Ludwig Boltzmann

From Wikipedia, the free encyclopedia

Ludwig Boltzmann
Ludwig Boltzmann
Born	Ludwig Eduard Boltzmann February 20, 1844 Vienna, Austrian Empire
Died	September 5, 1906 (aged 62) Tybein, Triest, Austria-Hungary
Residence	Austria, Germany
Nationality	Austrian
Alma mater	University of Vienna
Known for	Boltzmann constant Boltzmann equation Boltzmann distribution Detailed balance H-theorem Maxwell–Boltzmann distribution Stefan–Boltzmann constant Stefan–Boltzmann law Maxwell-Boltzmann statistics Boltzmann factor Epistemological idealism
Awards	ForMemRS (1899)
Scientific career
Fields	Physics
Institutions	University of Graz University of Vienna University of Munich University of Leipzig
Doctoral advisor	Josef Stefan
Other academic advisors	Robert Bunsen Leo Königsberger Gustav Kirchhoff Hermann von Helmholtz
Doctoral students	Paul Ehrenfest Philipp Frank Gustav Herglotz Franc Hočevar Ignacij Klemenčič
Other notable students	Lise Meitner Stefan Meyer
Signature

Ludwig Eduard Boltzmann (German pronunciation: [ˈluːtvɪç ˈbɔlt͡sman]; February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).

Boltzmann coined the word ergodic while he was working on a problem in statistical mechanics.

Biography

Childhood and education

Boltzmann was born in Vienna, the capital of the Austrian Empire. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died. 

Boltzmann studied physics at the University of Vienna, starting in 1863. Among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausen and Jozef Petzval. Boltzmann received his PhD degree in 1866 working under the supervision of Stefan; his dissertation was on the kinetic theory of gases. In 1867 he became a Privatdozent (lecturer). After obtaining his doctorate degree, Boltzmann worked two more years as Stefan's assistant. It was Stefan who introduced Boltzmann to Maxwell's work.

Academic career

In 1869 at age 25, thanks to a letter of recommendation written by Stefan, he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876. 

Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger

 

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann advised her to appeal, which she did, successfully. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters and two sons. Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature. 

Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890. 

In 1894, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.

Final years

Boltzmann spent a great deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. That same year Georg Helm and Wilhelm Ostwald presented their position on energetics at a meeting in Lübeck. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate. In 1900, Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902. In 1903, Boltzmann, together with Gustav von Escherich and Emil Müller, founded the Austrian Mathematical Society. His students included Karl Přibram, Paul Ehrenfest and Lise Meitner. 

In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on natural philosophy were very popular and received considerable attention. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace.

In 1906, Boltzmann's deteriorating mental condition forced him to resign his position. He committed suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in Duino, near Trieste (then Austria). He is buried in the Viennese Zentralfriedhof. His tombstone bears the inscription of Boltzmann's entropy formula:

${\displaystyle S=k\cdot \log W}$

Philosophy

Boltzmann's kinetic theory of gases seemed to presuppose the reality of atoms and molecules, but almost all German philosophers and many scientists like Ernst Mach and the physical chemist Wilhelm Ostwald disbelieved their existence. During the 1890s Boltzmann attempted to formulate a compromise position which would allow both atomists and anti-atomists to do physics without arguing over atoms. His solution was to use Hertz's theory that atoms were Bilder, that is, models or pictures. Atomists could think the pictures were the real atoms while the anti-atomists could think of the pictures as representing a useful but unreal model, but this did not fully satisfy either group. Furthermore, Ostwald and many defenders of "pure thermodynamics" were trying hard to refute the kinetic theory of gases and statistical mechanics because of Boltzmann's assumptions about atoms and molecules and especially statistical interpretation of the second law of thermodynamics. 

Around the turn of the century, Boltzmann's science was being threatened by another philosophical objection. Some physicists, including Mach's student, Gustav Jaumann, interpreted Hertz to mean that all electromagnetic behavior is continuous, as if there were no atoms and molecules, and likewise as if all physical behavior were ultimately electromagnetic. This movement around 1900 deeply depressed Boltzmann since it could mean the end of his kinetic theory and statistical interpretation of the second law of thermodynamics. 

After Mach's resignation in Vienna in 1901, Boltzmann returned there and decided to become a philosopher himself to refute philosophical objections to his physics, but he soon became discouraged again. In 1904 at a physics conference in St. Louis most physicists seemed to reject atoms and he was not even invited to the physics section. Rather, he was stuck in a section called "applied mathematics", he violently attacked philosophy, especially on allegedly Darwinian grounds but actually in terms of Lamarck's theory of the inheritance of acquired characteristics that people inherited bad philosophy from the past and that it was hard for scientists to overcome such inheritance. 

