title: Western Chalukya Empire

text: The intense competition between the kingdom of the western Deccan and those of the Tamil country came to the fore in the 11th century over the acutely contested fertile river valleys in the doab region of the Krishna and Godavari River called Vengi (modern coastal Andhra Pradesh). The Western Chalukyas and the Chola Dynasty fought many bitter wars over control of this strategic resource. The imperial Cholas gained power during the time of the famous king Rajaraja Chola I and the crown prince Rajendra Chola I.Chola Emperor Rajaraja Chola I conquered parts of Chalukya territory in present-day Southern Karnataka by subjugating the Western Ganga Dynasty of Gangavadi. The Eastern Chalukyas of Vengi were cousins of the Western Chalukyas but became increasingly influenced by the Cholas through their marital ties with the Tamil kingdom. As this was against the interests of the Western Chalukyas, they wasted no time in involving themselves politically and militarily in Vengi. When King Satyashraya succeeded Tailapa II to the throne, he was able to protect his kingdom from Chola aggression as well as his northern territories in Konkan and Gujarat although his control over Vengi was shaky.In 1007 CE Chola crown-prince Rajendra Chola I invaded Western Chalukyas and had a battle with Western Chalukya Emperor Satyashraya at Donur in Bijapur district of Karnataka. According to an inscription of Satyasraya from Dharwad, Rajaraja Nittavinoda Rajendra Vidyadhara, ornament of the Chola race, Nurmudi-Chola (one-hundred-crown Chola) invaded the Western Chalukya Empire in 1007 AD with an army of 900,000 soldiers, carrying fire and sword throughout the region. The invading troops advanced as far as Donur in Bijapur district on their way to the Chalukya capital Manyakheta, where they were met by the Chalukya army under Satyashraya. The Tanjore big temple inscriptions and Hottur inscriptions state that Rajendra Chola I destroyed the Western Chalukya capital. The result of the battle was Cholas conquered Gangapadi and Nolambapadi. Satyashraya's successor, Jayasimha II, fought many battles with the Cholas in the south around c. 1020–21 when both these powerful kingdoms struggled to choose the Vengi king. Shortly thereafter in c. 1024, Jayasimha II subdued the Paramara of central India and the rebellious Yadava King Bhillama.


title: Western Chalukya Empire

text: It is known from records that Jayasimha's son Someshvara I, whose rule historian Sen considers a brilliant period in the Western Chalukya rule, moved the Chalukya capital to Kalyani in c. 1042. Hostilities with the Cholas continued while both sides won and lost battles, though neither lost significant territory during the ongoing struggle to install a puppet on the Vengi throne.In 1066, Vikramaditya VI, Son of Someshwara I had invaded the Chola Empire penetrating as far as the capital Gangaikonda Cholapuram and threatening the city before being repulsed by Cholas. In the Battle of Vijayawada which was fought in 1068 between Someshvara I and Chola Emperor Virarajendra Chola, Someshwara I and his son Vikramaditya VI suffered defeat and lost Vengi to the Cholas. After the battle, Someshwara I due to incurable illnes drowned himself in the Tungabhadra River ("Paramayoga"). Despite many conflicts with the Cholas in the south, Someshvara I had managed to maintain control over the northern territories in Konkan, Gujarat, Malwa and Kalinga during his rule. His successor, his eldest son Someshvara II, feuded with his younger brother, Vikramaditya VI, an ambitious warrior who had initially been governor of Gangavadi in the southern Deccan when Someshvara II was the king. Before 1068, even as a prince, Vikramaditya VI had invaded Bengal, weakening the ruling Pala Empire. These incursions led to the establishment of "Karnata" dynasties such as the Sena dynasty and Varman dynasty in Bengal, and the Nayanadeva dynasty in Bihar., At the death of Someshvara I, his son Someshvara II came to the Chalukyan throne in April 1068 CE. Soon after a dispute broke out between him and his younger brother Vikramaditya and a civil war ensued in the Western Chalukya country. Vikramaditya VI went to Chola court and sought the help of Virarajendra Chola. Vikramaditya VI was well received by the king and the king Virarajendra himself records that he recognised Vikramaditya VI as the king of Western Chalukya. Virarajendra married his daughter to Vikramaditya VI and forged an alliance with him, halting the long feud between the two empires. Vikramaditya VI won the loyalty of the Chalukya feudatories: the Hoysala, the Seuna and the Kadambas of Hangal. In 1075 CE Vikramaditya overthrew Someshawara II and became the Western Chalukya Emperor. In 1075-76 CE during the Chola reign of Kulottunga I , the war began with the incursion of the Vikaramaditya's forces into the Chola territories and the two armies met in the Kolar district. What followed was the Chola counter-attack popularly known as the Nangili episode. In the ensuing battle, the Chalukyan army was completely routed and chased by the Chola forces from the rocky roads of Nangili all the way to the Tungabhadra via Manalur. Vikramaditya is said to have retreated hastily and fled.


title: Western Chalukya Empire

text: The fifty-year reign of Vikramaditya VI, the most successful of the later Chalukya rulers, was an important period in Karnataka's history and is referred to by historians as the "Chalukya Vikrama era". Not only was he successful in controlling his powerful feudatories in the north (Kadamba Jayakesi II of Goa, Silhara Bhoja and the Yadava King) and south (Hoysala Vishnuvardhana), he successfully dealt with the imperial Cholas whom he defeated in the battle of Vengi in 1093 and again in 1118. He retained this territory for many years despite ongoing hostilities with the Cholas. This victory in Vengi reduced the Chola influence in the eastern Deccan and made him emperor of territories stretching from the Kaveri River in the south to the Narmada River in the north, earning him the titles "Permadideva" and "Tribhuvanamalla" (lord of three worlds). The scholars of his time paid him glowing tributes for his military leadership, interest in fine arts and religious tolerance. Literature proliferated and scholars in Kannada and Sanskrit adorned his court. Poet Bilhana, who immigrated from far away Kashmir, eulogised the king in his well-known work "Vikramankadeva Charita". Vikramaditya VI was not only an able warrior but also a devout king as indicated by his numerous inscriptions that record grants made to scholars and centers of religion.


title: Western Chalukya Empire

text: The continual warring with the Cholas exhausted both empires, giving their subordinates the opportunity to rebel. In the decades after Vikramaditya VI's death in 1126, the empire steadily decreased in size as their powerful feudatories expanded in autonomy and territorial command. The time period between 1150 and 1200 saw many hard fought battles between the Chalukyas and their feudatories who were also at war with each other. By the time of Jagadhekamalla II, the Chalukyas had lost control of Vengi and his successor, Tailapa III, was defeated by the Kakatiya king Prola in 1149. Tailapa III was taken captive and later released bringing down the prestige of the Western Chalukyas. Seeing decadence and uncertainty seeping into Chalukya rule, the Hoysalas and Seunas also encroached upon the empire. Hoysala Narasimha I defeated and killed Tailapa III but was unable to overcome the Kalachuris who were vying for control of the same region. In 1157 the Kalachuris of Kalyanis under Bijjala II captured Kalyani and occupied it for the next twenty years, forcing the Chalukyas to move their capital to Annigeri in the present day Dharwad district.


title: Western Chalukya Empire

text: The Kalachuris were originally immigrants into the southern Deccan from central India and called themselves "Kalanjarapuravaradhisavaras". Bijjala II and his ancestors had governed as Chalukya commanders ("Mahamandaleshwar") over the Karhad-4000 and Tardavadi-1000 provinces (overlapping region in present-day Karnataka and Maharashtra) with Mangalavada or Annigeri as their capital. Bijjala II's Chikkalagi record of 1157 calls him "Mahabhujabala Chakravarti" ("emperor with powerful shoulders and arms") indicating he no longer was a subordinate of the Chalukyas. However the successors of Bijjala II were unable to hold on to Kalyani and their rule ended in 1183 when the last Chalukya scion, Someshvara IV made a final bid to regain the empire by recapturing Kalyani. Kalachuri King Sankama was killed by Chalukya general Narasimha in this conflict. During this time, Hoysala Veera Ballala II was growing ambitious and clashed on several occasions with the Chalukyas and the other claimants over their empire. He defeated Chalukya Someshvara IV and Seuna Bhillama V bringing large regions in the Krishna River valley under the Hoysala domains, but was unsuccessful against Kalachuris. The Seunas under Bhillama V were on an imperialistic expansion too when the Chalukyas regained Kalyani. Their ambitions were temporarily stemmed by their defeat against Chalukya general Barma in 1183 but they later had their vengeance in 1189.


title: Western Chalukya Empire

text: The overall effort by Someshvara IV to rebuild the Chalukya empire failed and the dynasty was ended by the Seuna rulers who drove Someshvara IV into exile in Banavasi 1189. After the fall of the Chalukyas, the Seunas and Hoysalas continued warring over the Krishna River region in 1191, each inflicting a defeat on the other at various points in time. This period saw the fall of two great empires, the Chalukyas of the western Deccan and the Cholas of Tamilakam. On the ruins of these two empires were built the Kingdoms of their feudatories whose mutual antagonisms filled the annals of Deccan history for over a hundred years, the Pandyas taking control over some regions of the erstwhile Chola empire.


title: Western Chalukya Empire

text: The Western Chalukya kingship was hereditary, passing to the king's brother if the king did not have a male heir. The administration was highly decentralised and feudatory clans such as the Alupas, the Hoysalas, the Kakatiya, the Seuna, the southern Kalachuri and others were allowed to rule their autonomous provinces, paying an annual tribute to the Chalukya emperor. Excavated inscriptions record titles such as "Mahapradhana" (Chief minister), "Sandhivigrahika", and "Dharmadhikari" (chief justice). Some positions such as "Tadeyadandanayaka" (commander of reserve army) were specialised in function while all ministerial positions included the role of "Dandanayaka" (commander), showing that cabinet members were trained as army commanders as well as in general administrative skills.


