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Circus Maximus

The Circus Maximus (Latin for "largest circus"; Italian: Circo Massimo) is an ancient Roman chariot-racing stadium and mass entertainment venue in Rome, Italy. In the valley between the Aventine and Palatine hills, it was the first and largest stadium in ancient Rome and its later Empire. It measured 621 m in length and 118 m in width and could accommodate over 150,000 spectators. In its fully developed form, it became the model for circuses throughout the Roman Empire. The site is now a public park.

Events and uses
The Circus was Rome's largest venue for ludi, public games connected to Roman religious festivals. Ludi were sponsored by leading Romans or the Roman state for the benefit of the Roman people (populus Romanus) and gods. Most were held annually or at annual intervals on the Roman calendar. Others might be given to fulfil a religious vow, such as the games in celebration of a triumph. In Roman tradition, the earliest triumphal ludi at the Circus were vowed by Tarquin the Proud to Jupiter in the late Regal era for his victory over Pometia.

Ludi ranged in duration and scope from one-day or even half-day events to spectacular multi-venue celebrations held over several days, with religious ceremonies and public feasts, horse and chariot racing, athletics, plays and recitals, beast-hunts and gladiator fights. Some included public executions. The greater ludi (meaning sport or game in Latin ) at the Circus began with a flamboyant parade (pompa circensis), much like the triumphal procession, which marked the purpose of the games and introduced the participants.

During the Roman Republic, the aediles organized the games. The most costly and complex of the ludi offered opportunities to assess an aedile's competence, generosity, and fitness for higher office. Some Circus events, however, seem to have been relatively small and intimate affairs. In 167 BC, "flute players, scenic artists and dancers" performed on a temporary stage, probably erected between the two central seating banks. Others were enlarged at enormous expense to fit the entire space. A venatio held there in 169 BC, one of several in the 2nd century, employed "63 leopards and 40 bears and elephants", with spectators presumably kept safe by a substantial barrier.

As Rome's provinces expanded, existing ludi were embellished and new ludi invented by politicians who competed for divine and popular support. By the late Republic, ludi were held on 57 days of the year; an unknown number of these would have required full use of the Circus. On many other days, charioteers and jockeys would need to practise on its track. Otherwise, it would have made a convenient corral for the animals traded in the nearby Forum Boarium, just outside the starting gate. Beneath the outer stands, next to the Circus' multiple entrances, were workshops and shops. When no games were being held, the Circus at the time of Catullus (mid-1st century BC) was probably "a dusty open space with shops and booths ... a colourful crowded disreputable area" frequented by "prostitutes, jugglers, fortune tellers and low-class performing artists."

Rome's emperors met the growing popular demand for regular ludi and the need for more specialised venues, as essential obligations of their office and cult. Over the several centuries of its development, the Circus Maximus became Rome's paramount specialist venue for chariot races. By the late 1st century AD, the Colosseum had been built to host most of the city's gladiator shows and smaller beast-hunts, and most track-athletes competed at the purpose-designed Stadium of Domitian, though long-distance foot races were still held at the Circus. Eventually, 135 days of the year were devoted to ludi.

Even at the height of its development as a chariot-racing circuit, the circus remained the most suitable space in Rome for religious processions on a grand scale and was the most popular venue for large-scale venationes; in the late 3rd century, the emperor Probus laid on a spectacular Circus show in which beasts were hunted through a veritable forest of trees, on a specially built stage. With the advent of Christianity as the official religion of the Empire, ludi gradually fell out of favour. The last known beast-hunt at the Circus Maximus took place in 523, and the last known races there were held by Totila in 549.

Regal era
The Circus Maximus was sited on the level ground of the Valley of Murcia (Vallis Murcia), between Rome's Aventine and Palatine Hills. In Rome's early days, the valley would have been rich agricultural land, prone to flooding from the river Tiber and the stream which divided the valley lengthwise. The stream was probably bridged at an early date, at the two points where the track had to cross it, and the earliest races would have been held within an agricultural landscape, "with nothing more than turning posts, banks where spectators could sit, and some shrines and sacred spots".

In Livy's History of Rome, the first Etruscan king of Rome, Lucius Tarquinius Priscus, built raised, wooden perimeter seating at the Circus for Rome's highest echelons (the equites and patricians), probably midway along the Palatine straight, with an awning against the sun and rain. His grandson, Tarquinius Superbus, added the first seating for citizen-commoners (plebs, or plebeians), either adjacent or on the opposite, Aventine side of the track. Otherwise, the Circus was probably still little more than a trackway through surrounding farmland. By this time, it may have been drained but the wooden stands and seats would have frequently rotted and been rebuilt. The turning posts (metae), each made of three conical stone pillars, may have been the earliest permanent Circus structures; an open drainage canal between the posts would have served as a dividing barrier.

Republican era
The games' sponsor (Latin editor) usually sat beside the images of attending gods, on a conspicuous, elevated stand (pulvinar) but seats at the track's perimeter offered the best, most dramatic close-ups. In 494 BC (very early in the Republican era) the dictator Manius Valerius Maximus and his descendants were granted rights to a curule chair at the southeastern turn, an excellent viewpoint for the thrills and spills of chariot racing. In the 190s BC, stone track-side seating was built, exclusively for senators.

Permanent wooden starting stalls were built in 329 BC. They were gated, brightly painted, and staggered to equalise the distances from each start place to the central barrier. In theory, they might have accommodated up to 25 four-horse chariots (Quadrigas) abreast but when team-racing was introduced, they were widened, and their number reduced. By the late Republican or early Imperial era, there were twelve stalls. Their divisions were fronted by herms that served as stops for spring-loaded gates, so that twelve light-weight, four-horse or two-horse chariots could be simultaneously released onto the track. The stalls were allocated by lottery, and the various racing teams were identified by their colors. Typically, there were seven laps per race. From at least 174 BC, they were counted off using large sculpted eggs. In 33 BC, an additional system of large bronze dolphin-shaped lap counters was added, positioned well above the central dividing barrier (euripus) for maximum visibility.

Julius Caesar's development of the Circus, commencing around 50 BC, extended the seating tiers to run almost the entire circuit of the track, barring the starting gates and a processional entrance at the semi-circular end. The track measured approximately 621 m in length and 150 m in breadth. A canal between the track perimeter and its seating protected spectators and help drain the track. The inner third of the seating formed a trackside cavea. Its front sections along the central straight were reserved for senators, and those immediately behind for equites. The outer tiers, two thirds of the total, were meant for Roman plebs and non-citizens. They were timber-built, with wooden-framed service buildings, shops and entrance-ways beneath. The total number of seats is uncertain, but was probably in the order of 150,000; Pliny the Elder's estimate of 250,000 seating places is unlikely. The wooden bleachers were damaged in a fire of 31 BC, either during or after construction.

Imperial era
The fire damage of 31 was probably repaired by Augustus (Caesar's successor and Rome's first emperor). He modestly claimed credit only for an obelisk and pulvinar at the site but both were major projects. Ever since its quarrying, long before Rome existed, the obelisk had been sacred to Egyptian Sun-gods. Augustus had it brought from Heliopolis at enormous expense, and erected midway along the dividing barrier of the Circus. It was Rome's first obelisk, an exotically sacred object and a permanent reminder of Augustus' victory over his Roman foes and their Egyptian allies in the recent civil wars. Thanks to him, Rome had secured both a lasting peace and a new Egyptian Province. The pulvinar was built on monumental scale, a shrine or temple (aedes) raised high above the trackside seats. Sometimes, while games were in progress, Augustus watched from there, alongside the gods. Occasionally, his family would join him there. This is the Circus described by Dionysius of Halicarnassus as "one of the most beautiful and admirable structures in Rome", with "entrances and ascents for the spectators at every shop, so that the countless thousands of people may enter and depart without inconvenience." The site remained prone to flooding, probably through the starting gates, until Claudius made improvements there; they probably included an extramural anti-flooding embankment. Fires in the crowded, wooden perimeter workshops and bleachers were a far greater danger. A fire of 36 AD seems to have started in a basket-maker's workshop under the stands, on the Aventine side; the emperor Tiberius compensated various small businesses there for their losses. In AD 64, during Nero's reign, fire broke out at the semi-circular end of the Circus, swept through the stands and shops, and destroyed much of the city. Games and festivals continued at the Circus, which was rebuilt over several years to the same footprint and design.

By the late 1st century AD, the central dividing barrier comprised a series of water basins, or else a single watercourse open in some places and bridged over in others. It offered opportunities for artistic embellishment and decorative swagger, and included the temples and statues of various deities, fountains, and refuges for those assistants involved in more dangerous circus activities, such as beast-hunts and the recovery of casualties during races.