In 1905 Boltzmann corresponded extensively with the Austro-German philosopher Franz Brentano with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.

Physics

Boltzmann's most important scientific contributions were in kinetic theory, including the Maxwell–Boltzmann distribution for molecular speeds in a gas. In addition, Maxwell–Boltzmann statistics and the Boltzmann distribution over energies remain the foundations of classical statistical mechanics. They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature. 

Boltzmann's 1898 I₂ molecule diagram showing atomic "sensitive region" (α, β) overlap.

 

Much of the physics establishment did not share his belief in the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States; and by most chemists since the discoveries of John Dalton in 1808. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's theoretical studies of 1905, confirmed the values of Avogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist. 

To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". This famous formula for entropy S is

${\displaystyle S=k_{B}\ln W}$

where k_B is Boltzmann's constant, and ln is the natural logarithm. W is Wahrscheinlichkeit, a German word meaning the probability of occurrence of a macrostate or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — number of (unobservable) "ways" in the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules. Boltzmann's paradigm was an ideal gas of N identical particles, of which N_i are in the ith microscopic condition (range) of position and momentum. W can be counted using the formula for permutations

${\displaystyle W=N!\prod _{i}{\frac {1}{N_{i}!}}}$

where i ranges over all possible molecular conditions. (${\displaystyle !}$ denotes factorial.) The "correction" in the denominator is because identical particles in the same condition are indistinguishable. 

Boltzmann was also one of the founders of quantum mechanics due to his suggestion in 1877 that the energy levels of a physical system could be discrete. 

The equation for S is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof — his second grave.

Boltzmann equation

Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.

The Boltzmann equation was developed to describe the dynamics of an ideal gas.

${\displaystyle {\frac {\partial f}{\partial t}}+v{\frac {\partial f}{\partial x}}+{\frac {F}{m}}{\frac {\partial f}{\partial v}}={\frac {\partial f}{\partial t}}\left.{\!\!{\frac {}{}}}\right|_{\mathrm {collision} }}$

where ƒ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell–Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles. 

This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions. 

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since ƒ can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function ƒ. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success. 

The form of the collision term assumed by Boltzmann was approximate. However, for an ideal gas the standard Chapman–Enskog solution of the Boltzmann equation is highly accurate. It is expected to lead to incorrect results for an ideal gas only under shock wave conditions. 

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem. However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure. 

Finally, in the 1970s E.G.D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently, nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green–Kubo relations, the fluctuation theorem, and other approaches instead.

Second thermodynamics law as a law of disorder

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.

 

The idea that the second law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to Boltzmann's view of the second law of thermodynamics. 

In particular, it was Boltzmann's attempt to reduce it to a stochastic collision function, or law of probability following from the random collisions of mechanical particles. Following Maxwell, Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients). The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. Because there are so many more possible disordered states than ordered ones, a system will almost always be found either in the state of maximum disorder – the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium – or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction", Boltzmann concluded, is thus "the most improbable case conceivable...an infinitely improbable configuration of energy." 

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.) The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary dice, with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system must move to one of the more probable states. However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes, and since statistically the data tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.

John Dalton

From Wikipedia, the free encyclopedia

John Dalton
Dalton by Charles Turner after James Lonsdale (1834, mezzotint)
Born	6 September 1766 Eaglesfield, Cumberland, England
Died	27 July 1844 (aged 77) Manchester, Lancashire, England
Nationality	British
Known for	Atomic theory, Law of Multiple Proportions, Dalton's Law of Partial Pressures, Daltonism
Awards	Royal Medal (1826)
Scientific career
Notable students	James Prescott Joule
Influences	John Gough
Author abbrev. (botany)	Jn.Dalton
Signature

John Dalton FRS (/ˈdɔːltən/; 6 September 1766 – 27 July 1844) was an English chemist, physicist, and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into color blindness, sometimes referred to as Daltonism in his honour.

Early life

John Dalton was born into a Quaker family in Eaglesfield, near Cockermouth, in Cumberland, England. His father was a weaver. He received his early education from his father and from Quaker John Fletcher, who ran a private school in the nearby village of Pardshaw Hall. Dalton's family was too poor to support him for long and he began to earn his living at the age of ten in the service of a wealthy local Quaker, Elihu Robinson.