title: Western Chalukya Empire

text: The kingdom was divided into provinces such as "Banavasi-12000", "Nolambavadi-32000", "Gangavadi-96000", each name including the number of villages under its jurisdiction. The large provinces were divided into smaller provinces containing a lesser number of villages, as in "Belavola-300". The big provinces were called "Mandala" and under them were "Nadu" further divided into "Kampanas" (groups of villages) and finally a "Bada" (village). A "Mandala" was under a member of the royal family, a trusted feudatory or a senior official. Tailapa II himself was in charge of Tardavadi province during the Rashtrakuta rule. Chiefs of "Mandalas" were transferable based on political developments. For example, an official named Bammanayya administered Banavasi-12000 under King Someshvara III but was later transferred to Halasige-12000. Women from the royal family also administered "Nadus" and "Kampanas". Army commanders were titled "Mahamandaleshwaras" and those who headed a "Nadu" were entitled "Nadugouvnda".


title: Western Chalukya Empire

text: The Western Chalukyas minted punch-marked gold pagodas with Kannada and Nagari legends which were large, thin gold coins with several varying punch marks on the obverse side. They usually carried multiple punches of symbols such as a stylised lion, "Sri" in Kannada, a spearhead, the king's title, a lotus and others. Jayasimha II used the legend "Sri Jaya", Someshvara I issued coins with "Sri Tre lo ka malla", Someshvara II used "Bhuvaneka malla", Lakshmideva's coin carried "Sri Lasha", and Jagadhekamalla II coinage had the legend "Sri Jagade". The Alupas, a feudatory, minted coins with the Kannada and "Nagari" legend "Sri Pandya Dhanamjaya". Lakkundi in Gadag district and Sudi in Dharwad district were the main mints ("Tankhashaley"). Their heaviest gold coin was Gadyanaka weighing 96 grains, Dramma weighed 65 grains, Kalanju 48 grains, Kasu 15 grains, Manjadi 2.5 grains, Akkam 1.25 grains and Pana 9.6 grain.


title: Western Chalukya Empire

text: Agriculture was the empire's main source of income through taxes on land and produce. The majority of the people lived in villages and worked farming the staple crops of rice, pulses, and cotton in the dry areas and sugarcane in areas having sufficient rainfall, with areca and betel being the chief cash crops. The living conditions of the labourers who farmed the land must have been bearable as there are no records of revolts by the landless against wealthy landlords. If peasants were disgruntled the common practice was to migrate in large numbers out of the jurisdiction of the ruler who was mistreating them, thereby depriving him of revenue from their labor.


title: Western Chalukya Empire

text: Taxes were levied on mining and forest products, and additional income was raised through tolls for the use of transportation facilities. The state also collected fees from customs, professional licenses, and judicial fines. Records show horses and salt were taxed as well as commodities (gold, textiles, perfumes) and agricultural produce (black pepper, paddy, spices, betel leaves, palm leaves, coconuts and sugar). Land tax assessment was based on frequent surveys evaluating the quality of land and the type of produce. Chalukya records specifically mention black soil and red soil lands in addition to wetland, dry land and wasteland in determining taxation rates.


title: Western Chalukya Empire

text: Key figures mentioned in inscriptions from rural areas were the Gavundas (officials) or Goudas. The Gavundas belonged to two levels of economic strata, the "Praja Gavunda" (people's Gavunda) and the "Prabhu Gavunda" (lord of Gavundas). They served the dual purpose of representing the people before the rulers as well as functioning as state appointees for tax collection and the raising of militias. They are mentioned in inscriptions related to land transactions, irrigation maintenance, village tax collection and village council duties.


title: Western Chalukya Empire

text: The organisation of corporate enterprises became common in the 11th century. Almost all arts and crafts were organised into guilds and work was done on a corporate basis; records do not mention individual artists, sculptors and craftsman. Only in the regions ruled by the Hoysala did individual sculptors etched their names below their creations.


title: Western Chalukya Empire

text: Merchants organised themselves into powerful guilds that transcended political divisions, allowing their operations to be largely unaffected by wars and revolutions. Their only threat was the possibility of theft from brigands when their ships and caravans traveled to distant lands. Powerful South Indian merchant guilds included the "Manigramam", the "Nagarattar" and the "Anjuvannam". Local guilds were called "nagaram", while the "Nanadesis" were traders from neighbouring kingdoms who perhaps mixed business with pleasure. The wealthiest and most influential and celebrated of all South Indian merchant guilds was the self-styled "Ainnurruvar", also known as the 500 "Svamis" of Ayyavolepura (Brahmins and "Mahajanas" of present-day Aihole), who conducted extensive land and sea trade and thereby contributed significantly to the total foreign trade of the empire. It fiercely protected its trade obligations ("Vira Bananjudharma" or law of the noble merchants) and its members often recorded their achievements in inscriptions ("prasasti"). Five hundred such excavated "Prasasti" inscriptions, with their own flag and emblem, the bull, record their pride in their business.


title: Western Chalukya Empire

text: Rich traders contributed significantly to the king's treasury through paying import and export taxes. The edicts of the Aihole "Svamis" mention trade ties with foreign kingdoms such as Chera, Pandya, Maleya (Malaysia), Magadh, Kaushal, Saurashtra, Kurumba, Kambhoja (Cambodia), Lata (Gujarat), Parasa (Persia) and Nepal. Travelling both land and sea routes, these merchants traded mostly in precious stones, spices and perfumes, and other specialty items such as camphor. Business flourished in precious stones such as diamonds, lapis lazuli, onyx, topaz, carbuncles and emeralds. Commonly traded spices were cardamom, saffron, and cloves, while perfumes included the by-products of sandalwood, bdellium, musk, civet and rose. These items were sold either in bulk or hawked on streets by local merchants in towns. The Western Chalukyas controlled most of South India's west coast and by the 10th century they had established extensive trade ties with the Tang Empire of China, the empires of Southeast Asia and the Abbasid Caliphate in Bhagdad, and by the 12th-century Chinese fleets were frequenting Indian ports. Exports to Song Dynasty China included textiles, spices, medicinal plants, jewels, ivory, rhino horn, ebony and camphor. The same products also reached ports in the west such as Dhofar and Aden. The final destinations for those trading with the west were Persia, Arabia and Egypt. The thriving trade center of Siraf, a port on the eastern coast of the Persian Gulf, served an international clientele of merchants including those from the Chalukya empire who were feasted by wealthy local merchants during business visits. An indicator of the Indian merchants' importance in Siraf comes from records describing dining plates reserved for them. In addition to this, Siraf received aloe wood, perfumes, sandalwood and condiments. The most expensive import to South India were Arabian horse shipments, this trade being monopolised by Arabs and local Brahmin merchants. Traveller Marco Polo, in the 13th century, recorded that the breeding of horses never succeeded in India due to differing climatic, soil and grassland conditions.


title: Western Chalukya Empire

text: The fall of the Rashtrakuta empire to the Western Chalukyas in the 10th century, coinciding with the defeat of the Western Ganga Dynasty by the Cholas in Gangavadi, was a setback to Jainism. The growth of Virashaivism in the Chalukya territory and Vaishnava Hinduism in the Hoysala region paralleled a general decreased interest in Jainism, although the succeeding kingdoms continued to be religiously tolerant. Two locations of Jain worship in the Hoysala territory continued to be patronaged, Shravanabelagola and Kambadahalli. The decline of Buddhism in South India had begun in the 8th century with the spread of Adi Shankara's Advaita philosophy. The only places of Buddhist worship that remained during the Western Chalukya rule were at Dambal and Balligavi. There is no mention of religious conflict in the writings and inscriptions of the time which suggest the religious transition was smooth.


title: Western Chalukya Empire

text: Although the origin of the Virashaiva faith has been debated, the movement grew through its association with Basavanna in the 12th century. Basavanna and other Virashaiva saints preached of a faith without a caste system. In his Vachanas (a form of poetry), Basavanna appealed to the masses in simple Kannada and wrote "work is worship" (Kayakave Kailasa). Also known as the Lingayats (worshipers of the "Linga", the universal symbol of Shiva), these Virashaivas questioned many of the established norms of society such as the belief in rituals and the theory of rebirth and supported the remarriage of widows and the marriage of unwed older women. This gave more social freedom to women but they were not accepted into the priesthood. Ramanujacharya, the head of the Vaishnava monastery in Srirangam, traveled to the Hoysala territory and preached the way of devotion (bhakti marga). He later wrote "Sribhashya", a commentary on Badarayana Brahmasutra, a critique on the Advaita philosophy of Adi Shankara. Ramanujacharya's stay in Melkote resulted in the Hoysala King Vishnuvardhana converting to Vaishnavism, a faith that his successors also followed.