In AD 81 the Senate built a triple arch honoring Titus at the semi-circular end of the Circus, to replace or augment a former processional entrance. The emperor Domitian built a new, multi-storey palace on the Palatine, connected somehow to the Circus; he likely watched the games in autocratic style, from high above and barely visible to those below. Repairs to fire damage during his reign may already have been under way before his assassination.

The risk of further fire-damage, coupled with Domitian's fate, may have prompted Trajan's decision to rebuild the Circus entirely in stone, and provide a new pulvinar in the stands where Rome's emperor could be seen and honoured as part of the Roman community, alongside their gods. Under Trajan, the Circus Maximus found its definitive form, which was unchanged thereafter save for some monumental additions by later emperors, an extensive, planned rebuilding of the starting gate area under Caracalla, and repairs and renewals to existing fabric. Of these, Pliny claims that Trajan's works gained a further 5,000 seats. Some repairs were unforeseen and extensive, such as those carried out in Diocletian's reign, after the collapse of a seating section killed some 13,000 people.

Religious significance
The southeastern turn of the track ran between two shrines which may have predated the Circus' formal development. One, at the outer southeast perimeter, was dedicated to the valley's eponymous goddess Murcia, an obscure deity associated with Venus, the myrtle shrub, a sacred spring, the stream that divided the valley, and the lesser peak of the Aventine Hill. The other was at the southeastern turning-post, where there was an underground shrine to Consus, a minor god of grain-stores, connected to the grain-goddess Ceres and to the underworld. According to Roman tradition, Romulus discovered this shrine shortly after the founding of Rome. He invented the Consualia festival, as a way of gathering his Sabine neighbours at a celebration that included horse-races and drinking. During these distractions, Romulus's men then abducted the Sabine daughters as brides. Thus the famous Roman myth of the Rape of the Sabine women had as its setting the Circus and the Consualia. In this quasi-legendary era, horse or chariot races would have been held at the Circus site. The track width may have been determined by the distance between Murcia's and Consus' shrines at the southeastern end, and its length by the distance between these two shrines and Hercules' Ara Maxima, supposedly older than Rome itself and sited behind the Circus' starting place. The position of Consus' shrine at the turn of the track recalls the placing of shrines to Roman Neptune's Greek equivalent, Poseidon, in Greek hippodromes. In later developments, the altar of Consus, as one of the Circus' patron deities, was incorporated into the fabric of the south-eastern turning post. When Murcia's stream was partly built over, to form a dividing barrier (the spina or euripus) between the turning posts, her shrine was either retained or rebuilt. In the Late Imperial period, both the southeastern turn and the circus itself were sometimes known as Vallis Murcia. The symbols used to count race-laps also held religious significance; Castor and Pollux, who were born from an egg, were patrons of horses, horsemen, and the equestrian order (equites). Likewise, the later use of dolphin-shaped lap counters reinforced associations between the races, swiftness, and Neptune, as god of earthquakes and horses; the Romans believed dolphins to be the swiftest of all creatures. When the Romans adopted the Phrygian Great Mother as an ancestral deity, a statue of her on lion-back was erected within the circus, probably on the dividing barrier.

Sun and Moon cults were probably represented at the Circus from its earliest phases. Their importance grew with the introduction of Roman cult to Apollo, and the development of Stoic and solar monism as a theological basis for the Roman Imperial cult. In the Imperial era, the Sun-god was divine patron of the Circus and its games. His sacred obelisk towered over the arena, set in the central barrier, close to his temple and the finishing line. The Sun-god was the ultimate, victorious charioteer, driving his four-horse chariot (quadriga) through the heavenly circuit from sunrise to sunset. His partner Luna drove her two-horse chariot (biga); together, they represented the predictable, orderly movement of the cosmos and the circuit of time, which found analogy in the Circus track. Luna's temple, which was probably built long before Apollo's, burned down in the Great Fire of 64 AD and was probably not replaced. Her cult was closely identified with that of Diana, who seems to have been represented in the processions that started Circus games, and with Sol Indiges, usually identified as her brother. After the loss of her temple, her cult may have been transferred to Sol's temple on the dividing barrier, or one beside it; both would have been open to the sky.

Temples to several deities overlooked the Circus; most are now lost. The temples to Ceres and Flora stood close together on the Aventine, more or less opposite the Circus' starting gate, which remained under Hercules' protection. Further southeast along the Aventine was a temple to Luna, the moon goddess. Aventine temples to Venus Obsequens, Mercury and Dis (or perhaps Summanus) stood on the slopes above the southeast turn. On the Palatine hill, opposite to Ceres's temple, stood the temple to Magna Mater and, more or less opposite Luna's temple, one to the sun-god Apollo.

Several festivals, some of uncertain foundation and date, were held at the Circus in historical times. The Consualia, with its semi-mythical establishment by Romulus, and the Cerealia, the major festival of Ceres, were probably older than the earliest historically attested "Roman Games" (Ludi Romani) held at the Circus in honour of Jupiter in 366 BC. In the early Imperial era, Ovid describes the opening of Cerealia (mid to late April) with a horse race at the Circus, followed by the nighttime release of foxes into the stadium, their tails ablaze with lighted torches. Some early connection is likely between Ceres as goddess of grain crops and Consus as a god of grain storage and patron of the Circus.

Modern status and uses
After the 6th century, the Circus fell into disuse and decay. The lower levels, ever prone to flooding, were gradually buried under waterlogged alluvial soil and accumulated debris, so that the original track is now buried six meters beneath the modern surface. In the 11th century, the Circus was "replaced by dwellings rented out by the congregation of Saint-Guy." In the 12th century, a watercourse was dug there to drain the soil, and by the 16th century the area was used as a market garden. During the renaissance, the site was one of many used as a convenient quarry for good quality building stone. Many of the Circus's standing structures survived these changes; in 1587, two obelisks were removed from the central barrier by Pope Sixtus V, and one of these was re-sited at the Piazza del Popolo. In 1852, a gas works was built on the site by the Anglo-Italian Gas Society. It remained in situ until 1910 when it was relocated to the edge of Rome. Mid-19th century workings at the circus site uncovered the lower parts of a seating tier and outer portico. Since then, a series of excavations has exposed further sections of the seating, curved turn and central barrier but further exploration has been limited by the scale, depth and waterlogging of the site. The Circus site now functions as a large park area, open to the public and often used for concerts, meetings, and celebrations.

title: Circus Maximus


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Aldehyde

In organic chemistry, an aldehyde is an organic compound containing a functional group with the structure R\sCH\dO. The functional group itself (without the "R" side chain) can be referred to as an aldehyde but can also be classified as a formyl group. Aldehydes are a common motif in many chemicals important in technology and biology.

Structure and bonding
Aldehyde molecules have a central carbon atom that is connected by a double bond to oxygen, a single bond to hydrogen and another single bond to a third substituent, which is carbon or, in the case of formaldehyde, hydrogen. The central carbon is often described as being sp2-hybridized. The aldehyde group is somewhat polar. The C\dO bond length is about 120–122 picometers.

Physical properties and characterization
Aldehydes have properties that are diverse and that depend on the remainder of the molecule. Smaller aldehydes are more soluble in water, formaldehyde and acetaldehyde completely so. The volatile aldehydes have pungent odors.

Aldehydes can be identified by spectroscopic methods. Using IR spectroscopy, they display a strong νCO band near 1700 cm−1. In their 1H NMR spectra, the formyl hydrogen center absorbs near δH 9.5 to 10, which is a distinctive part of the spectrum. This signal shows the characteristic coupling to any protons on the α carbon with a small coupling constant typically less than 3.0 Hz. The 13C NMR spectra of aldehydes and ketones gives a suppressed (weak) but distinctive signal at δC 190 to 205.

Applications and occurrence
Important aldehydes and related compounds. The aldehyde group (or formyl group) is colored red. From the left: (1) formaldehyde and (2) its trimer 1,3,5-trioxane, (3) acetaldehyde and (4) its enol vinyl alcohol, (5) glucose (pyranose form as α--glucopyranose), (6) the flavorant cinnamaldehyde, (7) retinal, which forms with opsins photoreceptors, and (8) the vitamin pyridoxal.

Naturally occurring aldehydes
Traces of many aldehydes are found in essential oils and often contribute to their favorable odours, e.g. cinnamaldehyde, cilantro, and vanillin. Possibly because of the high reactivity of the formyl group, aldehydes are not common in several of the natural building blocks: amino acids, nucleic acids, lipids. Most sugars, however, are derivatives of aldehydes. These aldoses exist as hemiacetals, a sort of masked form of the parent aldehyde. For example, in aqueous solution only a tiny fraction of glucose exists as the aldehyde.