Early career

When he was 15, Dalton joined his older brother Jonathan in running a Quaker school in Kendal, Westmorland, about 45 miles (72 km) from his home. Around the age of 23 Dalton may have considered studying law or medicine, but his relatives did not encourage him, perhaps because being a Dissenter, he was barred from attending English universities. He acquired much scientific knowledge from informal instruction by John Gough, a blind philosopher who was gifted in the sciences and arts. At the age of 27 he was appointed teacher of mathematics and natural philosophy at the "New College" in Manchester, a dissenting academy (the lineal predecessor, following a number of changes of location, of Harris Manchester College, Oxford). He remained there until the age of 34, when the college's worsening financial situation led him to resign his post and begin a new career as a private tutor in mathematics and natural philosophy.

Scientific contributions

Meteorology

Dalton's early life was influenced by a prominent Eaglesfield Quaker, Elihu Robinson, a competent meteorologist and instrument maker, who interested him in problems of mathematics and meteorology. During his years in Kendal, Dalton contributed solutions to problems and answered questions on various subjects in The Ladies' Diary and the Gentleman's Diary. In 1787 at age 21 he began his meteorological diary in which, during the succeeding 57 years, he entered more than 200,000 observations. He rediscovered George Hadley's theory of atmospheric circulation (now known as the Hadley cell) around this time. In 1793 Dalton's first publication, Meteorological Observations and Essays, contained the seeds of several of his later discoveries but despite the originality of his treatment, little attention was paid to them by other scholars. A second work by Dalton, Elements of English Grammar, was published in 1801.

Measuring mountains

After leaving the Lake District, Dalton returned annually to spend his holidays studying meteorology, something which involved a lot of hill-walking. Until the advent of aeroplanes and weather balloons, the only way to make measurements of temperature and humidity at altitude was to climb a mountain. Dalton estimated the height using a barometer. The Ordnance Survey did not publish maps for the Lake District until the 1860s. Before then, Dalton was one of the few authorities on the heights of the region's mountains. He was often accompanied by Jonathan Otley, who also made a study of the heights of the local peaks, using Dalton's figures as a comparison to check his work. Otley published his information in his map of 1818. Otley became both an assistant and a friend to Dalton.

Colour blindness

In 1794, shortly after his arrival in Manchester, Dalton was elected a member of the Manchester Literary and Philosophical Society, the "Lit & Phil", and a few weeks later he communicated his first paper on "Extraordinary facts relating to the vision of colours", in which he postulated that shortage in colour perception was caused by discoloration of the liquid medium of the eyeball. As both he and his brother were colour blind, he recognised that the condition must be hereditary.

Although Dalton's theory lost credence in his lifetime, the thorough and methodical nature of his research into his visual problem was so broadly recognised that Daltonism became a common term for colour blindness. Examination of his preserved eyeball in 1995 demonstrated that Dalton had a less common kind of colour blindness, deuteroanopia, in which medium wavelength sensitive cones are missing (rather than functioning with a mutated form of pigment, as in the most common type of colour blindness, deuteroanomaly). Besides the blue and purple of the optical spectrum he was only able to recognise one colour, yellow, or, as he said in a paper,

That part of the image which others call red, appears to me little more than a shade, or defect of light; after that the orange, yellow and green seem one colour, which descends pretty uniformly from an intense to a rare yellow, making what I should call different shades of yellow.

Gas laws

In 1800, Dalton became secretary of the Manchester Literary and Philosophical Society, and in the following year he presented an important series of lectures, entitled "Experimental Essays" on the constitution of mixed gases; the pressure of steam and other vapours at different temperatures in a vacuum and in air; on evaporation; and on the thermal expansion of gases. The four essays, presented between 2 and 30 October 1801, were published in the Memoirs of the Literary and Philosophical Society of Manchester in 1802. 

The second essay opens with the remark,

There can scarcely be a doubt entertained respecting the reducibility of all elastic fluids of whatever kind, into liquids; and we ought not to despair of effecting it in low temperatures and by strong pressures exerted upon the unmixed gases further.

After describing experiments to ascertain the pressure of steam at various points between 0 and 100 °C (32 and 212 °F), Dalton concluded from observations of the vapour pressure of six different liquids, that the variation of vapour pressure for all liquids is equivalent, for the same variation of temperature, reckoning from vapour of any given pressure.

