## Posts Tagged ‘Royal Society’

Sir Joseph Banks, President of the Royal Society in London, sat in the splendour of his office in Somerset House. It was an April morning in the year 1800. The clatter of horse-drawn carriages in the Strand rose to his window, but he did not notice; his attention was elsewhere. Staring into space, he clutched a letter that had been delivered to him that very morning. Dated March 20th and written in French, it had been sent from Como in Lombardy by an Italian professor of experimental physics named Alessandro Volta.

Professor Volta’s letter was clearly attended by some haste, since he had dispatched the first four pages in advance of the remainder, which was to follow. The subject matter was experiments on electricity, and the first pages of Volta’s letter to Banks described the invention of an apparatus “which will no doubt astonish you”.

Alessandro Volta (1745-1827) and his amazing invention

On that April morning in London, Banks read the letter and was duly astonished. Volta’s apparatus, consisting of a series of discs of two different metals in contact separated by brine-soaked pasteboard, was capable of generating a continuous current of electricity. This was a world apart from the static electricity of the celebrated Leyden jar and indeed a most astonishing discovery; no wonder Volta was so anxious to communicate it without delay to Banks and thereby to the Royal Society – of which Volta was also a fellow.

Still clutching the letter, Joseph Banks regained his composure and collected his thoughts. He must of course arrange for the letter to be read to the Society, after which it would duly appear in print in the Society’s Philosophical Transactions.

In the meantime, Banks was naturally obliged to keep Volta’s discovery confidential. But then again, with a such an astonishing discovery as this, it was sorely tempting to show Signor Volta’s letter – in the strictest confidence of course – to certain individuals in his large circle of scientific acquaintances, who would surely be fascinated by its contents. What could be the harm in that?

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Yielding to temptation

The state of mind into which Sir Joseph Banks was propelled by Professor Volta’s letter was pertinently observed (albeit almost a century later) by Oscar Wilde in his play Lady Windermere’s Fan, in which Lord Darlington famously quips “I can resist everything but temptation.”

32 Soho Square (right), the London home of Sir Joseph Banks

The London home of Joseph Banks, in Soho Square, was the centre of bustling scientific activity and attracted all the leading members of the scientific establishment. Within a month of receiving Volta’s letter, Banks had yielded to temptation and shown it to a number of acquaintances.

Among them was Anthony Carlisle, a fashionable London surgeon who was shortly to display remarkable abilities in the realm of physical chemistry. Having perused the letter, Carlisle immediately arranged for his friend the chemist William Nicholson to look over the pages with him, after which Carlisle set about constructing the apparatus according to Volta’s instructions – the fabled instrument we now call the Voltaic Pile.

Sir Anthony Carlisle (1768-1840), painted by Henry Bone in 1827

So within a month of Volta’s hastened communication to Banks, the details of the construction of the Voltaic Pile had been leaked to, among others, Carlisle and Nicholson, enabling the latter to begin experiments with Volta’s apparatus that would lead to their privileged discovery of electrolysis, before Volta’s letter had even been read to – let alone published by – the Royal Society.

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The chronology of the case

1800

March 20th
Volta sends a letter (in French) from Como, Lombardy, to Sir Joseph Banks at the Royal Society in London, announcing his invention of the Voltaic pile.

April
Banks leaks the contents of Volta’s letter to several acquaintances, including Anthony Carlisle, who arranges for William Nicholson to view the letter.

May
Carlisle and Nicholson construct a Voltaic Pile according to Volta’s instructions. With this apparatus they discover the electrolysis of water into hydrogen and oxygen.

June 26th
Volta’s letter is read to the Royal Society.

July
William Nicholson publishes a paper in The Journal of Natural Philosophy, Chemistry & the Arts, announcing the discovery of electrolysis by Anthony Carlisle and himself, using the Voltaic Pile.

September
Volta’s letter announcing his invention of the Voltaic pile is published in French in the Philosophical Transactions of the Royal Society, and in English in The Philosophical Magazine.