Synthesis
There are several methods for preparing aldehydes, but the dominant technology is hydroformylation. Illustrative is the generation of butyraldehyde by hydroformylation of propene:
 * H2 + CO + CH3CH\dCH2 → CH3CH2CH2CHO

Oxidative routes
Aldehydes are commonly generated by alcohol oxidation. Industry oxidizes methanol to formaldehyde on a large scale, and, in the Wacker process, ethylene to acetaldehyde in the presence of copper and palladium catalysts (acetaldehyde is also produced on a large scale by acetylene hydration). "Green" and cheap oxygen is the oxidant of choice. For sensitive substrates, Oppenauer transfer oxidation avoids overoxidation to a carboxylic acid. When a mixture of products may be acceptable, hydroformylation directly adds a carbonyl to a olefin.

Laboratories may instead apply a wide variety of specialized oxidizing agents; chromium(VI) reagents are popular. Oxidation can be achieved by heating the alcohol with an acidified solution of potassium dichromate. In this case, excess dichromate will further oxidize the aldehyde to a carboxylic acid, so either the aldehyde is distilled out as it forms (if volatile) or milder reagents such as PCC are used.
 * [O] + CH3(CH2)9OH → CH3(CH2)8CHO + H2O

A variety of reagent systems achieve aldehydes under chromium-free conditions. One such are the hypervalent organoiodine compounds (i.e., IBX acid, Dess–Martin periodinane), although these often also oxidize the α position. A Lux-Flood acid will activate other pre-oxidized substrates: various sulfoxides (e.g. the Swern oxidation), or amine oxides (e.g., the Ganem oxidation). Sterically-hindered nitroxyls (i.e., TEMPO) can catalyze aldehyde formation with a cheaper oxidant.

Alternatively, vicinal diols or their oxidized sequelae (acyloins or α-hydroxy acids) can be oxidized with cleavage to two aldehydes or an aldehyde and carbon dioxide.

Common reactions
Aldehydes participate in many reactions. From the industrial perspective, important reactions are:
 * condensations, e.g., to prepare plasticizers and polyols, and
 * reduction to produce alcohols, especially "oxo-alcohols". From the biological perspective, the key reactions involve addition of nucleophiles to the formyl carbon in the formation of imines (oxidative deamination) and hemiacetals (structures of aldose sugars).

Acid-base reactions
Because of resonance stabilization of the conjugate base, an α-hydrogen in an aldehyde is weakly acidic with a pKa near 17. Note, however, this is much more acidic than an alkane or ether hydrogen, which has pKa near 50 approximately, and is even more acidic than a ketone α-hydrogen which has pKa near 20. This acidification of the α-hydrogen in aldehyde is attributed to: The formyl proton itself does not readily undergo deprotonation.
 * the electron-withdrawing quality of the formyl center and
 * the fact that the conjugate base, an enolate anion, delocalizes its negative charge.

Enolization
Aldehydes (except those without an alpha carbon, or without protons on the alpha carbon, such as formaldehyde and benzaldehyde) can exist in either the keto or the enol tautomer. Keto–enol tautomerism is catalyzed by either acid or base. In neutral solution, the enol is the minority tautomer, reversing several times per second. But it becomes the dominant tautomer in strong acid or base solutions, and enolized aldehydes undergo nucleophilic attack at the α position.

Reduction
The formyl group can be readily reduced to a primary alcohol (\sCH2OH). Typically this conversion is accomplished by catalytic hydrogenation either directly or by transfer hydrogenation. Stoichiometric reductions are also popular, as can be effected with sodium borohydride.

Oxidation
The formyl group readily oxidizes to the corresponding carboxyl group (\sCOOH). The preferred oxidant in industry is oxygen or air. In the laboratory, popular oxidizing agents include potassium permanganate, nitric acid, chromium(VI) oxide, and chromic acid. The combination of manganese dioxide, cyanide, acetic acid and methanol will convert the aldehyde to a methyl ester.

Another oxidation reaction is the basis of the silver-mirror test. In this test, an aldehyde is treated with Tollens' reagent, which is prepared by adding a drop of sodium hydroxide solution into silver nitrate solution to give a precipitate of silver(I) oxide, and then adding just enough dilute ammonia solution to redissolve the precipitate in aqueous ammonia to produce [Ag(NH3)2]+ complex. This reagent converts aldehydes to carboxylic acids without attacking carbon–carbon double bonds. The name silver-mirror test arises because this reaction produces a precipitate of silver, whose presence can be used to test for the presence of an aldehyde.

A further oxidation reaction involves Fehling's reagent as a test. The Cu(2+) complex ions are reduced to a red-brick-coloured Cu2O precipitate.

If the aldehyde cannot form an enolate (e.g., benzaldehyde), addition of strong base induces the Cannizzaro reaction. This reaction results in disproportionation, producing a mixture of alcohol and carboxylic acid.

Nucleophilic addition reactions
Nucleophiles add readily to the carbonyl group. In the product, the carbonyl carbon becomes sp3-hybridized, being bonded to the nucleophile, and the oxygen center becomes protonated:
 * RCHO + Nu- → RCH(Nu)O-
 * RCH(Nu)O- + H+ → RCH(Nu)OH

In many cases, a water molecule is removed after the addition takes place; in this case, the reaction is classed as an addition–elimination or addition–condensation reaction. There are many variations of nucleophilic addition reactions.

Oxygen nucleophiles
In the acetalisation reaction, under acidic or basic conditions, an alcohol adds to the carbonyl group and a proton is transferred to form a hemiacetal. Under acidic conditions, the hemiacetal and the alcohol can further react to form an acetal and water. Simple hemiacetals are usually unstable, although cyclic ones such as glucose can be stable. Acetals are stable, but revert to the aldehyde in the presence of acid. Aldehydes can react with water to form hydrates, R\sCH(OH)2. These diols are stable when strong electron withdrawing groups are present, as in chloral hydrate. The mechanism of formation is identical to hemiacetal formation.

Nitrogen nucleophiles
In alkylimino-de-oxo-bisubstitution, a primary or secondary amine adds to the carbonyl group and a proton is transferred from the nitrogen to the oxygen atom to create a carbinolamine. In the case of a primary amine, a water molecule can be eliminated from the carbinolamine intermediate to yield an imine or its trimer, a hexahydrotriazine This reaction is catalyzed by acid. Hydroxylamine (NH2OH) can also add to the carbonyl group. After the elimination of water, this results in an oxime. An ammonia derivative of the form H2NNR2 such as hydrazine (H2NNH2) or 2,4-dinitrophenylhydrazine can also be the nucleophile and after the elimination of water, resulting in the formation of a hydrazone, which are usually orange crystalline solids. This reaction forms the basis of a test for aldehydes and ketones.

Carbon nucleophiles
The cyano group in HCN can add to the carbonyl group to form cyanohydrins, R\sCH(OH)CN. In this reaction the CN- ion is the nucleophile that attacks the partially positive carbon atom of the carbonyl group. The mechanism involves a pair of electrons from the carbonyl-group double bond transferring to the oxygen atom, leaving it single-bonded to carbon and giving the oxygen atom a negative charge. This intermediate ion rapidly reacts with H+, such as from the HCN molecule, to form the alcohol group of the cyanohydrin.

Organometallic compounds, such as organolithium reagents, Grignard reagents, or acetylides, undergo nucleophilic addition reactions, yielding a substituted alcohol group. Related reactions include organostannane additions, Barbier reactions, and the Nozaki–Hiyama–Kishi reaction.

In the aldol reaction, the metal enolates of ketones, esters, amides, and carboxylic acids add to aldehydes to form β-hydroxycarbonyl compounds (aldols). Acid or base-catalyzed dehydration then leads to α,β-unsaturated carbonyl compounds. The combination of these two steps is known as the aldol condensation.

The Prins reaction occurs when a nucleophilic alkene or alkyne reacts with an aldehyde as electrophile. The product of the Prins reaction varies with reaction conditions and substrates employed.

Bisulfite reaction
Aldehydes characteristically form "addition compounds" with bisulfites:
 * RCHO + HSO3- → RCH(OH)SO3-

This reaction is used as a test for aldehydes and is useful for separation or purification of aldehydes.

Dialdehydes
A dialdehyde is an organic chemical compound with two aldehyde groups. The nomenclature of dialdehydes have the ending -dial or sometimes -dialdehyde. Short aliphatic dialdehydes are sometimes named after the diacid from which they can be derived. An example is butanedial, which is also called succinaldehyde (from succinic acid).