In the fourth essay he remarks,

I see no sufficient reason why we may not conclude, that all elastic fluids under the same pressure expand equally by heat—and that for any given expansion of mercury, the corresponding expansion of air is proportionally something less, the higher the temperature. ... It seems, therefore, that general laws respecting the absolute quantity and the nature of heat, are more likely to be derived from elastic fluids than from other substances.

He enunciated Gay-Lussac's law, published in 1802 by Joseph Louis Gay-Lussac (Gay-Lussac credited the discovery to unpublished work from the 1780s by Jacques Charles). In the two or three years following the lectures, Dalton published several papers on similar topics. "On the Absorption of Gases by Water and other Liquids" (read as a lecture on 21 October 1803, first published in 1805) contained his law of partial pressures now known as Dalton's law.

Atomic theory

The most important of all Dalton's investigations are concerned with the atomic theory in chemistry. While his name is inseparably associated with this theory, the origin of Dalton's atomic theory is not fully understood. The theory may have been suggested to him either by researches on ethylene (olefiant gas) and methane (carburetted hydrogen) or by analysis of nitrous oxide (protoxide of azote) and nitrogen dioxide (deutoxide of azote), both views resting on the authority of Thomas Thomson.

From 1814 to 1819, Irish chemist William Higgins claimed that Dalton had plagiarised his ideas, but Higgins' theory did not address relative atomic mass. However, recent evidence suggests that Dalton's development of thought may have been influenced by the ideas of another Irish chemist Bryan Higgins, who was William's uncle. Bryan believed that an atom was a heavy central particle surrounded by an atmosphere of caloric, the supposed substance of heat at the time. The size of the atom was determined by the diameter of the caloric atmosphere. Based on the evidence, Dalton was aware of Bryan's theory and adopted very similar ideas and language, but he never acknowledged Bryan's anticipation of his caloric model. However, the essential novelty of Dalton's atomic theory is that he provided a method of calculating relative atomic weights for the chemical elements, something that neither Bryan nor William Higgins did; his priority for that crucial step is uncontested.

A study of Dalton's laboratory notebooks, discovered in the rooms of the Manchester Literary and Philosophical Society, concluded that so far from Dalton being led by his search for an explanation of the law of multiple proportions to the idea that chemical combination consists in the interaction of atoms of definite and characteristic weight, the idea of atoms arose in his mind as a purely physical concept, forced on him by study of the physical properties of the atmosphere and other gases. The first published indications of this idea are to be found at the end of his paper "On the Absorption of Gases by Water and other Liquids" already mentioned. There he says:

Why does not water admit its bulk of every kind of gas alike? This question I have duly considered, and though I am not able to satisfy myself completely I am nearly persuaded that the circumstance depends on the weight and number of the ultimate particles of the several gases.

He then proposes relative weights for the atoms of a few elements, without going into further detail.

The main points of Dalton's atomic theory, as it eventually developed, are:

1. Elements are made of extremely small particles called atoms.
2. Atoms of a given element are identical in size, mass and other properties; atoms of different elements differ in size, mass and other properties.
3. Atoms cannot be subdivided, created or destroyed.
4. Atoms of different elements combine in simple whole-number ratios to form chemical compounds.
5. In chemical reactions, atoms are combined, separated or rearranged.

In his first extended published discussion of the atomic theory (1808), Dalton proposed an additional (and controversial) "rule of greatest simplicity." This rule could not be independently confirmed, but some such assumption was necessary in order to propose formulas for a few simple molecules, upon which the calculation of atomic weights depended. This rule dictated that if the atoms of two different elements were known to form only a single compound, like hydrogen and oxygen forming water or hydrogen and nitrogen forming ammonia, the molecules of that compound shall be assumed to consist of one atom of each element. For elements that combined in multiple ratios, such as the then-known two oxides of carbon or the three oxides of nitrogen, their combinations were assumed to be the simplest ones possible. For example, if two such combinations are known, one must consist of an atom of each element, and the other must consist of one atom of one element and two atoms of the other.

This was merely an assumption, derived from faith in the simplicity of nature. No evidence was then available to scientists to deduce how many atoms of each element combine to form molecules. But this or some other such rule was absolutely necessary to any incipient theory, since one needed an assumed molecular formula in order to calculate relative atomic weights. Dalton's "rule of greatest simplicity" caused him to assume that the formula for water was OH and ammonia was NH, quite different from our modern understanding (H₂O, NH₃). On the other hand, his simplicity rule led him to propose the correct modern formulas for the two oxides of carbon (CO and CO₂). Despite the uncertainty at the heart of Dalton's atomic theory, the principles of the theory survived.