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Mouse-over links to original papers mentioned in this post

Volta’s letter to Banks (begins on page 289)

Nicholson’s paper (begins on page 179)

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The Honorable Robert Boyle FRS (1627-1691)

The fourteenth child of the immensely wealthy Richard Boyle, 1st Earl of Cork, Robert Boyle inherited land and property in England and Ireland which yielded a substantial income. He never had to work for a living, and following three years of travel and study as a teenager in Europe, Boyle decided at the age of 17 to devote his life to scientific research and the cultivation of what was called the “new philosophy”.

In Britain, Boyle was the leading figure in a move away from the Aristotelian view that knowledge was best obtained by the use of reason and logic. Boyle rejected this argument, and insisted that the path to knowledge was through empiricism and experiment. He won over many to his view, notably Isaac Newton, and in 1660 Boyle was a founding member of a society which believed that knowledge should be based first on experiment; we know it today as the Royal Society.

Boyle carried out a wealth of experiments in many areas of physics and chemistry, yet he seems to have been content with obtaining experimental results and generally stopped short of formulating theories to explain them.

Leibniz expressed astonishment that Boyle “who has so many fine experiments, had not come to some theory of chemistry after meditating so long on them”.

But what about Boyle’s law? you ask.

Well, it may surprise you to know that Robert Boyle did not originate the pressure-volume law commonly called Boyle’s law. A description of the reciprocal relation between the volume of air and its pressure does first appear in a book written by Boyle, but he refers to it as “Mr Towneley’s hypothesis”, for reasons we shall see.

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Torricelli leads the way

Torricelli using a lot more mercury than necessary to demonstrate the barometer.

It was Evangelista Torricelli (1608-1647) in Italy who started it all in the summer of 1644 with the invention of the mercury barometer. It was an impressive device, made all the more impressive by the insight that came with it. For one thing, Torricelli had no problem accepting the space above the mercury as a vacuum, in contrast to the vacuum-denying views of Aristotle and Descartes. For another, he was the first to appreciate the fact that air had weight, and to understand that the column of mercury was supported by the pressure of the atmosphere. As he put it: “We live submerged at the bottom of an ocean of air, which by unquestioned experiments is known to have weight.”

This led Torricelli to surmise that atmospheric pressure should be less in elevated places like mountains, an idea which was put to the test in France by Blaise Pascal, or more precisely by Pascal’s brother-in-law Florin Périer, who happened to live in Clermont-Ferrand, which has Puy de Dôme nearby.

Puy de Dôme in south-central France, close to Clermont-Ferrand.

On Saturday, September 19, 1648, Florin Périer and some friends performed the Torricelli experiment on the top of Puy de Dôme in south-central France. The height of the mercury column was substantially less – 85 mm less – than the control instrument stationed at the base of the mountain 1,400 metres below.

The Puy de Dôme experiment provided Pascal with convincing evidence that it was the weight of air, and thus atmospheric pressure, that balanced the weight of the mercury column. Torricelli’s instrument provided a convenient means of measuring this pressure. It was a barometer. The news quickly spread to England.

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Reaching new heights

The Torricellian experiment was demonstrated and discussed at the scientific centres of learning in London, Oxford and Cambridge from 1648 onwards. At Cambridge, there was an enthusiastic experimental scientist by the name of Henry Power, who was studying for a degree in medicine at Christ’s College. Power’s home was at Halifax in Yorkshire, and this gave him the opportunity to verify the Puy de Dôme experiment because unlike London, Oxford and Cambridge, the land around Halifax rises to significant heights.

The hills around Halifax in northern England

On Tuesday, May 6, 1653, Henry Power carried the Torricellian experiment to the summit of Halifax Hill, to the east of the town, where he was able to verify Pascal’s observation. In further experiments, he began to investigate the elasticity of air – i.e. its expansion and compression characteristics. And it was this change of focus that was to characterise England’s contribution to the scientific study of air.

The pioneering work in Italy and France had been concerned with the physical properties of the atmosphere. In England, attention was turning to the physical properties of air itself.

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The Spring of the Air

In 1654, the year after Henry Power’s excursion on Halifax Hill, Robert Boyle arrived in Oxford where he rented rooms to pursue his scientific studies. With the assistance of Robert Hooke, he constructed an air pump in 1659 and began a series of experiments on the properties of air. An account of this work was published in 1660 under the title “New Experiments Physico-Mechanicall, Touching The Spring of the Air, and its Effects”.