Biochemistry
Some aldehydes are substrates for aldehyde dehydrogenase enzymes which metabolize aldehydes in the body. There are toxicities associated with some aldehydes that are related to neurodegenerative disease, heart disease, and some types of cancer.

Examples of aldehydes

 * Formaldehyde (methanal)
 * Acetaldehyde (ethanal)
 * Propionaldehyde (propanal)
 * Butyraldehyde (butanal)
 * Isovaleraldehyde
 * Benzaldehyde (phenylmethanal)
 * Cinnamaldehyde
 * Vanillin
 * Tolualdehyde
 * Furfural
 * Retinaldehyde
 * Glycolaldehyde

Examples of dialdehydes

 * Glyoxal
 * Malondialdehyde
 * Succindialdehyde
 * Glutaraldehyde
 * Phthalaldehyde

Uses
Of all aldehydes, formaldehyde is produced on the largest scale, about $6,000,000 tons per year$. It is mainly used in the production of resins when combined with urea, melamine, and phenol (e.g., Bakelite). It is a precursor to methylene diphenyl diisocyanate ("MDI"), a precursor to polyurethanes. The second main aldehyde is butyraldehyde, of which about $2,500,000 tons per year$ are prepared by hydroformylation. It is the principal precursor to 2-ethylhexanol, which is used as a plasticizer. Acetaldehyde once was a dominating product, but production levels have declined to less than $1,000,000 tons per year$ because it mainly served as a precursor to acetic acid, which is now prepared by carbonylation of methanol. Many other aldehydes find commercial applications, often as precursors to alcohols, the so-called oxo alcohols, which are used in detergents. Some aldehydes are produced only on a small scale (less than 1000 tons per year) and are used as ingredients in flavours and perfumes such as Chanel No. 5. These include cinnamaldehyde and its derivatives, citral, and lilial.

IUPAC names for aldehydes
The common names for aldehydes do not strictly follow official guidelines, such as those recommended by IUPAC, but these rules are useful. IUPAC prescribes the following nomenclature for aldehydes:
 * 1) Acyclic aliphatic aldehydes are named as derivatives of the longest carbon chain containing the aldehyde group. Thus, HCHO is named as a derivative of methane, and CH3CH2CH2CHO is named as a derivative of butane. The name is formed by changing the suffix -e of the parent alkane to -al, so that HCHO is named methanal, and CH3CH2CH2CHO is named butanal.
 * 2) In other cases, such as when a \sCHO group is attached to a ring, the suffix -carbaldehyde may be used. Thus, C6H11CHO is known as cyclohexanecarbaldehyde. If the presence of another functional group demands the use of a suffix, the aldehyde group is named with the prefix formyl-. This prefix is preferred to methanoyl-.
 * 3) If the compound is a natural product or a carboxylic acid, the prefix oxo- may be used to indicate which carbon atom is part of the aldehyde group; for example, CHOCH2COOH is named 2-oxoethanoic acid.
 * 4) If replacing the aldehyde group with a carboxyl group (\sCOOH) would yield a carboxylic acid with a trivial name, the aldehyde may be named by replacing the suffix -ic acid or -oic acid in this trivial name by -aldehyde.

Etymology
The word aldehyde was coined by Justus von Liebig as a contraction of the Latin alcohol dehydrogenatus (dehydrogenated alcohol). In the past, aldehydes were sometimes named after the corresponding alcohols, for example, vinous aldehyde for acetaldehyde. (Vinous is from Latin vinum "wine", the traditional source of ethanol, cognate with vinyl.)

The term formyl group is derived from the Latin word formica "ant". This word can be recognized in the simplest aldehyde, formaldehyde, and in the simplest carboxylic acid, formic acid.

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title: Aldehyde


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Josiah Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis.

In 1863, Yale University awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his career at Yale, where he was a professor of mathematical physics from 1871 until his death in 1903. Working in relative isolation, he became the earliest theoretical scientist in the United States to earn an international reputation and was praised by Albert Einstein as "the greatest mind in American history." In 1901, Gibbs received what was then considered the highest honor awarded by the international scientific community, the Copley Medal of the Royal Society of London, "for his contributions to mathematical physics."

Commentators and biographers have remarked on the contrast between Gibbs's quiet, solitary life in turn of the century New England and the great international impact of his ideas. Though his work was almost entirely theoretical, the practical value of Gibbs's contributions became evident with the development of industrial chemistry during the first half of the 20th century. According to Robert A. Millikan, in pure science, Gibbs "did for statistical mechanics and thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure."

Family background

Gibbs was born in New Haven, Connecticut. He belonged to an old Yankee family that had produced distinguished American clergymen and academics since the 17th century. He was the fourth of five children and the only son of Josiah Willard Gibbs Sr., and his wife Mary Anna, née Van Cleve. On his father's side, he was descended from Samuel Willard, who served as acting President of Harvard College from 1701 to 1707. On his mother's side, one of his ancestors was the Rev. Jonathan Dickinson, the first president of the College of New Jersey (later Princeton University). Gibbs's given name, which he shared with his father and several other members of his extended family, derived from his ancestor Josiah Willard, who had been Secretary of the Province of Massachusetts Bay in the 18th century. His paternal grandmother, Mercy (Prescott) Gibbs, was the sister of Rebecca Minot Prescott Sherman, the wife of American founding father Roger Sherman; and he was the second cousin of Roger Sherman Baldwin, see the Amistad case below.

The elder Gibbs was generally known to his family and colleagues as "Josiah", while the son was called "Willard". Josiah Gibbs was a linguist and theologian who served as professor of sacred literature at Yale Divinity School from 1824 until his death in 1861. He is chiefly remembered today as the abolitionist who found an interpreter for the African passengers of the ship Amistad, allowing them to testify during the trial that followed their rebellion against being sold as slaves.

Education
Willard Gibbs was educated at the Hopkins School and entered Yale College in 1854 at the age of 15. At Yale, Gibbs received prizes for excellence in mathematics and Latin, and he graduated in 1858, near the top of his class. He remained at Yale as a graduate student at the Sheffield Scientific School. At age 19, soon after his graduation from college, Gibbs was inducted into the Connecticut Academy of Arts and Sciences, a scholarly institution composed primarily of members of the Yale faculty.

Relatively few documents from the period survive and it is difficult to reconstruct the details of Gibbs's early career with precision. In the opinion of biographers, Gibbs's principal mentor and champion, both at Yale and in the Connecticut Academy, was probably the astronomer and mathematician Hubert Anson Newton, a leading authority on meteors, who remained Gibbs's lifelong friend and confidant. After the death of his father in 1861, Gibbs inherited enough money to make him financially independent.

Recurrent pulmonary trouble ailed the young Gibbs and his physicians were concerned that he might be susceptible to tuberculosis, which had killed his mother. He also suffered from astigmatism, whose treatment was then still largely unfamiliar to oculists, so that Gibbs had to diagnose himself and grind his own lenses. Though in later years he used glasses only for reading or other close work, Gibbs's delicate health and imperfect eyesight probably explain why he did not volunteer to fight in the Civil War of 1861–65. He was not conscripted and he remained at Yale for the duration of the war.

In 1863, Gibbs received the first Doctorate of Philosophy (PhD) in engineering granted in the US, for a thesis entitled "On the Form of the Teeth of Wheels in Spur Gearing", in which he used geometrical techniques to investigate the optimum design for gears. In 1861, Yale had become the first US university to offer a PhD degree and Gibbs's was only the fifth PhD granted in the US in any subject.

Career, 1863–73
After graduation, Gibbs was appointed as tutor at the college for a term of three years. During the first two years, he taught Latin and during the third year, he taught "natural philosophy" (i.e., physics). In 1866, he patented a design for a railway brake and read a paper before the Connecticut Academy, entitled "The Proper Magnitude of the Units of Length", in which he proposed a scheme for rationalizing the system of units of measurement used in mechanics.

After his term as tutor ended, Gibbs traveled to Europe with his sisters. They spent the winter of 1866–67 in Paris, where Gibbs attended lectures at the Sorbonne and the Collège de France, given by such distinguished mathematical scientists as Joseph Liouville and Michel Chasles. Having undertaken a punishing regimen of study, Gibbs caught a serious cold and a doctor, fearing tuberculosis, advised him to rest on the Riviera, where he and his sisters spent several months and where he made a full recovery.