Atomic weights

Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808).

 

Dalton published his first table of relative atomic weights containing six elements (hydrogen, oxygen, nitrogen, carbon, sulfur and phosphorus), relative to the weight of an atom of hydrogen conventionally taken as 1. Since these were only relative weights, they do not have a unit of weight attached to them. Dalton provided no indication in this paper how he had arrived at these numbers, but in his laboratory notebook, dated 6 September 1803, is a list in which he set out the relative weights of the atoms of a number of elements, derived from analysis of water, ammonia, carbon dioxide, etc. by chemists of the time.

The extension of this idea to substances in general necessarily led him to the law of multiple proportions, and the comparison with experiment brilliantly confirmed his deduction. In the paper "On the Proportion of the Several Gases in the Atmosphere", read by him in November 1802, the law of multiple proportions appears to be anticipated in the words:

The elements of oxygen may combine with a certain portion of nitrous gas or with twice that portion, but with no intermediate quantity.

But there is reason to suspect that this sentence may have been added some time after the reading of the paper, which was not published until 1805.

Compounds were listed as binary, ternary, quaternary, etc. (molecules composed of two, three, four, etc. atoms) in the New System of Chemical Philosophy depending on the number of atoms a compound had in its simplest, empirical form.

Dalton hypothesised the structure of compounds can be represented in whole number ratios. So, one atom of element X combining with one atom of element Y is a binary compound. Furthermore, one atom of element X combining with two atoms of element Y or vice versa, is a ternary compound. Many of the first compounds listed in the New System of Chemical Philosophy correspond to modern views, although many others do not.

Dalton used his own symbols to visually represent the atomic structure of compounds. They were depicted in the New System of Chemical Philosophy, where he listed 20 elements and 17 simple molecules.

Other investigations

Dalton published papers on such diverse topics as rain and dew and the origin of springs (hydrosphere); on heat, the colour of the sky, steam and the reflection and refraction of light; and on the grammatical subjects of the auxiliary verbs and participles of the English language.

Experimental approach

As an investigator, Dalton was often content with rough and inaccurate instruments, even though better ones were obtainable. Sir Humphry Davy described him as "a very coarse experimenter", who almost always found the results he required, trusting to his head rather than his hands. On the other hand, historians who have replicated some of his crucial experiments have confirmed Dalton's skill and precision.

In the preface to the second part of Volume I of his New System, he says he had so often been misled by taking for granted the results of others that he determined to write "as little as possible but what I can attest by my own experience", but this independence he carried so far that it sometimes resembled lack of receptivity. Thus he distrusted, and probably never fully accepted, Gay-Lussac's conclusions as to the combining volumes of gases.

He held unconventional views on chlorine. Even after its elementary character had been settled by Davy, he persisted in using the atomic weights he himself had adopted, even when they had been superseded by the more accurate determinations of other chemists.

He always objected to the chemical notation devised by Jöns Jakob Berzelius, although most thought that it was much simpler and more convenient than his own cumbersome system of circular symbols.

Other publications

For Rees's Cyclopædia Dalton contributed articles on Chemistry and Meteorology, but the topics are not known.

He contributed 117 Memoirs of the Literary and Philosophical Society of Manchester from 1817 until his death in 1844 while president of that organisation. Of these the earlier are the most important. In one of them, read in 1814, he explains the principles of volumetric analysis, in which he was one of the earliest researchers. In 1840 a paper on phosphates and arsenates, often regarded as a weaker work, was refused by the Royal Society, and he was so incensed that he published it himself. He took the same course soon afterwards with four other papers, two of which ("On the quantity of acids, bases and salts in different varieties of salts" and "On a new and easy method of analysing sugar") contain his discovery, regarded by him as second in importance only to atomic theory, that certain anhydrates, when dissolved in water, cause no increase in its volume, his inference being that the salt enters into the pores of the water.

Public life

Even before he had propounded the atomic theory, Dalton had attained a considerable scientific reputation. In 1803, he was chosen to give a series of lectures on natural philosophy at the Royal Institution in London, and he delivered another series of lectures there in 1809–1810. Some witnesses reported that he was deficient in the qualities that make an attractive lecturer, being harsh and indistinct in voice, ineffective in the treatment of his subject, and singularly wanting in the language and power of illustration. 