Boyle’s book was a landmark work, in which were reported the first controlled experiments on the effects of reduced air pressure. The experiments are divided into seven groups, the first of which concern “the spring of the air” i.e. the pressure exerted by the air when its volume is changed. It is clear that Boyle had an interest not only in demonstrating the elastic nature of air, but also in finding a quantitative expression of its elasticity. Due to inefficiencies in the air pump and the inherent difficulties of the experiment, Boyle failed in his first attempt. But it was not for want of trying.

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Enter Mr Towneley

Richard Towneley, whose home was near Burnley in Lancashire, northern England, was curiously similar to Robert Boyle in that the Towneley family estate also generated an income which meant that Richard did not have to work for a living. And just like Boyle, Towneley devoted his time to scientific studies.

Richard Towneley’s home, Towneley Hall in northern England, painted by JMW Turner in 1799

Now it just so happened that the previously-mentioned Henry Power of Halifax was the Towneley family’s physician. This gave Richard and Henry regular opportunities to share their enthusiasm for scientific experiments and discuss the latest scientific news.

In 1660 they both read Robert Boyle’s New Experiments Physico-Mechanicall, and this prompted further interest in the study of air pressure which Power had conducted on Halifax Hill seven years earlier. Not far to the north of Towneley Hall is Pendle Hill, whose summit is 1,827 feet (557 meters) above sea level, and it was here that Power and Towneley conducted an experiment that made history.

Pendle Hill, photographed by Lee Pilkington

On Wednesday 27th April 1661, they introduced a quantity of air above the mercury in a Torricellian tube. They measured its volume, and then using the tube as a barometer, they measured the air pressure. They then ascended Pendle Hill and at the summit repeated the measurements of volume and air pressure. As expected, there was an increase in volume and a decrease in pressure.

Although their measurements were only roughly accurate and doubtless affected by temperature differences between the base and summit of the hill, the numerical data was sufficient to give them the intuitive realization of a reciprocal relationship between the pressure and volume of air

On a high hill in northern England, nature revealed one of its secrets to Henry Power and Richard Towneley. Now they needed to communicate their finding.

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Boyle reports the news

It was not until two years after the Pendle Hill experiment that Henry Power eventually got around to publishing the results in Experimental Philosophy (1663). This delay explains why history has never associated the names of Power and Towneley with the gas law they discovered, because the news from Pendle Hill was first given to, and first reported by, Robert Boyle.

The second edition of 1662

In the appendix to the second edition of his New Experiments Physico-Mechanical published in 1662, Boyle reports Power and Towneley’s experimental activities, which in error he ascribes solely to Richard Towneley. It was on the basis of this second edition of Boyle’s book that the reciprocal relationship between the volume of air and its pressure became known as “Mr. Towneley’s hypothesis” by contemporary authors such as Robert Hooke and Isaac Newton.

A complication was added by the fact that Power and Towneley’s experiment led Boyle to the idea of compressing air in a J-shaped tube by pouring mercury into the long arm and measuring the volume and applied pressure.

From this experiment, conducted in September 1661, Boyle discovered that the volume of air was halved when the pressure was doubled. Curiously, he translated this finding into the hypothesis that there was a direct proportionality between the density of air and the applied pressure.

It didn’t occur to Boyle that the direct relation between density and pressure was the same thing as the reciprocal relation between volume and pressure discovered earlier by Power and Towneley. Boyle seems to have thought that compression was somehow different to expansion, and that his experiment broke new ground.

For this reason Boyle believed he had discovered something new, and since his name was far better known in scientific circles than that of Henry Power and Richard Towneley, it was inevitable that Boyle’s name would be associated with the newly-published hypothesis, which in time became Boyle’s law.

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Postscript : La loi de Mariotte

The pressure-volume law discovered by Power and Towneley, and confirmed by Boyle, is known as Boyle’s law only in Britain, America, Australia, the West Indies and other parts of what was once called the British Empire. Elsewhere it is called Mariotte’s law, after the French physicist Edme Mariotte.

Mariotte stated the pressure-volume relationship in his book De la nature de l’air, published in 1679, some 17 years after the second edition of Boyle’s New Experiments Physico-Mechanical. Mariotte made no claim of originality, nor did he make any reference to Boyle. But he was an effective publicist for the law, with the result that his name became widely associated with it.

