, and chemical change... The most comprehensive exposition was given in 1847 by Hermann von Helmholtz... In 1848, J. P. Joule [demonstrated that]... whether he produced heat by the passage of an electric current, or by mechanical effort, the conversion took place at fixed, measurable rates. ...[I]t was natural to look again for an explanation ...Perhaps the production of heat by friction merely transferred mechanical energy from a visible level to an invisible one... the increased motion of the molecules... Clausius and Maxwell turned this view... into a fully-developed branch of mathematics (...from 1857 to 1866.) ...[H]eat theory had been united into the general theory of 'matter in motion'... the random agitation of vast numbers of invisibly-small particles.
 * Stephen Toulmin, June Goodfield, The Architecture of Matter (1962)


 * From Dalton in 1803 to Maxwell in 1866 the atomic picture of matter had progressively taken on shape and detail: by Maxwell's time it... lay at the heart of the classical system. ...all matter was composed of ponderable atoms and, with the 'death' of caloric, the division between corporeals and incorporeals became absolutely sharp. The known incorporeal agencies—radiant heat, light, magnetisim and electricity—had to be dealt with in terms of other concepts.
 * ,, The Architecture of Matter (1962)


 * The question whether our elementary atoms are in their nature indivisible, or whether they are built up of smaller particles, is one upon which I, as a chemist, have no hold whatever, and I may say that in chemistry the question is not raised by any evidence whatever.
 * Alexander William Williamson, "On the Atomic Theory," J. Chem. Soc., 2nd Ser., 1869, 7:328-365, on p. 365.


 * The physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus.
 * Alfred North Whitehead, Science and the Modern World (1925).

It will be convenient now to mention the chief electrical theories of atomic structure which have been proposed. According to Sir J. J. Thomson, atoms consist of solid spheres of positive electricity inside which negative electrons move about freely. ...The electrons will distribute themselves uniformly throughout the sphere so as to neutralize it as completely as possible and can vibrate about their positions of equilibrium. According to Sir J. Larmor, atoms consist of a number of positive and negative electrons describing orbits about each other. ...On this view an atom is a sort of small gaseous nebula without any sort of solid foundation. A third theory recently adopted by Rutherford regards the atom as containing a nucleus of positive electricity with negative electrons outside it; probably describing orbits around it. On this view the atom is a sort of minute solar system. The positive nucleus... provides a definite foundation fixing the identity of the atom. The same may be said of the sphere in Sir J. J. Thomson's theory. ... The most important property of atoms is their extraordinary stability... Negative electrons can be knocked out of atoms by the impact of rapidly moving particles such as the cathode rays and α rays, yet the atoms retain their identity and after regaining negative electrons are unaffected. Facts like these appear to be decisive against Sir J. Larmor's theory. ... These [monatomic] gases ...give spectra containing many lines so that it is certain that their atoms contain electrons which can vibrate. It is necessary to suppose that collisions between these atoms do not set their electrons in vibration, which seems to require the electrons to be protected in some way. This seems to be strongly in favor of Sir J. J. Thomson's theory and against the other two theories, for if the electrons were describing orbits outside it is hard to see how they could escape violent disturbance during a collision. ... Sir J. Larmor's theory and Rutherford's planetary theory are difficult to reconcile with the idea that atoms become firmly fixed together in compounds and rigid solids. On such theories we should expect to have nothing but gases and liquids and only very simple compounds. ... The scattering of α rays led Rutherford to adopt the idea of a positive nucleus, since some α rays are turned through a larger angle than can be explained by the electric forces due to a charge equal to that on one electron. It may be, however, that other forces besides ordinary electric force act on α rays when moving through matter. The α rays are helium atoms which have a radius about 10-8 cm., so that they probably only get through by displacing the atoms of the matter. If we suppose the positive sphere of one atom can not penetrate into that of another then the scattering of a rays by matter can probably be explained on Sir J. J. Thomson's theory.
 * The absence of effects due to the earth's motion relative to the ether can be explained on the electromagnetic theory if it is supposed that this theory covers all phenomena. This appears to be a strong argument in favor of the purely electrical nature of matter.
 * H. A. Wilson, The Structure of Atoms, as quoted by Alfred D. Cole, Science (Mar. 29, 1912) Vol. 35, pp. 511-513

Opticks (1704)

 * Isaac Newton, as quoted from the Fourth Edition, corrected (1730) unless otherwise noted, source.


 * Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting, and inflecting them, but also upon one another for producing a great Part of the Phænomena of Nature? For it's well known that Bodies act one upon another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self. How these Attractions may be perform'd, I do not here consider. What I call Attraction may be perform'd by impulse, or by some other means unknown to me. I use that Word here to signify only in general any Force by which Bodies tend towards one another, whatsoever be the Cause. For we must learn from the Phenomena of Nature what Bodies attract one another, and what are the Laws and Properties of the Attraction, before we enquire the Cause by which the Attraction is perform'd. The Attractions of Gravity, Magnetism, and Electricity, reach to very sensible distances, and so have been observed by vulgar Eyes, and there may be others which reach to so small distances as hitherto escape Observation; and perhaps electrical Attraction may reach to such small distances, even without being excited by Friction.
 * Book III, Quest. 31.


 * And when Water and Oil of Vitriol poured successively into the same Vessel grow very hot in the mixing, does not this Heat argue a great Motion in the Parts of the Liquors? And does not this Motion argue, that the Parts of the two Liquors in mixing coalesce with Violence, and by consequence rush towards one another with an accelerated Motion?
 * Book III, Quest. 31.


 * And when Aqua fortis, or Spirit of Vitriol poured upon Filings of Iron, dissolves the Filings with a great Heat and Ebullition, is not this Heat and Ebullition effected by a violent Motion of the Parts, and does not that Motion argue that the acid Parts of the Liquor rush towards the Parts of the Metal with violence, and run forcibly into its Pores till they get between its outmost Particles, and the main Mass of the Metal, and surrounding those Particles loosen them from the main Mass, and set them at liberty to float off into the Water? And when the acid particles, which alone would distil with an easy Heat, will not separate from the Particles of the Metal without a very violent Heat, does not this confirm the Attraction between them?
 * Book III, Quest. 31.


 * And is it not from the mutual Attraction of the Ingredients that they stick together for compounding these Minerals... And the same Question may be put concerning all, or almost all the gross Bodies in Nature. For all the Parts of Animals and Vegetables are composed of Substances volatile and fix'd, fluid and solid, as appears by their Analysis; and so are Salts and Minerals, so far as Chymists have been hitherto able to examine their Composition.
 * Book III, Quest. 31.


 * The Parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked Atoms, which is begging the Question; and others tell us that Bodies are glued together by rest, that is, by an occult Quality, or rather by nothing; and others, that they stick together by conspiring Motions, that is, by relative rest amongst themselves. I had rather infer from their Cohesion, that their Particles attract one another by some Force, which in immediate Contact is exceeding strong, at small distances performs the chymical Operations above-mention'd, and reaches not far from the Particles with any sensible Effect.
 * Book III, Quest. 31.


 * If two plane polish'd Plates of Glass... be laid together, so that their sides be parallel and at a very small distance from one another, and then their lower edges be dipped into Water, the Water will rise up between them. And the less the distance of the Glasses is, the greater will be the height to which the Water will rise. ...And in like manner, Water ascends between two Marbles polish'd plane, when their polished sides are parallel, and at a very little distance from one another. And if slender Pipes of Glass be dipped at one end into stagnating Water, the Water will rife up within the Pipe, and the height to which it rises will be reciprocally proportional to the Diameter of the Cavity of the Pipe, and will equal the height to which it rises between two Planes of Glass, if the Semidiameter of the Cavity of the Pipe be equal to the distance between the Planes, or thereabouts. And these Experiments succeed after the same manner in vacuo as in the open Air, (as hath been tried before the Royal Society,) and therefore are not influenced by the Weight or Pressure of the Atmosphere. ...There are therefore Agents in Nature able to make the Particles of Bodies stick together by very strong Attractions. And it is the Business of experimental Philosophy to find them out.
 * Book III, Quest. 31.


 * And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiæ is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion.
 * Book III, Quest. 31.