Moving to Berlin, Gibbs attended the lectures taught by mathematicians Karl Weierstrass and Leopold Kronecker, as well as by chemist Heinrich Gustav Magnus. In August 1867, Gibbs's sister Julia was married in Berlin to Addison Van Name, who had been Gibbs's classmate at Yale. The newly married couple returned to New Haven, leaving Gibbs and his sister Anna in Germany. In Heidelberg, Gibbs was exposed to the work of physicists Gustav Kirchhoff and Hermann von Helmholtz, and chemist Robert Bunsen. At the time, German academics were the leading authorities in the natural sciences, especially chemistry and thermodynamics.

Gibbs returned to Yale in June 1869 and briefly taught French to engineering students. It was probably also around this time that he worked on a new design for a steam-engine governor, his last significant investigation in mechanical engineering. In 1871, he was appointed Professor of Mathematical Physics at Yale, the first such professorship in the United States. Gibbs, who had independent means and had yet to publish anything, was assigned to teach graduate students exclusively and was hired without salary.

Career, 1873–80

Gibbs published his first work in 1873. His papers on the geometric representation of thermodynamic quantities appeared in the Transactions of the Connecticut Academy. These papers introduced the use of different type phase diagrams, which were his favorite aids to the imagination process when doing research, rather than the mechanical models, such as the ones that Maxwell used in constructing his electromagnetic theory, which might not completely represent their corresponding phenomena. Although the journal had few readers capable of understanding Gibbs's work, he shared reprints with correspondents in Europe and received an enthusiastic response from James Clerk Maxwell at Cambridge. Maxwell even made, with his own hands, a clay model illustrating Gibbs's construct. He then produced two plaster casts of his model and mailed one to Gibbs. That cast is on display at the Yale physics department.

Maxwell included a chapter on Gibbs's work in the next edition of his Theory of Heat, published in 1875. He explained the usefulness of Gibbs's graphical methods in a lecture to the Chemical Society of London and even referred to it in the article on "Diagrams" that he wrote for the Encyclopædia Britannica. Prospects of collaboration between him and Gibbs were cut short by Maxwell's early death in 1879, aged 48. The joke later circulated in New Haven that "only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead."

Gibbs then extended his thermodynamic analysis to multi-phase chemical systems (i.e., to systems composed of more than one form of matter) and considered a variety of concrete applications. He described that research in a monograph titled "On the Equilibrium of Heterogeneous Substances", published by the Connecticut Academy in two parts that appeared respectively in 1875 and 1878. That work, which covers about three hundred pages and contains exactly seven hundred numbered mathematical equations, begins with a quotation from Rudolf Clausius that expresses what would later be called the first and second laws of thermodynamics: "The energy of the world is constant. The entropy of the world tends towards a maximum."

Gibbs's monograph rigorously and ingeniously applied his thermodynamic techniques to the interpretation of physico-chemical phenomena, explaining and relating what had previously been a mass of isolated facts and observations. The work has been described as "the Principia of thermodynamics" and as a work of "practically unlimited scope". It solidly laid the foundation for physical Chemistry. Wilhelm Ostwald, who translated Gibbs's monograph into German, referred to Gibbs as the "founder of chemical energetics". According to modern commentators,

"It is universally recognised that its publication was an event of the first importance in the history of chemistry ... Nevertheless it was a number of years before its value was generally known, this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficult reading for anyone, and especially so for students of experimental chemistry whom it most concerns."

Gibbs continued to work without pay until 1880, when the new Johns Hopkins University in Baltimore, Maryland offered him a position paying $3,000 per year. In response, Yale offered him an annual salary of $2,000, which he was content to accept.

In 1879, Gibbs derived the Gibbs-Appell equation of motion, rediscovered in 1900 by Paul Émile Appell.

Career, 1880–1903

From 1880 to 1884, Gibbs worked on developing the exterior algebra of Hermann Grassmann into a vector calculus well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the dot and cross products of two vectors and introduced the concept of dyadics. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer Oliver Heaviside. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with Peter Guthrie Tait and others in the pages of Nature.

Gibbs's lecture notes on vector calculus were privately printed in 1881 and 1884 for the use of his students, and were later adapted by Edwin Bidwell Wilson into a textbook, Vector Analysis, published in 1901. That book helped to popularize the "del" notation that is widely used today in electrodynamics and fluid mechanics. In other mathematical work, he re-discovered the "Gibbs phenomenon" in the theory of Fourier series (which, unbeknownst to him and to later scholars, had been described fifty years before by an obscure English mathematician, Henry Wilbraham).

From 1882 to 1889, Gibbs wrote five papers on physical optics, in which he investigated birefringence and other optical phenomena and defended Maxwell's electromagnetic theory of light against the mechanical theories of Lord Kelvin and others. In his work on optics, just as much as in his work on thermodynamics, Gibbs deliberately avoided speculating about the microscopic structure of matter and purposefully confined his research problems to those that can be solved from broad general principles and experimentally confirmed facts. The methods that he used were highly original and the obtained results showed decisively the correctness of Maxwell's electromagnetic theory.

Gibbs coined the term statistical mechanics and introduced key concepts in the corresponding mathematical description of physical systems, including the notions of chemical potential (1876), and statistical ensemble (1902). Gibbs's derivation of the laws of thermodynamics from the statistical properties of systems consisting of many particles was presented in his highly influential textbook Elementary Principles in Statistical Mechanics, published in 1902, a year before his death.

Gibbs's retiring personality and intense focus on his work limited his accessibility to students. His principal protégé was Edwin Bidwell Wilson, who nonetheless explained that "except in the classroom I saw very little of Gibbs. He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home—a little exercise between work and dinner—and one might occasionally come across him at that time." Gibbs did supervise the doctoral thesis on mathematical economics written by Irving Fisher in 1891. After Gibbs's death, Fisher financed the publication of his Collected Works. Another distinguished student was Lee De Forest, later a pioneer of radio technology.

Gibbs died in New Haven on April 28, 1903, at the age of 64, the victim of an acute intestinal obstruction. A funeral was conducted two days later at his home on 121 High Street, and his body was buried in the nearby Grove Street Cemetery. In May, Yale organized a memorial meeting at the Sloane Laboratory. The eminent British physicist J. J. Thomson was in attendance and delivered a brief address.

Personal life and character

Gibbs never married, living all his life in his childhood home with his sister Julia and her husband Addison Van Name, who was the Yale librarian. Except for his customary summer vacations in the Adirondacks (at Keene Valley, New York) and later at the White Mountains (in Intervale, New Hampshire), his sojourn in Europe in 1866–69 was almost the only time that Gibbs spent outside New Haven. He joined Yale's College Church (a Congregational church) at the end of his freshman year and remained a regular attendant for the rest of his life. Gibbs generally voted for the Republican candidate in presidential elections but, like other "Mugwumps", his concern over the growing corruption associated with machine politics led him to support Grover Cleveland, a conservative Democrat, in the election of 1884. Little else is known of his religious or political views, which he mostly kept to himself.

Gibbs did not produce a substantial personal correspondence and many of his letters were later lost or destroyed. Beyond the technical writings concerning his research, he published only two other pieces: a brief obituary for Rudolf Clausius, one of the founders of the mathematical theory of thermodynamics, and a longer biographical memoir of his mentor at Yale, H. A. Newton. In Edward Bidwell Wilson's view,

"Gibbs was not an advertiser for personal renown nor a propagandist for science; he was a scholar, scion of an old scholarly family, living before the days when research had become résearch ... Gibbs was not a freak, he had no striking ways, he was a kindly dignified gentleman."

According to Lynde Wheeler, who had been Gibbs's student at Yale, in his later years Gibbs

"was always neatly dressed, usually wore a felt hat on the street, and never exhibited any of the physical mannerisms or eccentricities sometimes thought to be inseparable from genius ... His manner was cordial without being effusive and conveyed clearly the innate simplicity and sincerity of his nature."

He was a careful investor and financial manager, and at his death in 1903 his estate was valued at $100,000 (roughly $ today). For many years, he served as trustee, secretary, and treasurer of his alma mater, the Hopkins School. US President Chester A. Arthur appointed him as one of the commissioners to the National Conference of Electricians, which convened in Philadelphia in September 1884, and Gibbs presided over one of its sessions. A keen and skilled horseman, Gibbs was seen habitually in New Haven driving his sister's carriage. In an obituary published in the American Journal of Science, Gibbs's former student Henry A. Bumstead referred to Gibbs's personal character:

"Unassuming in manner, genial and kindly in his intercourse with his fellow-men, never showing impatience or irritation, devoid of personal ambition of the baser sort or of the slightest desire to exalt himself, he went far toward realizing the ideal of the unselfish, Christian gentleman. In the minds of those who knew him, the greatness of his intellectual achievements will never overshadow the beauty and dignity of his life."