title: Western Chalukya Empire

text: The impact of these religious developments on the culture, literature, and architecture in South India was profound. Important works of metaphysics and poetry based on the teachings of these philosophers were written over the next centuries. Akka Mahadevi, Allama Prabhu, and a host of Basavanna's followers, including Chenna Basava, Prabhudeva, Siddharama, and Kondaguli Kesiraja wrote hundreds of poems called Vachanas in praise of Lord Shiva. The esteemed scholars in the Hoysala court, Harihara and Raghavanka, were Virashaivas. This tradition continued into the Vijayanagar empire with such well-known scholars as Singiraja, Mallanarya, Lakkana Dandesa and other prolific writers of Virashaiva literature. The Saluva, Tuluva and Aravidu dynasties of the Vijayanagar empire were followers of Vaishnavism and a Vaishnava temple with an image of Ramanujacharya exists today in the Vitthalapura area of Vijayanagara. Scholars in the succeeding Mysore Kingdom wrote Vaishnavite works supporting the teachings of Ramanujacharya. King Vishnuvardhana built many temples after his conversion from Jainism to Vaishnavism.


title: Western Chalukya Empire

text: The rise of Veerashaivaism was revolutionary and challenged the prevailing Hindu caste system which retained royal support. The social role of women largely depended on their economic status and level of education in this relatively liberal period. Freedom was more available to women in the royal and affluent urban families. Records describe the participation of women in the fine arts, such as Chalukya queen Chandala Devi's and Kalachuris of Kalyani queen Sovala Devi's skill in dance and music. The compositions of thirty Vachana women poets included the work of the 12th-century Virashaiva mystic Akka Mahadevi whose devotion to the "bhakti" movement is well known. Contemporary records indicate some royal women were involved in administrative and martial affairs such as princess Akkadevi, (sister of King Jayasimha II) who fought and defeated rebellious feudals. Inscriptions emphasise public acceptance of widowhood indicating that Sati (a custom in which a dead man's widow used to immolate herself on her husband's funeral pyre) though present was on a voluntary basis. Ritual deaths to achieve salvation were seen among the Jains who preferred to fast to death (Sallekhana), while people of some other communities chose to jump on spikes ("Shoolabrahma") or walking into fire on an eclipse.


title: Western Chalukya Empire

text: In a Hindu caste system that was conspicuously present, Brahmins enjoyed a privileged position as providers of knowledge and local justice. These Brahmins were normally involved in careers that revolved around religion and learning with the exception of a few who achieved success in martial affairs. They were patronised by kings, nobles and wealthy aristocrats who persuaded learned Brahmins to settle in specific towns and villages by making them grants of land and houses. The relocation of Brahmin scholars was calculated to be in the interest of the kingdom as they were viewed as persons detached from wealth and power and their knowledge was a useful tool to educate and teach ethical conduct and discipline in local communities. Brahmins were also actively involved in solving local problems by functioning as neutral arbiters ("Panchayat").


title: Western Chalukya Empire

text: Regarding eating habits, Brahmins, Jains, Buddhists and Shaivas were strictly vegetarian while the partaking of different kinds of meat was popular among other communities. Marketplace vendors sold meat from domesticated animals such as goats, sheep, pigs and fowl as well as exotic meat including partridge, hare, wild fowl and boar. People found indoor amusement by attending wrestling matches ("Kusti") or watching animals fight such as cock fights and ram fights or by gambling. Horse racing was a popular outdoor pastime. In addition to these leisurely activities, festivals and fairs were frequent and entertainment by traveling troupes of acrobats, dancers, dramatists and musicians was often provided.


title: Western Chalukya Empire

text: Schools and hospitals are mentioned in records and these were built in the vicinity of temples. Marketplaces served as open air town halls where people gathered to discuss and ponder local issues. Choirs, whose main function was to sing devotional hymns, were maintained at temple expense. Young men were trained to sing in choirs in schools attached to monasteries such as Hindu "Matha", Jain "Palli" and Buddhist "Vihara". These institutions provided advanced education in religion and ethics and were well equipped with libraries ("Saraswati Bhandara"). Learning was imparted in the local language and in Sanskrit. Schools of higher learning were called "Brahmapuri" (or "Ghatika" or "Agrahara"). Teaching Sanskrit was a near monopoly of Brahmins who received royal endowments for their cause. Inscriptions record that the number of subjects taught varied from four to eighteen. The four most popular subjects with royal students were Economics ("Vartta"), Political Science ("Dandaniti"), Veda ("trayi") and Philosophy ("Anvikshiki"), subjects that are mentioned as early as Kautilyas Arthashastra.


title: Western Chalukya Empire

text: The Western Chalukya era was one of substantial literary activity in the native Kannada, and Sanskrit. In a golden age of Kannada literature, Jain scholars wrote about the life of Tirthankaras and Virashaiva poets expressed their closeness to God through pithy poems called Vachanas. Nearly three hundred contemporary "Vachanakaras" ("Vachana" poets) including thirty women poets have been recorded. Early works by Brahmin writers were on the epics, Ramayana, Mahabharata, Bhagavata, Puranas and Vedas. In the field of secular literature, subjects such as romance, erotics, medicine, lexicon, mathematics, astrology, encyclopedia etc. were written for the first time.


title: Western Chalukya Empire

text: Most notable among Kannada scholars were Ranna, grammarian Nagavarma II, minister Durgasimha and the Virashaiva saint and social reformer Basavanna. Ranna who was patronised by king Tailapa II and Satyashraya is one among the "three gems of Kannada literature". He was bestowed the title "Emperor among poets" ("Kavi Chakravathi") by King Tailapa II and has five major works to his credit. Of these, "Saahasabheema Vijayam" (or "Gada yuddha") of 982 in "Champu" style is a eulogy of his patron King Satyashraya whom he compares to Bhima in valour and achievements and narrates the duel between Bhima and Duryodhana using clubs on the eighteenth day of the Mahabharata war. He wrote "Ajitha purana" in 993 describing the life of the second Tirthankara, Ajitanatha.


title: Western Chalukya Empire

text: Nagavarma II, poet laureate ("Katakacharya") of King Jagadhekamalla II made contributions to Kannada literature in various subjects. His works in poetry, prosody, grammar and vocabulary are standard authorities and their importance to the study of Kannada language is well acknowledged. "Kavyavalokana" in poetics, "Karnataka-Bhashabhushana" on grammar and "Vastukosa" a lexicon (with Kannada equivalents for Sanskrit words) are some of his comprehensive contributions. Several works on medicine were produced during this period. Notable among them were Jagaddala Somanatha's "Karnataka Kalyana Karaka".


title: Western Chalukya Empire

text: A unique and native form of poetic literature in Kannada called Vachanas developed during this time. They were written by mystics, who expressed their devotion to God in simple poems that could appeal to the masses. Basavanna, Akka Mahadevi, Allama Prabhu, Channabasavanna and Siddharama are the best known among them.


title: Western Chalukya Empire

text: In Sanskrit, a well-known poem ("Mahakavya") in 18 cantos called "Vikramankadeva Charita" by Kashmiri poet Bilhana recounts in epic style the life and achievements of his patron king Vikramaditya VI. The work narrates the episode of Vikramaditya VI's accession to the Chalukya throne after overthrowing his elder brother Someshvara II. The great Indian mathematician Bhāskara II (born c.1114) flourished during this time. From his own account in his famous work "Siddhanta Siromani" (c. 1150, comprising the "Lilavati", "Bijaganita" on algebra, "Goladhaya" on the celestial globe and "Grahaganita" on planets) Bijjada Bida (modern Bijapur) was his native place.


title: Western Chalukya Empire

text: "Manasollasa" or "Abhilashitartha Chintamani" by king Someshvara III (1129) was a Sanskrit work intended for all sections of society. This is an example of an early encyclopedia in Sanskrit covering many subjects including medicine, magic, veterinary science, valuing of precious stones and pearls, fortifications, painting, music, games, amusements etc. While the book does not give any of dealt topics particular hierarchy of importance, it serves as a landmark in understanding the state of knowledge in those subjects at that time. Someshwara III also authored a biography of his famous father Vikramaditya VI called Vikraman-Kabhyudaya. The text is a historical prose narrative which also includes a graphic description of the geography and people of Karnataka.


title: Western Chalukya Empire

text: A Sanskrit scholar Vijnaneshwara became famous in the field of legal literature for his "Mitakshara", in the court of Vikramaditya VI. Perhaps the most acknowledged work in that field, Mitakshara is a treatise on law (commentary on "Yajnavalkya") based on earlier writings and has found acceptance in most parts of modern India. An Englishman Colebrooke later translated into English the section on inheritance giving it currency in the British Indian court system. Some important literary works of the time related to music and musical instruments were "Sangita Chudamani", "Sangita Samayasara" and "Sangita Ratnakara".


title: Western Chalukya Empire

text: The reign of Western Chalukya dynasty was an important period in the development of Deccan architecture. The architecture designed during this time served as a conceptual link between the Badami Chalukya Architecture of the 8th century and the Hoysala architecture popularised in the 13th century. The art of the Western Chalukyas is sometimes called the "Gadag style" after the number of ornate temples they built in the Tungabhadra River-Krishna River doab region of present-day Gadag district in Karnataka. The dynasty's temple building activity reached its maturity and culmination in the 12th century with over a hundred temples built across the Deccan, more than half of them in present-day central Karnataka. Apart from temples, the dynasty's architecture is well known for the ornate stepped wells ("Pushkarni") which served as ritual bathing places, a few of which are well preserved in Lakkundi. These stepped well designs were later incorporated by the Hoysalas and the Vijayanagara empire in the coming centuries.