Some might argue that the attribution is not quite deserved. However, Edme Mariotte stated something immensely important that Robert Boyle neglected to mention. He pointed out that temperature must be held constant for the pressure-volume relationship to hold:

In the view of CarnotCycle, the pressure-volume law so stated can with justification be called Mariotte’s law.

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## Rankine on Entropy, Love and Marriage

Posted: February 1, 2013 in thermodynamics
Tags: , , , , ,

William John Macquorn Rankine (1820-1872) Photo credit: Wikipedia

On Thursday 19 January 1854, a 33-year-old Scottish engineer and physicist named William Rankine read a paper before the Royal Society in London, of which he had just recently been elected a fellow.

Rankine’s paper, entitled “On the geometrical representation of the expansive action of heat, and the theory of thermodynamic engines”, came at crucial time in the development of the new science of heat and work. James Joule and William Thomson had begun publishing the results of their important experiments in Manchester (see my previous post for more on this), and Rudolf Clausius in Germany had recently given a mathematical statement of the first law, equating the change in the internal energy of a thermodynamic system to the heat received and the mechanical work done:

ΔU = Q – W.

Rankine was in the right place at the right time to build on the theoretical foundations that Thomson and Clausius were already fashioning, but he did no such thing. He was not one for following anyone else’s lead. Like Kipling’s Cat, He Walked by Himself. He had his own way of looking at things; he did things his way.

The engineer from Edinburgh certainly had the necessary attributes for doing so. He had plenty of practical experience as a railway and waterway engineer, he had a thorough grounding in higher mathematics, dynamics and physics, and he was the possessor of a remarkable scientific imagination – a characteristic that was to prove not altogether advantageous, as we shall see.

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Indications of Rankine’s different way of looking at things were evident right from the start of his paper. Apart from using the pressure volume diagram as his geometrical framework, there is little if anything in common with the ‘Carnot Cycle’ analytical approach previously taken by Clapeyron and Clausius.

For a start, Rankine dispenses completely with isothermal curves in Fig.3, where OX is the line of no pressure and OY is the line of no volume. His ‘cycle’ consists of an upper and lower curve of no transmission of heat [i.e. adiabatic curves] which are infinitely extended, a line of constant volume, and a curvilinear line ACB representing an arbitrary succession of volumes and pressures through which the working substance is supposed to pass in changing from state A to state B.

He draws ordinates AVA and BVB from points A and B down to the line of no pressure, and calls the area VAACBVB the ‘expansive power’ developed during the operation ACB. He shows by an astute piece of reasoning that the indefinitely-prolonged area MACBN is exactly equal to the ‘heat received’ (HA,B) by the working substance during the operation ACB. He then advances the theorem that the difference between the ‘heat received’ and the ‘expansive power’:

depends simply on the initial and final points A and B, and not on the form of the curve ACB. The above expression is regarded by Rankine as the energy stored up (his italics) in the working substance during the operation ACB. He identifies this stored energy as the sum of two quantities – the increase of what he calls the ‘actual energy of heat’ (Q) of the substance in passing from state A to state B:

ΔQ = QB – QA

and the change in what he calls the ‘potential energy of molecular action’ (S) [not to be confused with the modern symbol for entropy] in passing from state A to state B:

ΔS = SB – SA

Thus:

This is a form of what he calls the general equation of the expansive action of heat, which was the object of his geometrical reasoning. Rankine’s approach is thus wholly different to that of Clausius, who gained his insights into path-independent thermodynamic functions by considering the operations of a complete cycle. Rankine instead arrives at a path-independent result by considering an arbitrary curve on a diagram of energy.

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Rankine’s ‘potential energy of molecular action’ needed to be expressed in terms of measurable quantities in order to give a definite form to equation 2, and in the next section of the paper he does this, at the same time introducing the symbol Ψ to denote the sum of the actual energy of heat and the potential energy of molecular action present in the working substance in any state:

Rankine assigns no name to Ψ, and although it is clear from the theorem already advanced that a change in this quantity between initial and final states is independent of path, he draws no attention to the fact. Perhaps Rankine simply didn’t recognise at the time that he had defined the thermodynamic state function known as internal energy, albeit on his own terms.