Chemical and electrochemical thermodynamics

Gibbs's papers from the 1870s introduced the idea of expressing the internal energy U of a system in terms of the entropy S, in addition to the usual state-variables of volume V, pressure p, and temperature T. He also introduced the concept of the chemical potential $$\mu$$ of a given chemical species, defined to be the rate of the increase in U associated with the increase in the number N of molecules of that species (at constant entropy and volume). Thus, it was Gibbs who first combined the first and second laws of thermodynamics by expressing the infinitesimal change in the internal energy, dU, of a closed system in the form:

 * $$\mathrm{d}U = T\mathrm{d}S - p \,\mathrm{d}V + \sum_i \mu_i \,\mathrm{d} N_i\,$$

where T is the absolute temperature, p is the pressure, dS is an infinitesimal change in entropy and dV is an infinitesimal change of volume. The last term is the sum, over all the chemical species in a chemical reaction, of the chemical potential, μi, of the ith species, multiplied by the infinitesimal change in the number of moles, dNi of that species. By taking the Legendre transform of this expression, he defined the concepts of enthalpy, H and Gibbs free energy, G.
 * $$G_{(p,T)} = H - TS $$

This compares to the expression for Helmholtz free energy, A.
 * $$A_{(v,T)} = U-TS\,$$

When the Gibbs free energy for a chemical reaction is negative the reaction will proceed spontaneously. When a chemical system is at equilibrium, the change in Gibbs free energy is zero. An equilibrium constant is simply related to the free energy change when the reactants are in their standard states.
 * $$\Delta G^\ominus=-RT \ln K^\ominus$$

Chemical potential is usually defined as partial molar Gibbs free energy.
 * $$\mu_i=\left(\frac{\partial G}{\partial N_i}\right)_{T,P,N_{j\neq i}}$$

Gibbs also obtained what later came to be known as the "Gibbs–Duhem equation".

In an electrochemical reaction characterized by an electromotive force ℰ and an amount of transferred charge Q, Gibbs's starting equation becomes
 * $$\mathrm{d}U = T\mathrm{d}S - p \,\mathrm{d}V + \mathcal{E}\mathrm{d}Q$$.

The publication of the paper "On the Equilibrium of Heterogeneous Substances" (1874–78) is now regarded as a landmark in the development of chemistry. In it, Gibbs developed a rigorous mathematical theory for various transport phenomena, including adsorption, electrochemistry, and the Marangoni effect in fluid mixtures. He also formulated the phase rule

 * $$ F\;=\;C\;-\;P\;+\;2 $$

for the number F of variables that may be independently controlled in an equilibrium mixture of C components existing in P phases. Phase rule is very useful in diverse areas, such as metallurgy, mineralogy, and petrology. It can also be applied to various research problems in physical chemistry.

Statistical mechanics
Together with James Clerk Maxwell and Ludwig Boltzmann, Gibbs founded "statistical mechanics", a term that he coined to identify the branch of theoretical physics that accounts for the observed thermodynamic properties of systems in terms of the statistics of ensembles of all possible physical states of a system composed of many particles. He introduced the concept of "phase of a mechanical system". He used the concept to define the microcanonical, canonical, and grand canonical ensembles; all related to the Gibbs measure, thus obtaining a more general formulation of the statistical properties of many-particle systems than Maxwell and Boltzmann had achieved before him.

Gibbs generalized Boltzmann's statistical interpretation of entropy $$S$$ by defining the entropy of an arbitrary ensemble as
 * $$S = -k_\text{B}\,\sum_i p_i \ln \,p_i$$,

where $$k_\text{B}$$ is the Boltzmann constant, while the sum is over all possible microstates $$i$$, with $$p_i$$ the corresponding probability of the microstate (see Gibbs entropy formula). This same formula would later play a central role in Claude Shannon's information theory and is therefore often seen as the basis of the modern information-theoretical interpretation of thermodynamics.

According to Henri Poincaré, writing in 1904, even though Maxwell and Boltzmann had previously explained the irreversibility of macroscopic physical processes in probabilistic terms, "the one who has seen it most clearly, in a book too little read because it is a little difficult to read, is Gibbs, in his Elementary Principles of Statistical Mechanics." Gibbs's analysis of irreversibility, and his formulation of Boltzmann's H-theorem and of the ergodic hypothesis, were major influences on the mathematical physics of the 20th century.

Gibbs was well aware that the application of the equipartition theorem to large systems of classical particles failed to explain the measurements of the specific heats of both solids and gases, and he argued that this was evidence of the danger of basing thermodynamics on "hypotheses about the constitution of matter". Gibbs's own framework for statistical mechanics, based on ensembles of macroscopically indistinguishable microstates, could be carried over almost intact after the discovery that the microscopic laws of nature obey quantum rules, rather than the classical laws known to Gibbs and to his contemporaries. His resolution of the so-called "Gibbs paradox", about the entropy of the mixing of gases, is now often cited as a prefiguration of the indistinguishability of particles required by quantum physics.

Vector analysis

British scientists, including Maxwell, had relied on Hamilton's quaternions in order to express the dynamics of physical quantities, like the electric and magnetic fields, having both a magnitude and a direction in three-dimensional space. Following W. K. Clifford in his Elements of Dynamic (1888), Gibbs noted that the product of quaternions could be separated into two parts: a one-dimensional (scalar) quantity and a three-dimensional vector, so that the use of quaternions involved mathematical complications and redundancies that could be avoided in the interest of simplicity and to facilitate teaching. In his Yale classroom notes he defined distinct dot and cross products for pairs of vectors and introduced the now common notation for them. Through the 1901 textbook Vector Analysis prepared by E. B. Wilson from Gibbs notes, he was largely responsible for the development of the vector calculus techniques still used today in electrodynamics and fluid mechanics.

While he was working on vector analysis in the late 1870s, Gibbs discovered that his approach was similar to the one that Grassmann had taken in his "multiple algebra". Gibbs then sought to publicize Grassmann's work, stressing that it was both more general and historically prior to Hamilton's quaternionic algebra. To establish priority of Grassmann's ideas, Gibbs convinced Grassmann's heirs to seek the publication in Germany of the essay "Theorie der Ebbe und Flut" on tides that Grassmann had submitted in 1840 to the faculty at the University of Berlin, in which he had first introduced the notion of what would later be called a vector space (linear space).

As Gibbs had advocated in the 1880s and 1890s, quaternions were eventually all but abandoned by physicists in favor of the vectorial approach developed by him and, independently, by Oliver Heaviside. Gibbs applied his vector methods to the determination of planetary and comet orbits. He also developed the concept of mutually reciprocal triads of vectors that later proved to be of importance in crystallography.

Physical optics

Though Gibbs's research on physical optics is less well known today than his other work, it made a significant contribution to classical electromagnetism by applying Maxwell's equations to the theory of optical processes such as birefringence, dispersion, and optical activity. In that work, Gibbs showed that those processes could be accounted for by Maxwell's equations without any special assumptions about the microscopic structure of matter or about the nature of the medium in which electromagnetic waves were supposed to propagate (the so-called luminiferous ether). Gibbs also stressed that the absence of a longitudinal electromagnetic wave, which is needed to account for the observed properties of light, is automatically guaranteed by Maxwell's equations (by virtue of what is now called their "gauge invariance"), whereas in mechanical theories of light, such as Lord Kelvin's, it must be imposed as an ad hoc condition on the properties of the aether.

In his last paper on physical optics, Gibbs concluded that

"it may be said for the electrical theory [of light] that it is not obliged to invent hypotheses, but only to apply the laws furnished by the science of electricity, and that it is difficult to account for the coincidences between the electrical and optical properties of media unless we regard the motions of light as electrical."

Shortly afterwards, the electromagnetic nature of light was demonstrated by the experiments of Heinrich Hertz in Germany.

Scientific recognition
Gibbs worked at a time when there was little tradition of rigorous theoretical science in the United States. His research was not easily understandable to his students or his colleagues, and he made no effort to popularize his ideas or to simplify their exposition to make them more accessible. His seminal work on thermodynamics was published mostly in the Transactions of the Connecticut Academy, a journal edited by his librarian brother-in-law, which was little read in the US and even less so in Europe. When Gibbs submitted his long paper on the equilibrium of heterogeneous substances to the academy, both Elias Loomis and H. A. Newton protested that they did not understand Gibbs's work at all, but they helped to raise the money needed to pay for the typesetting of the many mathematical symbols in the paper. Several Yale faculty members, as well as business and professional men in New Haven, contributed funds for that purpose.