title: Western Chalukya Empire

text: The Kasivisvesvara Temple at Lakkundi (Gadag district), the Dodda Basappa Temple at Dambal (Gadag district), the Mallikarjuna Temple at Kuruvatti (Bellary district), the Kallesvara Temple at Bagali (Davangere district), the Siddhesvara Temple at Haveri (Haveri district), the Amrtesvara Temple at Annigeri (Dharwad district), the Mahadeva Temple at Itagi (Koppal district), the Kaitabheshvara Temple at Kubatur, and the Kedareshvara Temple at Balligavi are the finest examples produced by the later Chalukya architects. The 12th-century Mahadeva Temple with its well executed sculptures is an exquisite example of decorative detail. The intricate, finely crafted carvings on walls, pillars and towers speak volumes about Chalukya taste and culture. An inscription outside the temple calls it "Emperor of Temples" ("devalaya chakravarti") and relates that it was built by Mahadeva, a commander in the army of king Vikramaditya VI. The Kedareswara Temple (1060) at Balligavi is an example of a transitional Chalukya-Hoysala architectural style. The Western Chalukyas built temples in Badami and Aihole during their early phase of temple building activity, such as Mallikarjuna Temple, the Yellamma Temple and the Bhutanatha group of Temples.


title: Western Chalukya Empire

text: The "vimana" of their temples (tower over the shrine) is a compromise in detail between the plain stepped style of the early Chalukyas and the decorative finish of the Hoysalas. To the credit of the Western Chalukya architects is the development of the lathe turned (tuned) pillars and use of Soapstone (Chloritic Schist) as basic building and sculptural material, a very popular idiom in later Hoysala temples. They popularised the use of decorative "Kirtimukha" (demon faces) in their sculptures. Famous architects in the Hoysala kingdom included Chalukyan architects who were natives of places such as Balligavi. The artistic wall decor and the general sculptural idiom was dravidian architecture. This style is sometimes called "Karnata dravida", one of the notable traditions in Indian architecture.


title: Western Chalukya Empire

text: The local language Kannada was mostly used in Western (Kalyani) Chalukya inscriptions and epigraphs. Some historians assert that ninety percent of their inscriptions are in the Kannada language while the remaining are in Sanskrit. More inscriptions in Kannada are attributed to Vikramaditya VI than any other king prior to the 12th century, many of which have been deciphered and translated by historians of the Archaeological Survey of India. Inscriptions were generally either on stone ("Shilashasana") or copper plates ("Tamarashasana"). This period saw the growth of Kannada as a language of literature and poetry, impetus to which came from the devotional movement of the Virashaivas (called Lingayatism) who expressed their closeness to their deity in the form of simple lyrics called Vachanas. At an administrative level, the regional language was used to record locations and rights related to land grants. When bilingual inscriptions were written, the section stating the title, genealogy, origin myths of the king and benedictions were generally done in Sanskrit. Kannada was used to state terms of the grants, including information on the land, its boundaries, the participation of local authorities, rights and obligations of the grantee, taxes and dues, and witnesses. This ensured the content was clearly understood by the local people without any ambiguity.


title: Western Chalukya Empire

text: In addition to inscriptions, chronicles called "Vamshavalis" were written to provide historical details of dynasties. Writings in Sanskrit included poetry, grammar, lexicon, manuals, rhetoric, commentaries on older works, prose fiction and drama. In Kannada, writings on secular subjects became popular. Some well-known works are "Chandombudhi", a prosody, and "Karnataka Kadambari", a romance, both written by Nagavarma I, a lexicon called "Rannakanda" by Ranna (993), a book on medicine called "Karnataka-Kalyanakaraka" by Jagaddala Somanatha, the earliest writing on astrology called "Jatakatilaka" by Sridharacharya (1049), a writing on erotics called "Madanakatilaka" by Chandraraja, and an encyclopedia called "Lokapakara" by Chavundaraya II (1025).


title: Martha Vickers

text: Martha Vickers (born Martha MacVicar; May 28, 1925 – November 2, 1971) was an American model and actress.


title: Martha Vickers

text: Vickers was born Martha MacVicar in Ann Arbor, Michigan; her father was an automobile dealer. She began her career as a model and cover girl. Her family moved to Hollywood when her father assumed control of an agency in Burbank, California. Vickers was 15 at that time.


title: Martha Vickers

text: She played minor roles in several films during the early 1940s, working first at Universal Studios and then at RKO Pictures. She next went to Warner Bros., where "they gave her the star push, rearranging her surname to 'Vickers.'" Her work there included the role of Carmen Sternwood, the promiscuous, drug-addicted younger sister of Lauren Bacall's character in "The Big Sleep" (1946). She also featured in a musical, "The Time, the Place and the Girl" (also 1946), followed by two Warner Bros. comedies, "Love and Learn" and "That Way with Women" (both 1947).


title: Martha Vickers

text: Vickers's TV appearances included the 1959 "Perry Mason" episode, "The Case of the Jaded Joker", in which she played Sheila Hayes. Her final two performances, in 1960, were on "The Rebel", starring Nick Adams.


title: Martha Vickers

text: Vickers was married three times, to A.C. Lyles (March 15, 1948 – September 28, 1948), Mickey Rooney (June 3, 1949 – September 25, 1951), and actor Manuel Rojas (September 1, 1954 – May 5, 1965). Each marriage ended in divorce. Vickers had one son with Mickey Rooney, and two daughters with Rojas.


title: Martha Vickers

text: Vickers died, aged 46, of esophageal cancer at Valley Presbyterian Hospital in Los Angeles on November 2, 1971. She is buried in Valhalla Memorial Park Cemetery in North Hollywood, California.


title: Taisho Otome Fairy Tale

text: It is late 1921, the 10th year of the Taishō era. Tamahiko Shima, second son of the wealthy Shima family, has his life turned upside-down after his right arm is paralyzed in a car accident that also claims the life of his mother. Now seen as worthless to his calculating father's long-term plans for his business empire, his family treats him as “dead”. But since it would bring shame to the family were they to disown him outright, he instead finds himself shunted off to a villa in the mountains of Chiba, out of public view. Though he quickly resigns himself to the idea that he will die alone and forgotten, one snowy December night a girl appears at his doorstep and announces that she is there to be his live-in caretaker, and when she is old enough, his bride. The girl, named Yuzuki Tachibana, or “Yuzu” for short, was purchased from her impoverished home by Tamahiko's father, and while she too finds herself uprooted from her home and family, she throws herself into her new role with gusto.


title: Taisho Otome Fairy Tale

text: Tamahiko is initially extremely cynical and depressed due to his exile, and Yuzuki's irrepressibly sunny disposition grates on his nerves at first, but her presence gradually helps brighten his mood. In time, Tamahiko and Yuzuki fall in love. In 1922, Tamahiko's younger sister, Tamako, visits the couple, and, though initially cold, warms up to Yuzuki. They also meet Ryō Atsumi, the older sister and caretaker of a number of younger siblings, who teases, picks on and steals from Tamahiko. However, she grows close to him and Yuzuki, and Tamahiko helps her younger siblings with school.


title: Taisho Otome Fairy Tale

text: In 1923, Yuzuki and one of Ryō's brothers, Ryotaro, leave for Tokyo - the former to see her friend from school, and the latter to pursue an apprenticeship. However, they are caught up in the 1923 Great Kantō earthquake, leading Tamahiko and Ryō to walk to Tokyo, with Tamahiko leaving his house open as a temporary shelter for the affected population in his town. Tamahiko finds Yuzuki, bringing her to a temporary hospital run by his estranged uncle. After the earthquake, the famous singer Kotori Shiratori visits Chiba and plays a show with Yuzuki and Ryō attending. Later on, Tamahiko returns to school, passing the entrance exams and making friends with Kotori's twin brother, Hakaru. Kotori visits Yuzuki and Tamahiko and asks them about love to support her songwriting.


title: Taisho Otome Fairy Tale

text: Yuzuki suddenly leaves one day, and Tamahiko falls back into his depressed state. It is revealed that the heir to the Shima family, Tamaki, has died, and Tamahiko, despite being previously ostracized, is invited back into the family to serve as heir. As a result, Yuzuki is assigned to become the wife of Tamahiko's brother Tamao. Tamahiko goes back to Tokyo, gets Yuzuki back, and cuts ties with his father, with Tamako and Tamao following him, leaving only the oldest sister, Tamayo, to succeed the Shima family. In preparation for their wedding, Tamahiko and Yuzuki visit Yuzuki's family in Iwate. Eventually, Tamahiko takes Yuzuki's last name, Tachibana, and becomes a teacher. Tamao and Tamako are adopted by their uncle.


title: Taisho Otome Fairy Tale

text: "Taisho Otome Fairy Tale", written and illustrated by Sana Kirioka, ran in Shueisha's "Jump Square" magazine from July 4, 2015, to September 4, 2017. Shueisha collected its chapters in five "tankōbon" volumes, released from February 4, 2016, to October 4, 2017.


title: Taisho Otome Fairy Tale

text: A sequel, titled , was serialized on Shueisha's "Shōnen Jump+" online magazine from August 21, 2018, to May 12, 2020. Shueisha collected its chapters in five "tankōbon" volumes, released from January 4, 2019, to July 3, 2020.


title: Taisho Otome Fairy Tale

text: A spin-off series, titled , was serialized on "Shōnen Jump+" from July 3 to December 31, 2021. Shueisha released the first volume on October 4, 2021. Volume 2 was March 4, 2022.


title: Taisho Otome Fairy Tale

text: On December 20, 2020, at the Jump Festa '21 online event, it was announced that the series would receive an anime television series adaptation by SynergySP. It is directed by Jun Hatori, with scripts written by Hiroko Fukuda and Mayu Watanabe designing the characters. Yasuharu Takanashi is composing the series' music. It aired from October 9 to December 25, 2021, on TV Tokyo, TVO, BS11, and AT-X. Garnidelia performed the opening theme , while Shun'ichi Toki performed the ending theme . Ayasa Itō performed the ending theme of episode 12. Funimation licensed the series while Muse Communication licensed it in Southeast Asia.