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As he continued with the reading of his paper before the Royal Society on that January day in 1854, neither Rankine nor his audience were aware that a defining moment in the history of thermodynamics was shortly to take place.

It began at the third corollary to the general equation of the expansive action of heat, where Rankine observes that for two adiabatic curves infinitely close together, “the ratio of the heat consumed in passing from one of those curves to the other, to the actual heat present, will be the same”. He expresses this ratio as:

and proceeds to show that F, which he simply labels “a thermodynamic function”, has a constant value for any adiabatic curve. This was the second thermodynamic function that Rankine had introduced in as many pages, although again he seems not to have attached particular significance to this.

In the fourth section of his paper, having introduced the relation

between the ‘actual energy of heat’ of a substance, its specific heat, and the absolute temperature, Rankine converts F into a more convenient thermodynamic function Φ by defining:

The fortunate effect of this conversion is to remove the functional relationship with the dubiously-defined Q and give Φ the dimensions of energy (as heat received) per degree of absolute temperature. To students of classical thermodynamics, those units will no doubt sound familiar.

In a theorem under Proposition XII, Rankine then introduces both Ψ and Φ into his general equation of the expansive action of heat, with the following result:

I have no way of knowing what reaction this equation elicited from those assembled at the Royal Society when Rankine wrote it on the blackboard, or recited it, or whatever. What I do know is that when I first saw it in a volume of Rankine’s miscellaneous papers held at the University of Wisconsin and publicly available on archive.org, I nearly fell off my chair.

Exchanging Rankine’s symbols for their modern equivalents, the equation reads:

$\Delta U=\int TdS-\int PdV$

This is the fundamental relation of thermodynamics.

Eleven years before Clausius, Rankine gave mathematical expression to the thermodynamic state function we now call entropy, from a consideration of infinitely close adiabatic curves (incidentally it was Rankine who introduced the term ‘adiabatic’). And by putting both internal energy (Ψ) and entropy (Φ) together in equation 40A, Rankine made the first mathematical statement that combined both the first and second laws of thermodynamics.

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Although Φ appeared in print more than a decade before Clausius arrived at another symbolic expression  for the same thing and called it entropy, Rankine’s thermodynamic function gained little from its antecedence. The reason derives principally from the fact that Rankine was a model-based thinker with a fanciful imagination. He formed intricate mental pictures of molecular motion to explain the phenomenon of heat, and when the math he applied appeared to produce sensible results, he assumed that his model – which he called the hypothesis of molecular vortices – was correct.

Up to this point in the article I have deliberately refrained from mentioning this aspect, so as not to obscure the (surprisingly) hypothesis-independent sequence of deduction by which Rankine reaches equation 40A. But there is no escaping the fact that much of the paper read by Rankine before the Royal Society in January 1854 is laden with hypothetical apparatus, accompanied by a lexicon of abstruse terminology such as ‘actual energy of heat’, to which it is difficult to attach any distinct meaning.

It proved altogether too much for Rankine’s contemporaries to swallow. When Clausius presented his conception of entropy in 1865, they found it much more palatable, and Rankine’s Φ was forgotten.

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Rankine may have failed to convince colleagues of his molecular vortices, but in no way did this dampen his academic enthusiasm. In 1855 he wrote the very first formal treatise on thermodynamics for Nichol’s Cyclopedia, and in 1857 he penned an important treatise on shipbuilding as well as his famous Manual of Applied Mechanics. He followed this up with his Manual of Civil Engineering in 1861, and by 1865 had become a consulting engineer. In 1869, another great engineering treatise, Machinery and Millwork, appeared. During his time as a fellow of the Royal Society, Rankine published no fewer than 150 papers on mathematical, thermodynamic and engineering subjects, yet still found time to study botany, learn to play the cello and piano, and develop other creative aspects of his intellect, including the writing of humorous songs. One of his early efforts was “The mathematician in love”, in the following stanzas of which Rankine wittily propounds his theory of love and marriage:

William Rankine never found the time to test this theory in practice. He died a bachelor on Christmas Eve 1872, at the age of 52, of overwork.

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