Even though it had been immediately embraced by Maxwell, Gibbs's graphical formulation of the laws of thermodynamics came into widespread use only in the mid 20th century, with the work of László Tisza and Herbert Callen. According to James Gerald Crowther,

"in his later years [Gibbs] was a tall, dignified gentleman, with a healthy stride and ruddy complexion, performing his share of household chores, approachable and kind (if unintelligible) to students. Gibbs was highly esteemed by his friends, but American science was too preoccupied with practical questions to make much use of his profound theoretical work during his lifetime. He lived out his quiet life at Yale, deeply admired by a few able students but making no immediate impress on American science commensurate with his genius."

On the other hand, Gibbs did receive the major honors then possible for an academic scientist in the US. He was elected to the National Academy of Sciences in 1879 and received the 1880 Rumford Prize from the American Academy of Arts and Sciences for his work on chemical thermodynamics. In 1895, he was elected to the American Philosophical Society in 1895. He was also awarded honorary doctorates by Princeton University and Williams College.

In Europe, Gibbs was inducted as honorary member of the London Mathematical Society in 1892 and elected Foreign Member of the Royal Society in 1897. He was elected as corresponding member of the Prussian and French Academies of Science and received honorary doctorates from the universities of Dublin, Erlangen, and Christiania (now Oslo). The Royal Society further honored Gibbs in 1901 with the Copley Medal, then regarded as the highest international award in the natural sciences, noting that he had been "the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical and thermal energy and capacity for external work." Gibbs, who remained in New Haven, was represented at the award ceremony by Commander Richardson Clover, the US naval attaché in London.

In his autobiography, mathematician Gian-Carlo Rota tells of casually browsing the mathematical stacks of Sterling Library and stumbling on a handwritten mailing list, attached to some of Gibbs's course notes, which listed over two hundred notable scientists of his day, including Poincaré, Boltzmann, David Hilbert, and Ernst Mach. From this, Rota concluded that Gibbs's work was better known among the scientific elite of his day than the published material suggests. Lynde Wheeler reproduces that mailing list in an appendix to his biography of Gibbs. That Gibbs succeeded in interesting his European correspondents in his work is demonstrated by the fact that his monograph "On the Equilibrium of Heterogeneous Substances" was translated into German (then the leading language for chemistry) by Wilhelm Ostwald in 1892 and into French by Henri Louis Le Châtelier in 1899.

Influence
Gibbs's most immediate and obvious influence was on physical chemistry and statistical mechanics, two disciplines which he greatly helped to found. During Gibbs's lifetime, his phase rule was experimentally validated by Dutch chemist H. W. Bakhuis Roozeboom, who showed how to apply it in a variety of situations, thereby assuring it of widespread use. In industrial chemistry, Gibbs's thermodynamics found many applications during the early 20th century, from electrochemistry to the development of the Haber process for the synthesis of ammonia.

When Dutch physicist J. D. van der Waals received the 1910 Nobel Prize "for his work on the equation of state for gases and liquids" he acknowledged the great influence of Gibbs's work on that subject. Max Planck received the 1918 Nobel Prize for his work on quantum mechanics, particularly his 1900 paper on Planck's law for quantized black-body radiation. That work was based largely on the thermodynamics of Kirchhoff, Boltzmann, and Gibbs. Planck declared that Gibbs's name "not only in America but in the whole world will ever be reckoned among the most renowned theoretical physicists of all times."

The first half of the 20th century saw the publication of two influential textbooks that soon came to be regarded as founding documents of chemical thermodynamics, both of which used and extended Gibbs's work in that field: these were Thermodynamics and the Free Energy of Chemical Processes (1923), by Gilbert N. Lewis and Merle Randall, and Modern Thermodynamics by the Methods of Willard Gibbs (1933), by Edward A. Guggenheim.

Gibbs's work on statistical ensembles, as presented in his 1902 textbook, has had a great impact in both theoretical physics and in pure mathematics. According to mathematical physicist Arthur Wightman,

"It is one of the striking features of the work of Gibbs, noticed by every student of thermodynamics and statistical mechanics, that his formulations of physical concepts were so felicitously chosen that they have survived 100 years of turbulent development in theoretical physics and mathematics."

Initially unaware of Gibbs's contributions in that field, Albert Einstein wrote three papers on statistical mechanics, published between 1902 and 1904. After reading Gibbs's textbook (which was translated into German by Ernst Zermelo in 1905), Einstein declared that Gibbs's treatment was superior to his own and explained that he would not have written those papers if he had known Gibbs's work. Gibbs's early papers on the use of graphical methods in thermodynamics reflect a powerfully original understanding of what mathematicians would later call "convex analysis", including ideas that, according to Barry Simon, "lay dormant for about seventy-five years". Important mathematical concepts based on Gibbs's work on thermodynamics and statistical mechanics include the Gibbs lemma in game theory, the Gibbs inequality in information theory, as well as Gibbs sampling in computational statistics.

The development of vector calculus was Gibbs's other great contribution to mathematics. The publication in 1901 of E. B. Wilson's textbook Vector Analysis, based on Gibbs's lectures at Yale, did much to propagate the use of vectorial methods and notation in both mathematics and theoretical physics, definitively displacing the quaternions that had until then been dominant in the scientific literature.

At Yale, Gibbs was also mentor to Lee De Forest, who went on to invent the triode amplifier and has been called the "father of radio". De Forest credited Gibbs's influence for the realization "that the leaders in electrical development would be those who pursued the higher theory of waves and oscillations and the transmission by these means of intelligence and power." Another student of Gibbs who played a significant role in the development of radio technology was Lynde Wheeler.

Gibbs also had an indirect influence on mathematical economics. He supervised the thesis of Irving Fisher, who received the first PhD in economics from Yale in 1891. In that work, published in 1892 as Mathematical Investigations in the Theory of Value and Prices, Fisher drew a direct analogy between Gibbsian equilibrium in physical and chemical systems, and the general equilibrium of markets, and he used Gibbs's vectorial notation. Gibbs's protégé Edwin Bidwell Wilson became, in turn, a mentor to leading American economist and Nobel Laureate Paul Samuelson. In 1947, Samuelson published Foundations of Economic Analysis, based on his doctoral dissertation, in which he used as epigraph a remark attributed to Gibbs: "Mathematics is a language." Samuelson later explained that in his understanding of prices his "debts were not primarily to Pareto or Slutsky, but to the great thermodynamicist, Willard Gibbs of Yale."

Mathematician Norbert Wiener cited Gibbs's use of probability in the formulation of statistical mechanics as "the first great revolution of twentieth century physics" and as a major influence on his conception of cybernetics. Wiener explained in the preface to his book The Human Use of Human Beings that it was "devoted to the impact of the Gibbsian point of view on modern life, both through the substantive changes it has made to working science, and through the changes it has made indirectly in our attitude to life in general."

Commemoration

When the German physical chemist Walther Nernst visited Yale in 1906 to give the Silliman lecture, he was surprised to find no tangible memorial for Gibbs. Nernst donated his $500 lecture fee to the university to help pay for a suitable monument. This was finally unveiled in 1912, in the form of a bronze bas-relief by sculptor Lee Lawrie, installed in the Sloane Physics Laboratory. In 1910, the American Chemical Society established the Willard Gibbs Award for eminent work in pure or applied chemistry. In 1923, the American Mathematical Society endowed the Josiah Willard Gibbs Lectureship, "to show the public some idea of the aspects of mathematics and its applications".

In 1945, Yale University created the J. Willard Gibbs Professorship in Theoretical Chemistry, held until 1973 by Lars Onsager. Onsager, who much like Gibbs, focused on applying new mathematical ideas to problems in physical chemistry, won the 1968 Nobel Prize in chemistry. In addition to establishing the Josiah Willard Gibbs Laboratories and the J. Willard Gibbs Assistant Professorship in Mathematics, Yale has also hosted two symposia dedicated to Gibbs's life and work, one in 1989 and another on the centenary of his death, in 2003. Rutgers University endowed a J. Willard Gibbs Professorship of Thermomechanics, held as of 2014 by Bernard Coleman.

Gibbs was elected in 1950 to the Hall of Fame for Great Americans. The oceanographic research ship USNS Josiah Willard Gibbs (T-AGOR-1) was in service with the United States Navy from 1958 to 1971. Gibbs crater, near the eastern limb of the Moon, was named in the scientist's honor in 1964.

Edward Guggenheim introduced the symbol G for the Gibbs free energy in 1933, and this was used also by Dirk ter Haar in 1966. This notation is now universal and is recommended by the IUPAC. In 1960, William Giauque and others suggested the name "gibbs" (abbreviated gbs.) for the unit of entropy calorie per kelvin, but this usage did not become common, and the corresponding SI unit joule per kelvin carries no special name.