title: Taisho Otome Fairy Tale

text: The anime adaptation's first episode garnered mixed reviews from Anime News Network's staff during the Fall 2021 season previews. Richard Eisenbeis critiqued that a familiarity with the Taisho era is needed to enjoy the show and that Yuzuki's characteristics made her more of a plot device for Tamahiko's story, calling it "a perfectly watchable anime" that he had little reason to continue watching it. Nicholas Dupree understood the fluffy approach the show was going for but felt it lacked bite to explore its given topics and make its couple more romantically engaging beyond trite sentiment, concluding that: "Overall this is a perfectly pleasant experience, but one I'm not interested in repeating." James Beckett observed that while the show had "a decent period setting and a couple of chuckle-worthy jokes", he criticized the main couple for lacking chemistry with each other and the marriage angle for overusing an arc that's bereft of mature storytelling, saying that audiences who prefer "a perfectly nice, unambitious take" on historical romance will enjoy it. Rebecca Silverman wrote that: "While this isn't treading any new ground, there's a sort of wholesome charm to it. That goes a long way to making up for hackneyed plots or lines and the simple, at times lackluster artwork. At its heart this is a familiar story about two people coming to care for each other and overcome the obstacles life has seen fit to throw in their way. As long as it keeps that heart warm and beating, this could be a quiet charmer of a show."


title: Taisho Otome Fairy Tale

text: Fellow ANN editor Caitlin Moore reviewed the complete anime series in 2022 and gave it a B– grade. She praised the "pleasant and cheerful" narrative, the exploration of damaged people navigating the world and finding solace in one's community and its depiction of Tamahiko's disability, but was critical of Yuzuki's "one-dimensional[ly] cheery" demeanor lacking interiority during her situation and the "lackluster visual direction" failing to further elevate the story, concluding that: "Overall, "Taisho Otome Fairy Tale" is a nice enough series, but it's held back by a hesitation to venture into anything beyond nice [...] As it is, it's good as a relaxing watch if you're tired of the "cute girls doing cute things" rigmarole, or if you're looking for something with well-handled disability representation."


title: Marillion discography

text: This is the discography of the British rock band Marillion. Mostly associated with the progressive rock genre, they emerged as the most successful band of its second wave, neo-progressive rock, but they have also achieved over 20 UK Top 40 singles, including four which reached the Top 10. They have released nine albums which reached the Top 10 of the UK Albums Chart. Their discography includes two albums which have been Platinum-certified by the British Phonographic Industry and five which have achieved Gold status, all of which were released during their commercial peak in the 1980s.


title: Marillion discography

text: The table below only lists live albums which were released to retail on a major label. In addition, there have been many live releases on the band's own Racket Records label, which are detailed separately in the relevant section below.


title: Marillion discography

text: The tables above only list videos which were released to retail on a major label. In addition, there have been many video releases on the band's own Racket Records label, which are detailed separately in the relevant section below.


title: Marillion discography

text: Racket Records is Marillion's own label – Racket releases are only available direct from Marillion's online shop. Some of the early releases are now out of print as CDs and DVDs, but most are available as audio downloads.


title: Marillion discography

text: Three live concerts at The Forum in London were recorded by Abbey Road Live and released on CD-R discs for sale at the venue immediately after the shows finished. These discs are joint productions between Abbey Road Live and Racket Records, and therefore are not in the regular catalogue number sequence.


title: Marillion discography

text: Racket have also released a small number of titles by artists other than Marillion (usually band members' side projects).


title: Marillion discography

text: Racket 91 was released on PAL and NTSC VHS – the P and N suffixes for this release denote the VHS versions.


title: Marillion discography

text: Free issue to Fan Club members only, very limited runs. CDs were released from 1998 to 2008; DVDs were released from 2009 onwards. All titles now out of print, although are available for purchase as download only when taking out or renewing Fan Club membership. Most contain a Christmas message from the band members, one new Christmas-themed song, and an assortment of other tracks.


title: Marillion discography

text: The Front Row Club was a subscription-only service by which CDs of raw concert recordings, originally made by the band for their own reference, were released. Members paid for a subscription (initially lasting six releases; later reduced to four releases), and as the shows were released, they were automatically mailed to members. There were also occasional optional releases, which were only mailed on request - these were generally reissues of previously released material. The only FRC issue which was available to non-subscribers was the "Curtain Call" box set - this was the only FRC release of material recorded before Steve Hogarth joined the band, and was sold via both Marillion and Fish's online stores, as well as being an optional FRC release.


title: Marillion discography

text: After the release of FRC-040 in January 2008, the FRC changed to a download-only digital distribution format. This lasted for a further three issues - after FRC-043, the FRC was closed. (Starting with the "Happiness On The Road" tour, Marillion moved to publishing the majority of their live performances from desk recordings as digital downloads, rendering the FRC redundant.)


title: Marillion discography

text: Only a limited number of copies were manufactured for each FRC release (believed to be no more than 3,000) and were not re-issued once sold out. Most of the FRC releases are now out of print on CD, but are still available from the band's website as downloads.


title: Marillion discography

text: Jacqueline Chekroun, "Marillion, l'ère du Poisson", France 1994. JC éditions, 99 Vallon des Vaux 06 800 Cagnes-sur-mer, France


title: Admission to the Union

text: Admission to the Union is provided by the Admissions Clause of the United States Constitution in Article IV, Section 3, , which authorizes the United States Congress to admit new states into the Union beyond the thirteen states that already existed when the Constitution came into effect. The Constitution went into effect on June 21, 1788 in the nine states that had ratified it, and the U.S. federal government began operations under it on March 4, 1789, when it was in effect in 11 out of the 13 states. Since then, 37 states have been admitted into the Union. Each new state has been admitted on an equal footing with those already in existence.


title: Admission to the Union

text: Of the 37 states admitted to the Union by Congress, all but six have been established within existing U.S. organized incorporated territories. A state that was so created might encompass all or part of a territory. When the people of a territory or a region have grown to a sufficient population and have made their desire for statehood known to the federal government, Congress in most cases has passed an enabling act, authorizing the people of that territory or region to frame a proposed state constitution as a step toward admission to the Union. The use of an enabling act has been a common historic practice, but several states were admitted to the Union without one.


title: Admission to the Union

text: In many instances, an enabling act would detail the mechanism by which the territory would be admitted as a state after the ratification of their constitution and the election of state officers. Although the use of such an act is a traditional historic practice, several territories have drafted constitutions for submission to Congress absent an enabling act but were subsequently admitted. The broad outline for the process was established by the Land Ordinance of 1784 and the 1787 Northwest Ordinance, both of which predate the U.S. Constitution.


title: Admission to the Union

text: The Admission to the Union Clause forbids the creation of new states from parts of existing states without the consent of all of the affected states and that of Congress. The primary intent of the caveat was to give the four Eastern States that still had western land claims (Connecticut, Georgia, North Carolina, and Virginia) a veto over whether their western counties could become states. The clause has since served the same function each time that a proposal to partition an existing state or states has arisen.


title: Admission to the Union

text: Between 1781 and 1789, the United States was governed by a unicameral Congress, the Congress of the Confederation, which operated under authority granted to it by the Articles of Confederation, the nation's first constitution. The 11th Article authorized Congress to admit new states to the Union provided nine states consented. Under the Articles, each state cast one vote on each proposed measure in Congress.


title: Admission to the Union

text: During this period, the Confederation Congress enacted two ordinances governing the admission of new states into the Union. The first such ordinance was the Land Ordinance of 1784, enacted April 23, 1784. Thomas Jefferson was its principal author. The ordinance called for the land (recently confirmed as part of the United States by the Treaty of Paris) west of the Appalachian Mountains, north of the Ohio River and east of the Mississippi River to eventually be divided into ten states. Once a given area reached 20,000 inhabitants, it could call a constitutional convention and form a provisional government. Then, upon enacting a state constitution which affirmed that the new state would forever be part of the Confederation, it would be admitted on an equal footing with all other states, based on a majority vote in Congress. Stipulations for new state dictated that it would be subject to the Articles of Confederation and acts of Congress; would be subject to payment for federal debts; would not tax federal properties within the state border or tax non-residents at a rate higher than residents; and would have a republican form of government. Jefferson's original draft of the ordinance gave names to the proposed states and contained a provision that "After the year 1800 there shall be neither slavery nor involuntary servitude in any of them."


title: Admission to the Union

text: The 1784 ordinance was superseded three years later by the Northwest Ordinance of 1787. Enacted by the Confederation Congress on July 13, 1787, it created the Northwest Territory, the first organized incorporated territory of the United States. The Northwest Ordinance (Article V) provided for the admission of several new states from within its bounds:


title: Admission to the Union

text: While the Articles of Confederation were in effect, the Congress considered various ordinances admitting particular new states into the Union, none of which were approved:


title: Admission to the Union

text: Considered one of the most important legislative acts of the Confederation Congress, the Northwest Ordinance established the precedent by which the Federal government would be sovereign and expand westward with the admission of new states, rather than with the expansion of existing states and their established sovereignty under the Articles of Confederation. No new states were formed in the Northwest Territory under either ordinance. In 1789, the 1st United States Congress reaffirmed the Northwest Ordinance with slight modifications. The Northwest Territory remained in existence until 1803, when the southeastern portion of it was admitted to the Union as the State of Ohio, and the remainder was reorganized.