In 1810, Sir Humphry Davy asked him to offer himself as a candidate for the fellowship of the Royal Society, but Dalton declined, possibly for financial reasons. In 1822 he was proposed without his knowledge, and on election paid the usual fee. Six years previously he had been made a corresponding member of the French Académie des Sciences, and in 1830 he was elected as one of its eight foreign associates in place of Davy. In 1833, Earl Grey's government conferred on him a pension of £150, raised in 1836 to £300. Dalton was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1834.

A young James Prescott Joule, who later studied and published (1843) on the nature of heat and its relationship to mechanical work, was a pupil of Dalton in his last years.

Personal life

Dalton in later life by Thomas Phillips, National Portrait Gallery, London (1835).

 

Dalton never married and had only a few close friends. As a Quaker, he lived a modest and unassuming personal life.

For the 26 years prior to his death, Dalton lived in a room in the home of the Rev W. Johns, a published botanist, and his wife, in George Street, Manchester. Dalton and Johns died in the same year (1844).

Dalton's daily round of laboratory work and tutoring in Manchester was broken only by annual excursions to the Lake District and occasional visits to London. In 1822 he paid a short visit to Paris, where he met many distinguished resident men of science. He attended several of the earlier meetings of the British Association at York, Oxford, Dublin and Bristol.

Disability and death

Dalton suffered a minor stroke in 1837, and a second in 1838 left him with a speech impairment, although he remained able to perform experiments. In May 1844 he had another stroke; on 26 July 1844 he recorded with trembling hand his last meteorological observation. On 27 July 1844, in Manchester, Dalton fell from his bed and was found lifeless by his attendant.

Dalton was accorded a civic funeral with full honours. His body lay in state in Manchester Town Hall for four days and more than 40,000 people filed past his coffin. The funeral procession included representatives of the city's major civic, commercial, and scientific bodies. He was buried in Manchester in Ardwick cemetery. The cemetery is now a playing field, but pictures of the original grave may be found in published materials.

Legacy

Bust of Dalton by Chantrey, 1854

 

Statue of Dalton by Chantrey.

• Much of Dalton's written work, collected by the Manchester Literary and Philosophical Society, was damaged during bombing on 24 December 1940. It prompted Isaac Asimov to say, "John Dalton's records, carefully preserved for a century, were destroyed during the World War II bombing of Manchester. It is not only the living who are killed in war". The damaged papers are in the John Rylands Library.
• A bust of Dalton, by Chantrey, paid for by public subscription was placed in the entrance hall of the Royal Manchester Institution. Chantrey's large statue of Dalton, erected while Dalton was alive was placed in Manchester Town Hall in 1877. He "is probably the only scientist who got a statue in his lifetime".
• The Manchester-based Swiss phrenologist and sculptor William Bally made a cast of the interior of Dalton's cranium and of a cyst therein, having arrived at the Manchester Royal Infirmary too late to make a caste of the head and face. A cast of the head was made, by a Mr Politi, whose arrival at the scene preceded that of Bally.
• John Dalton Street connects Deansgate and Albert Square in the centre of Manchester.
• The John Dalton building at Manchester Metropolitan University is occupied by the Faculty of Science and Engineering. Outside it stands William Theed's statue of Dalton, erected in Piccadilly in 1855, and moved there in 1966 .
• A blue plaque commemorates the site of his laboratory at 36 George Street in Manchester.
• The University of Manchester established two Dalton Chemical Scholarships, two Dalton Mathematical Scholarships, and a Dalton Prize for Natural History. A hall of residence is named Dalton Hall.
• The Dalton Medal, has been awarded only twelve times by the Manchester Literary and Philosophical Society.
• A lunar crater was named after Dalton.
• "Daltonism" became a common term for colour blindness and daltonien is the French word for "colour blind".
• The inorganic section of the UK's Royal Society of Chemistry is named after Dalton (Dalton Division), and the society's academic journal for inorganic chemistry also bears his name (Dalton Transactions).
• In honour of Dalton's work, many chemists and biochemists use the (unofficial) designation dalton (abbreviated Da) to denote one atomic mass unit (1/12 the weight of a neutral atom of carbon-12).
• Quaker schools have named buildings after Dalton: for example, a school house in the primary sector of Ackworth School, is called Dalton.
• Dalton Township in southern Ontario was named after him. In 2001 the name was lost when the township was absorbed into the City of Kawartha Lakes but in 2002 the Dalton name was affixed to a new park, Dalton Digby Wildlands Provincial Park.