In 1954, a year before his death, Albert Einstein was asked by an interviewer who were the greatest thinkers that he had known. Einstein replied: "Lorentz", adding "I never met Willard Gibbs; perhaps, had I done so, I might have placed him beside Lorentz." Author Bill Bryson in his bestselling popular science book A Short History of Nearly Everything ranks Gibbs as "perhaps the most brilliant person that most people have never heard of".

In 1958, USS San Carlos was renamed USNS Josiah Willard Gibbs and re-designated as an oceanographic research ship.

In literature
In 1909, the American historian and novelist Henry Adams finished an essay entitled "The Rule of Phase Applied to History", in which he sought to apply Gibbs's phase rule and other thermodynamic concepts to a general theory of human history. William James, Henry Bumstead, and others criticized both Adams's tenuous grasp of the scientific concepts that he invoked, as well as the arbitrariness of his application of those concepts as metaphors for the evolution of human thought and society. The essay remained unpublished until it appeared posthumously in 1919, in The Degradation of the Democratic Dogma, edited by Henry Adams's younger brother Brooks.

In the 1930s, feminist poet Muriel Rukeyser became fascinated by Willard Gibbs and wrote a long poem about his life and work ("Gibbs", included in the collection A Turning Wind, published in 1939), as well as a book-length biography (Willard Gibbs, 1942). According to Rukeyser:

"Willard Gibbs is the type of the imagination at work in the world. His story is that of an opening up which has had its effect on our lives and our thinking; and, it seems to me, it is the emblem of the naked imagination—which is called abstract and impractical, but whose discoveries can be used by anyone who is interested, in whatever 'field'—an imagination which for me, more than that of any other figure in American thought, any poet, or political, or religious figure, stands for imagination at its essential points."

In 1946, Fortune magazine illustrated a cover story on "Fundamental Science" with a representation of the thermodynamic surface that Maxwell had built based on Gibbs's proposal. Rukeyser called this surface a "statue of water" and the magazine saw in it "the abstract creation of a great American scientist that lends itself to the symbolism of contemporary art forms." The artwork by Arthur Lidov also included Gibbs's mathematical expression of the phase rule for heterogeneous mixtures, as well as a radar screen, an oscilloscope waveform, Newton's apple, and a small rendition of a three-dimensional phase diagram.

Gibbs's nephew, Ralph Gibbs Van Name, a professor of physical chemistry at Yale, was unhappy with Rukeyser's biography, in part because of her lack of scientific training. Van Name had withheld the family papers from her and, after her book was published in 1942 to positive literary but mixed scientific reviews, he tried to encourage Gibbs's former students to produce a more technically oriented biography. Rukeyser's approach to Gibbs was also sharply criticized by Gibbs's former student and protégé Edwin Wilson. With Van Name's and Wilson's encouragement, physicist Lynde Wheeler published a new biography of Gibbs in 1951.

Both Gibbs and Rukeyser's biography of him figure prominently in the poetry collection True North (1997) by Stephanie Strickland. In fiction, Gibbs appears as the mentor to character Kit Traverse in Thomas Pynchon's novel Against the Day (2006). That novel also prominently discusses the birefringence of Iceland spar, an optical phenomenon that Gibbs investigated.

Gibbs stamp (2005)
In 2005, the United States Postal Service issued the American Scientists commemorative postage stamp series designed by artist Victor Stabin, depicting Gibbs, John von Neumann, Barbara McClintock, and Richard Feynman. The first day of issue ceremony for the series was held on May 4 at Yale University's Luce Hall and was attended by John Marburger, scientific advisor to the president of the United States, Rick Levin, president of Yale, and family members of the scientists honored, including physician John W. Gibbs, a distant cousin of Willard Gibbs.

Kenneth R. Jolls, a professor of chemical engineering at Iowa State University and an expert on graphical methods in thermodynamics, consulted on the design of the stamp honoring Gibbs. The stamp identifies Gibbs as a "thermodynamicist" and features a diagram from the 4th edition of Maxwell's Theory of Heat, published in 1875, which illustrates Gibbs's thermodynamic surface for water. Microprinting on the collar of Gibbs's portrait depicts his original mathematical equation for the change in the energy of a substance in terms of its entropy and the other state variables.

Outline of principal work

 * Physical chemistry: free energy, phase diagram, phase rule, transport phenomena
 * Statistical mechanics: statistical ensemble, phase space, chemical potential, Gibbs entropy, Gibbs paradox
 * Mathematics: Vector Analysis, convex analysis, Gibbs phenomenon
 * Electromagnetism: Maxwell's equations, birefringence

Primary

 * L. P. Wheeler, E. O. Waters and S. W. Dudley (eds.),The Early Work of Willard Gibbs in Applied Mechanics, (New York: Henry Schuman, 1947). ISBN 1-881987-17-5. This contains previously unpublished work by Gibbs, from the period between 1863 and 1871.
 * J. W. Gibbs, "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy of Arts and Sciences, 3, 108–248, 343–524, (1874–1878). Reproduced in both The Scientific Papers (1906), pp. 55–353 and The Collected Works of J. Willard Gibbs (1928), pp. 55–353.
 * E. B. Wilson, Vector Analysis, a text-book for the use of students of Mathematics and Physics, founded upon the Lectures of J. Willard Gibbs, (New Haven: Yale University Press, 1929 [1901]).
 * J. W. Gibbs, Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics, (New York: Dover Publications, 1960 [1902]).

Gibbs's other papers are included in both:
 * The Scientific Papers of J. Willard Gibbs, in two volumes, eds. H. A. Bumstead and R. G. Van Name, (Woodbridge, CT: Ox Bow Press, 1993 [1906]). ISBN 0-918024-77-3. For scans of the 1906 printing, see vol. I and vol. II.
 *  The Collected Works of J. Willard Gibbs, in two volumes, eds. W. R. Longley and R. G. Van Name, (New Haven: Yale University Press, 1957 [1928]). For scans of the 1928 printing, see vol. I and vol. II.

Secondary

 * . Reprinted with some additions in both The Scientific Papers, vol. I, pp. xiii–xxviiii (1906) and The Collected Works of J. Willard Gibbs, vol. I, pp. xiii–xxviiii (1928).  Also available here.
 * D. G. Caldi and G. D. Mostow (eds.), Proceedings of the Gibbs Symposium, Yale University, May 15–17, 1989, (American Mathematical Society and American Institute of Physics, 1990).
 * W. H. Cropper, "The Greatest Simplicity: Willard Gibbs", in Great Physicists, (Oxford: Oxford University Press, 2001), pp. 106–123. ISBN 0-19-517324-4
 * M. J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, (New York: Dover, 1994 [1967]). ISBN 0-486-67910-1
 * J. G. Crowther, Famous American Men of Science, (Freeport, NY: Books for Libraries Press, 1969 [1937]). ISBN 0-8369-0040-5
 * F. G. Donnan and A. E. Hass (eds.), A Commentary on the Scientific Writings of J. Willard Gibbs, in two volumes, (New York: Arno, 1980 [1936]). ISBN 0-405-12544-5. Only vol I. is currently available online.
 * P. Duhem, Josiah-Willard Gibbs à propos de la publication de ses Mémoires scientifiques, (Paris: A. Herman, 1908).
 * C. S. Hastings, "Josiah Willard Gibbs", Biographical Memoirs of the National Academy of Sciences, 6, 373–393 (1909).
 * M. J. Klein, "Gibbs, Josiah Willard", in Complete Dictionary of Scientific Biography, vol. 5, (Detroit: Charles Scribner's Sons, 2008), pp. 386–393.
 * M. Rukeyser, Willard Gibbs: American Genius, (Woodbridge, CT: Ox Bow Press, 1988 [1942]). ISBN 0-918024-57-9
 * R. J. Seeger, J. Willard Gibbs, American mathematical physicist par excellence, (Oxford and New York: Pergamon Press, 1974). ISBN 0-08-018013-2
 * L. P. Wheeler, Josiah Willard Gibbs, The History of a Great Mind, (Woodbridge, CT: Ox Bow Press, 1998 [1951]). ISBN 1-881987-11-6
 * A. S. Wightman, "Convexity and the notion of equilibrium state in thermodynamics and statistical mechanics". Published as an introduction to R. B. Israel, Convexity in the Theory of Lattice Gases, (Princeton, NJ: Princeton University Press, 1979), pp. ix–lxxxv.  ISBN 0-691-08209-X
 * E. B. Wilson, "Reminiscences of Gibbs by a student and colleague", Bulletin of the American Mathematical Society, 37, 401–416 (1931).

title: Josiah Willard Gibbs