title: Admission to the Union

text: At the 1787 Constitutional Convention, a proposal to include the phrase "new States shall be admitted on the same terms with the original States" in the "new states" clause was defeated. That proposal would have taken the policy articulated in the Ordinance of 1784 and made it a constitutional imperative. Many delegates objected to including the phrase, fearing that the political power of future new western states would ultimately overwhelm that of the established eastern states.


title: Admission to the Union

text: Delegates, understanding that the number of states would inevitably increase, did agree to include wording into this clause to preclude formation of a new state out of an established one without the consent of the established state as well as the Congress. It was anticipated that Kentucky (which was a part of Virginia), Franklin (which was a part of North Carolina, and later became part of the Southwest Territory), Vermont (to which New York asserted a disputed claim), and Maine (which was a part of Massachusetts), would become states. As a result of this compromise, new breakaway states are permitted to join the Union but only with the proper consents.


title: Admission to the Union

text: Shortly after the new Constitution went into effect Congress admitted Vermont and Kentucky on equal terms with the existing 13 states and thereafter formalized the condition in its acts of admission for subsequent states. Thus the Congress, utilizing the discretion allowed by the framers, adopted a policy of equal status for all newly admitted states. The constitutional principle derived from these actions is known as the equal footing doctrine. With the growth of states' rights advocacy during the antebellum period, the Supreme Court asserted, in "Lessee of Pollard v. Hagan" (1845), that the Constitution mandated admission of new states on the basis of equality.


title: Admission to the Union

text: Historically, most new states formed by Congress have been established from an organized incorporated U.S. territory, created and governed by Congress in accord with its plenary power under Article IV, Section 3, of the Constitution. In some cases, an entire territory became a state; in others some part of a territory became a state. In most cases, the organized government of a territory made known the sentiment of its population in favor of statehood, usually by referendum. Congress then empowered that government to organize a constitutional convention to write a state constitution. Upon acceptance of that constitution, by the people of the territory and then by Congress, Congress would adopt by simple majority vote a joint resolution granting statehood. Then the President of the United States would sign the resolution and issue a proclamation announcing that a new state had been added to the Union. While Congress, which has ultimate authority over the admission of new states, has usually followed this procedure, there have been occasions when it did not.


title: Admission to the Union

text: Congress is under no obligation to admit states, even in those areas whose population expresses a desire for statehood. In one instance, Mormon pioneers in Salt Lake City sought to establish the state of Deseret in 1849. It existed for slightly over two years and was never approved by the Congress. In 1905, leaders of the Five Civilized Tribes (Cherokee, Chickasaw, Choctaw, Creek, and Seminole) in Indian Territory proposed to establish the state of Sequoyah as a means to retain control of their lands. The proposed constitution ultimately failed in Congress. Instead, the Indian Territory was incorporated into the new state of Oklahoma in 1907.


title: Admission to the Union

text: Some U.S. territories existed only a short time before becoming states, while others remained territories for decades. The shortest-lived was Alabama Territory at 2 years, while New Mexico and Hawaii territories both were in existence for more than 50 years. The entry of several states into the Union has been delayed by complicating factors. Among them, Michigan Territory, which petitioned Congress for statehood in 1835, was not admitted to the Union until 1837, because of a boundary dispute with the adjacent state of Ohio. The independent Republic of Texas requested annexation to the United States in 1837, but fears about potential conflict with Mexico delayed the admission of Texas for nine years. Also, statehood for Kansas Territory was held up for several years (1854–1861) because of a series of internal violent conflicts involving anti-slavery and pro-slavery factions.


title: Admission to the Union

text: Once established, most state borders have, with few exceptions, been generally stable. Notable exceptions include: the various portions (the Western land claims) of several original states ceded over a period of several years to the federal government, which in turn became the Northwest Territory, Southwest Territory, and Mississippi Territory; the 1791 cession by Maryland and Virginia of land to create the District of Columbia (Virginia's portion was returned in 1847); and the creation, on at least three occasions, of a new state (Kentucky, Maine and West Virginia) from a region of an existing state (Vermont was created from what was disputedly claimed to be a part of New York and was not admitted until New York consented); two large additions to Nevada, which became a state in 1864, were made in 1866 and 1867. There have been numerous minor adjustments to state boundaries over the years as a result of improved surveys, resolution of ambiguous or disputed boundary definitions, or minor mutually agreed boundary adjustments for administrative convenience or other purposes. One notable example is the case "New Jersey v. New York", in which New Jersey won roughly 90% of Ellis Island from New York in 1998.


title: Admission to the Union

text: In addition to the original 13, six subsequent states were never part of an organized incorporated U.S. territory:


title: 2014–15 UEFA Europa League

text: The 2014–15 UEFA Europa League was the 44th season of Europe's secondary club football tournament organised by UEFA, and the sixth season since it was renamed from the UEFA Cup to the UEFA Europa League.


title: 2014–15 UEFA Europa League

text: The 2015 UEFA Europa League Final was played at the Stadion Narodowy in Warsaw, with Spanish side and title holders Sevilla defeating Ukrainian side Dnipro Dnipropetrovsk 3–2 to win a record fourth title.


title: 2014–15 UEFA Europa League

text: This season was the first where clubs must comply with UEFA Financial Fair Play Regulations in order to participate. Moreover, this season was the first where a club from Gibraltar competed in the tournament, after the Gibraltar Football Association was accepted as the 54th UEFA member at the UEFA Congress in May 2013. They were granted one spot in the Europa League, which was taken by College Europa, the runners-up of the 2014 Rock Cup.


title: 2014–15 UEFA Europa League

text: Starting from this edition, the UEFA Europa League winners automatically qualify for the subsequent UEFA Champions League season even if they do not qualify for the Champions League through their domestic performance. Therefore, the winners of this tournament qualify for the 2015–16 UEFA Champions League. They are guaranteed to enter at least the play-off round, and since the group stage berth reserved for the Champions League title holders will not be used (the winners of the 2014–15 UEFA Champions League are guaranteed to qualify for the group stage through domestic performance), they will be elevated to enter the group stage via this berth.


title: 2014–15 UEFA Europa League

text: On 17 July 2014, the UEFA emergency panel ruled that Ukrainian and Russian clubs would not be drawn against each other "until further notice" due to the political unrest between the countries. Another ruling centred in regional instability was also made where Israeli teams were prohibited from hosting any UEFA competitions due to the 2014 Israel–Gaza conflict (whilst the ruling ended a short time after the war, all the country's sides were eliminated before it ended). The rules regarding suspension due to yellow card accumulation were also changed such that all bookings expired on completion of the quarter-finals and were not carried forward to the semi-finals. Moreover, this was the first season in which vanishing spray was used.


title: 2014–15 UEFA Europa League

text: A total of 195 teams from all 54 UEFA member associations participate in the 2014–15 UEFA Europa League. The association ranking based on the UEFA country coefficients is used to determine the number of participating teams for each association:


title: 2014–15 UEFA Europa League

text: The winners of the 2013–14 UEFA Europa League are given an additional entry as title holders if they do not qualify for the 2014–15 UEFA Champions League or Europa League through their domestic performance. However, this additional entry is not necessary for this season since the title holders qualified for European competitions through their domestic performance.


title: 2014–15 UEFA Europa League

text: For the 2014–15 UEFA Europa League, the associations are allocated places according to their 2013 UEFA country coefficients, which takes into account their performance in European competitions from 2008–09 to 2012–13.


title: 2014–15 UEFA Europa League

text: Apart from the allocation based on the country coefficients, associations may have additional teams participating in the Europa League, as noted below:


title: 2014–15 UEFA Europa League

text: Since title holders Sevilla qualified for the Europa League through their domestic performance, the spot which they qualified for in the group stage (as the fifth-placed team of the 2013–14 La Liga) is vacated, and the following changes to the default allocation system were made:


title: 2014–15 UEFA Europa League

text: A Europa League place is vacated when a team qualifies for both the Champions League and the Europa League, or qualifies for the Europa League by more than one method. When a place is vacated, it is redistributed within the national association by the following rules:


title: 2014–15 UEFA Europa League

text: Notably three teams take part in the competition that do not currently play in their national top-division. They are Santos Tartu (3rd tier), St. Pölten (2nd) and Tromsø (2nd).


title: 2014–15 UEFA Europa League

text: The schedule of the competition is as follows (all draws held at UEFA headquarters in Nyon, Switzerland, unless stated otherwise).


title: 2014–15 UEFA Europa League

text: Matches in the qualifying, play-off, and knockout rounds may also be played on Tuesdays or Wednesdays instead of the regular Thursdays due to scheduling conflicts.


title: 2014–15 UEFA Europa League

text: In the qualifying rounds and the play-off round, teams were divided into seeded and unseeded teams based on their 2014 UEFA club coefficients, and then drawn into two-legged home-and-away ties. Teams from the same association could not be drawn against each other.


title: 2014–15 UEFA Europa League

text: The draw for the first and second qualifying rounds was held on 23 June 2014. The first legs were played on 1 and 3 July, and the second legs were played on 8, 10 and 11 July 2014.


title: 2014–15 UEFA Europa League

text: The draw for the third qualifying round was held on 18 July 2014. The first legs were played on 31 July, and the second legs were played on 7 August 2014.


title: 2014–15 UEFA Europa League

text: The draw for the play-off round was held on 8 August 2014. The first legs were played on 20 and 21 August, and the second legs were played on 28 August 2014.


title: 2014–15 UEFA Europa League

text: The draw for the group stage was held in Monaco on 29 August 2014. The 48 teams were allocated into four pots based on their 2014 UEFA club coefficients, with the title holders being placed in Pot 1 automatically. They were drawn into twelve groups of four, with the restriction that teams from the same association could not be drawn against each other.


title: 2014–15 UEFA Europa League

text: In each group, teams played against each other home-and-away in a round-robin format. The matchdays were 18 September, 2 October, 23 October (one home match of Metalist Kharkiv played on 22 October), 6 November, 27 November, and 11 December 2014.


title: 2014–15 UEFA Europa League

text: A total of 26 national associations were represented in the group stage. Wolfsburg, Torino, Feyenoord, Guingamp, Saint-Étienne, Rio Ave, Dynamo Moscow, Krasnodar, Lokeren, Asteras Tripoli, Qarabağ, HJK, Astra Giurgiu, Dinamo Minsk and AaB made their debut appearances in the UEFA Europa League group stage (not counting UEFA Cup group stage appearances), although Wolfsburg had already disputed the 2009–10 UEFA Europa League knockout phase after a third place in the 2009–10 UEFA Champions League group stage.


title: 2014–15 UEFA Europa League

text: The group winners and runners-up advanced to the round of 32, where they were joined by the eight third-placed teams of the 2014–15 UEFA Champions League group stage. See 2014–15 UEFA Europa League group stage#Tiebreakers for tiebreakers if two or more teams are equal on points.


title: 2014–15 UEFA Europa League

text: In the knockout phase, teams played against each other over two legs on a home-and-away basis, except for the one-match final. The mechanism of the draws for each round was as follows:


title: 2014–15 UEFA Europa League

text: The draw for the round of 32 was held on 15 December 2014. The first legs were played on 19 February, and the second legs were played on 26 February 2015.


title: 2014–15 UEFA Europa League

text: The draw for the round of 16 was held on 27 February 2015. The first legs were played on 12 March, and the second legs were played on 19 March 2015.


title: 2014–15 UEFA Europa League

text: The draw for the quarter-finals was held on 20 March 2015. The first legs were played on 16 April, and the second legs were played on 23 April 2015.


title: 2014–15 UEFA Europa League

text: The draw for the semi-finals and final (to determine the "home" team for administrative purposes) was held on 24 April 2015. The first legs were played on 7 May, and the second legs were played on 14 May 2015.


title: Composition with Red Blue and Yellow

text: Composition with Red, Blue and Yellow is a 1930 painting by Piet Mondrian, a Dutch artist who was a leading figure in the Neo-Plasticism movement. It consists of thick, black brushwork, defining the borders of colored rectangles. As the title suggests, the only colors used in it besides black and white are red, blue, and yellow. The piece is very similar to Mondrian's 1930 Composition II in Red, Blue, and Yellow. According to Dr. Stephanie Chadwick, associate professor of art history at Lamar University, "Mondrian's Composition with Red, Blue, and Yellow demonstrates his commitment to relational opposites, asymmetry, and pure planes of color. Mondrian composed this painting as a harmony of contrasts that signifies both balance and the tension of dynamic forces."


title: Thermodynamic temperature

text: Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.


title: Thermodynamic temperature

text: Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as manifestations of the kinetic energy of free motion of microscopic particles such as atoms, molecules, and electrons. From the thermodynamic viewpoint, for historical reasons, because of how it is defined and measured, this microscopic kinetic definition is regarded as an "empirical" temperature. It was adopted because in practice it can generally be measured more precisely than can Kelvin's thermodynamic temperature.


title: Thermodynamic temperature

text: A thermodynamic temperature reading of zero is of particular importance for the third law of thermodynamics. By convention, it is reported on the "Kelvin scale" of temperature in which the unit of measurement is the "kelvin" (unit symbol: K). For comparison, a temperature of 295 K is equal to 21.85 °C and 71.33 °F.


title: Thermodynamic temperature

text: Thermodynamic temperature, as distinct from SI temperature, is defined in terms of a macroscopic Carnot cycle. Thermodynamic temperature is of importance in thermodynamics because it is defined in purely thermodynamic terms. SI temperature is conceptually far different from thermodynamic temperature. Thermodynamic temperature was rigorously defined historically long before there was a fair knowledge of microscopic particles such as atoms, molecules, and electrons.


title: Thermodynamic temperature

text: The International System of Units (SI) specifies the international absolute scale for measuring temperature, and the unit of measure "kelvin" (unit symbol: K) for specific values along the scale. The kelvin is also used for denoting temperature "intervals" (a span or difference between two temperatures) as per the following example usage: "A 60/40 tin/lead solder is non-eutectic and is plastic through a range of 5 kelvins as it solidifies." A temperature interval of one degree Celsius is the same magnitude as one kelvin.


title: Thermodynamic temperature

text: The magnitude of the kelvin was redefined in 2019 in relation to the "very physical property" underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The redefinition fixed the Boltzmann constant at precisely (J/K). The compound unit of measure for the Boltzmann constant is often also written as J·K, with a multiplication dot (·) and a kelvin symbol that is followed by a superscripted "negative 1" exponent. This is another mathematical syntax denoting the same measure: "joules" (the SI unit for energy, including kinetic energy) "per kelvin".


title: Thermodynamic temperature

text: The microscopic property that imbues material substances with a temperature can be readily understood by examining the ideal gas law, which relates, per the Boltzmann constant, how heat energy causes precisely defined changes in the pressure and temperature of certain gases. This is because monatomic gases like helium and argon behave kinetically like freely moving perfectly elastic and spherical billiard balls that move only in a specific subset of the possible motions that can occur in matter: that comprising the "three translational" degrees of freedom. The translational degrees of freedom are the familiar billiard ball-like movements along the X, Y, and Z axes of 3D space (see "Fig. 1", below). This is why the noble gases all have the same specific heat capacity per atom and why that value is lowest of all the gases.


title: Thermodynamic temperature

text: Molecules (two or more chemically bound atoms), however, have "internal structure" and therefore have additional "internal" degrees of freedom (see "Fig. 3", below), which makes molecules absorb more heat energy for any given amount of temperature rise than do the monatomic gases. Heat energy is born in all available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same temperature as their three external degrees of freedom. However, the property that gives all gases their pressure, which is the net force per unit area on a container arising from gas particles recoiling off it, is a function of the kinetic energy borne in the freely moving atoms’ and molecules’ three translational degrees of freedom.


title: Thermodynamic temperature

text: Fixing the Boltzmann constant at a specific value, along with other rule making, had the effect of precisely establishing the magnitude of the unit interval of SI temperature, the kelvin, in terms of the average kinetic behavior of the noble gases. Moreover, the "starting point" of the thermodynamic temperature scale, absolute zero, was reaffirmed as the point at which "zero average kinetic energy" remains in a sample; the only remaining particle motion being that comprising random vibrations due to zero-point energy.


title: Thermodynamic temperature

text: Temperature scales are numerical. The numerical zero of a temperature scale is not bound to the absolute zero of temperature. Nevertheless, some temperature scales have their numerical zero coincident with the absolute zero of temperature. Examples are the International SI temperature scale, the Rankine temperature scale, and the thermodynamic temperature scale. Other temperature scales have their numerical zero far from the absolute zero of temperature. Examples are the Fahrenheit scale and the Celsius scale.


title: Thermodynamic temperature

text: At the zero point of thermodynamic temperature, absolute zero, the particle constituents of matter have minimal motion and can become no colder. Absolute zero, which is a temperature of zero kelvins (0 K), is precisely equal to −273.15 °C and −459.67 °F. Matter at absolute zero has no remaining transferable average kinetic energy and the only remaining particle motion is due to an ever-pervasive quantum mechanical phenomenon called ZPE (Zero-Point Energy). Though the atoms in, for instance, a container of liquid helium that was "precisely" at absolute zero would still jostle slightly due to zero-point energy, a theoretically perfect heat engine with such helium as one of its working fluids could never transfer any net kinetic energy (heat energy) to the other working fluid and no thermodynamic work could occur.


title: Thermodynamic temperature

text: Temperature is generally expressed in absolute terms when scientifically examining temperature's interrelationships with certain other physical properties of matter such as its volume or pressure (see Gay-Lussac's law), or the wavelength of its emitted black-body radiation. Absolute temperature is also useful when calculating chemical reaction rates (see Arrhenius equation). Furthermore, absolute temperature is typically used in cryogenics and related phenomena like superconductivity, as per the following example usage:


title: Thermodynamic temperature

text: "Conveniently, tantalum's transition temperature ("T") of 4.4924 kelvin is slightly above the 4.2221 K boiling point of helium."


title: Thermodynamic temperature

text: The Boltzmann constant and its related formulas describe the realm of particle kinetics and velocity vectors whereas ZPE (zero-point energy) is an energy field that jostles particles in ways described by the mathematics of quantum mechanics. In atomic and molecular collisions in gases, ZPE introduces a degree of "chaos", i.e., unpredictability, to rebound kinetics; it is as likely that there will be "less" ZPE-induced particle motion after a given collision as "more". This random nature of ZPE is why it has no net effect upon either the pressure or volume of any "bulk quantity" (a statistically significant quantity of particles) of gases. However, in temperature condensed matter; e.g., solids and liquids, ZPE causes inter-atomic jostling where atoms would otherwise be perfectly stationary. Inasmuch as the real-world effects that ZPE has on substances can vary as one alters a thermodynamic system (for example, due to ZPE, helium won't freeze unless under a pressure of at least 2.5 MPa (25 bar)), ZPE is very much a form of thermal energy and may properly be included when tallying a substance's internal energy.


title: Thermodynamic temperature

text: Though there have been many other temperature scales throughout history, there have been only two scales for measuring thermodynamic temperature where absolute zero is their null point (0): The Kelvin scale and the Rankine scale.


title: Thermodynamic temperature

text: Throughout the scientific world where modern measurements are nearly always made using the International System of Units, thermodynamic temperature is measured using the Kelvin scale. The Rankine scale is part of English engineering units in the United States and finds use in certain engineering fields, particularly in legacy reference works. The Rankine scale uses the "degree Rankine" (symbol: °R) as its unit, which is the same magnitude as the degree Fahrenheit (symbol: °F).


title: Thermodynamic temperature

text: A unit increment of one degree Rankine is precisely 1.8 times smaller in magnitude than one kelvin; thus, to convert a specific temperature on the Kelvin scale to the Rankine scale, , and to convert from a temperature on the Rankine scale to the Kelvin scale, . Consequently, absolute zero is "0" for both scales, but the melting point of water ice (0 °C and 273.15 K) is 491.67 °R.


title: Thermodynamic temperature

text: To convert temperature "intervals" (a span or difference between two temperatures), one uses the same formulas from the preceding paragraph; for instance, a range of 5 kelvins is precisely equal to a range of 9 degrees Rankine.


title: Thermodynamic temperature

text: For 65 years, between 1954 and the 2019 redefinition of the SI base units, a temperature interval of one kelvin was defined as the difference between the triple point of water and absolute zero. The 1954 resolution by the International Bureau of Weights and Measures (known by the French-language acronym BIPM), plus later resolutions and publications, defined the triple point of water as precisely 273.16 K and acknowledged that it was "common practice" to accept that due to previous conventions (namely, that 0 °C had long been defined as the melting point of water and that the triple point of water had long been experimentally determined to be indistinguishably close to 0.01 °C), the difference between the Celsius scale and Kelvin scale is accepted as 273.15 kelvins; which is to say, 0 °C equals 273.15 kelvins. The net effect of this as well as later resolutions was twofold: 1) they defined absolute zero as precisely 0 K, and 2) they defined that the triple point of special isotopically controlled water called Vienna Standard Mean Ocean Water was precisely 273.16 K and 0.01 °C. One effect of the aforementioned resolutions was that the melting point of water, while "very" close to 273.15 K and 0 °C, was not a defining value and was subject to refinement with more precise measurements.


title: Thermodynamic temperature

text: The 1954 BIPM standard did a good job of establishing—within the uncertainties due to isotopic variations between water samples—temperatures around the freezing and triple points of water, but required that "intermediate values" between the triple point and absolute zero, as well as extrapolated values from room temperature and beyond, to be experimentally determined via apparatus and procedures in individual labs. This shortcoming was addressed by the International Temperature Scale of 1990, or ITS90, which defined 13 additional points, from 13.8033 K, to 1,357.77 K. While definitional, ITS90 had—and still has—some challenges, partly because eight of its extrapolated values depend upon the melting or freezing points of metal samples, which must remain exceedingly pure lest their melting or freezing points be affected—usually depressed.


title: Thermodynamic temperature

text: The 2019 redefinition of the SI base units was primarily for the purpose of decoupling much of the SI system's definitional underpinnings from the kilogram, which was the last physical artifact defining an SI base unit (a platinum/iridium cylinder stored under three nested bell jars in a safe located in France) and which had highly questionable stability. The solution required that four physical constants, including the Boltzmann constant, be definitionally fixed.


title: Thermodynamic temperature

text: Assigning the Boltzmann constant a precisely defined value had no practical effect on modern thermometry except for the most exquisitely precise measurements. Before the redefinition, the triple point of water was exactly 273.16 K and 0.01 °C and the Boltzmann constant was experimentally determined to be , where the "(51)" denotes the uncertainty in the two least significant digits (the 03) and equals a relative standard uncertainty of 0.37 ppm. Afterwards, by defining the Boltzmann constant as exactly , the 0.37 ppm uncertainty was transferred to the triple point of water, which became an experimentally determined value of (). That the triple point of water ended up being exceedingly close to 273.16 K after the SI redefinition was no accident; the final value of the Boltzmann constant was determined, in part, through clever experiments with argon and helium that used the triple point of water for their key reference temperature.


title: Thermodynamic temperature

text: Notwithstanding the 2019 redefinition, water triple-point cells continue to serve in modern thermometry as exceedingly precise calibration references at 273.16 K and 0.01 °C. Moreover, the triple point of water remains one of the 14 calibration points comprising ITS90, which spans from the triple point of hydrogen (13.8033 K) to the freezing point of copper (1,357.77 K), which is a nearly hundredfold range of thermodynamic temperature.


title: Thermodynamic temperature

text: The thermodynamic temperature of any "bulk quantity" of a substance (a statistically significant quantity of particles) is directly proportional to the mean average kinetic energy of a specific kind of particle motion known as "translational motion". These simple movements in the three X, Y, and Z–axis dimensions of space means the particles move in the three spatial "degrees of freedom". This particular form of kinetic energy is sometimes referred to as "kinetic temperature". Translational motion is but one form of heat energy and is what gives gases not only their temperature, but also their pressure and the vast majority of their volume. This relationship between the temperature, pressure, and volume of gases is established by the ideal gas law's formula and is embodied in the gas laws.


title: Thermodynamic temperature

text: Though the kinetic energy borne exclusively in the three translational degrees of freedom comprise the thermodynamic temperature of a substance, molecules, as can be seen in "Fig. 3", can have other degrees of freedom, all of which fall under three categories: bond length, bond angle, and rotational. All three additional categories are not necessarily available to all molecules, and even for molecules that "can" experience all three, some can be "frozen out" below a certain temperature. Nonetheless, all those degrees of freedom that are available to the molecules under a particular set of conditions contribute to the specific heat capacity of a substance; which is to say, they increase the amount of heat (kinetic energy) required to raise a given amount of the substance by one kelvin or one degree Celsius.


title: Thermodynamic temperature

text: The relationship of kinetic energy, mass, and velocity is given by the formula "E" = "mv". Accordingly, particles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy, and precisely the same temperature, as those with four times the mass but half the velocity.


title: Thermodynamic temperature

text: The extent to which the kinetic energy of translational motion in a statistically significant collection of atoms or molecules in a gas contributes to the pressure and volume of that gas is a proportional function of thermodynamic temperature as established by the Boltzmann constant (symbol: "k"). The Boltzmann constant also relates the thermodynamic temperature of a gas to the mean kinetic energy of an "individual" particles’ translational motion as follows:


title: Thermodynamic temperature

text: While the Boltzmann constant is useful for finding the mean kinetic energy in a sample of particles, it is important to note that even when a substance is isolated and in thermodynamic equilibrium (all parts are at a uniform temperature and no heat is going into or out of it), the translational motions of individual atoms and molecules occurs across a wide range of speeds (see animation in "Fig. 1 "above). At any one instant, the proportion of particles moving at a given speed within this range is determined by probability as described by the Maxwell–Boltzmann distribution. The graph shown here in "Fig. 2"  shows the speed distribution of 5500 K helium atoms. They have a "most probable" speed of 4.780 km/s (0.2092 s/km). However, a certain proportion of atoms at any given instant are moving faster while others are moving relatively slowly; some are momentarily at a virtual standstill (off the "x"–axis to the right). This graph uses "inverse speed" for its "x"–axis so the shape of the curve can easily be compared to the curves in "" below. In both graphs, zero on the "x"–axis represents infinite temperature. Additionally, the "x" and "y"–axis on both graphs are scaled proportionally.


title: Thermodynamic temperature

text: Although very specialized laboratory equipment is required to directly detect translational motions, the resultant collisions by atoms or molecules with small particles suspended in a fluid produces Brownian motion that can be seen with an ordinary microscope. The translational motions of elementary particles are "very" fast and temperatures close to absolute zero are required to directly observe them. For instance, when scientists at the NIST achieved a record-setting cold temperature of 700 nK (billionths of a kelvin) in 1994, they used optical lattice laser equipment to adiabatically cool cesium atoms. They then turned off the entrapment lasers and directly measured atom velocities of 7 mm per second to in order to calculate their temperature.  Formulas for calculating the velocity and speed of translational motion are given in the following footnote.


title: Thermodynamic temperature

text: It is neither difficult to imagine atomic motions due to kinetic temperature, nor distinguish between such motions and those due to zero-point energy. Consider the following hypothetical thought experiment, as illustrated in "Fig. 2.5" at left, with an atom that is exceedingly close to absolute zero. Imagine peering through a common optical microscope set to 400 power, which is about the maximum practical magnification for optical microscopes. Such microscopes generally provide fields of view a bit over 0.4 mm in diameter. At the center of the field of view is a single levitated argon atom (argon comprises about 0.93% of air) that is illuminated and glowing against a dark backdrop. If this argon atom was at a beyond-record-setting "one-trillionth" of a kelvin above absolute zero, and was moving perpendicular to the field of view towards the right, it would require 13.9 seconds to move from the center of the image to the 200-micron tick mark; this travel distance is about the same as the width of the period at the end of this sentence on modern computer monitors. As the argon atom slowly moved, the positional jitter due to zero-point energy would be much less than the 200-nanometer (0.0002 mm) resolution of an optical microscope. Importantly, the atom's translational velocity of 14.43 microns per second constitutes all its retained kinetic energy due to not being precisely at absolute zero. Were the atom "precisely" at absolute zero, imperceptible jostling due to zero-point energy would cause it to very slightly wander, but the atom would perpetually be located, on average, at the same spot within the field of view. This is analogous to a boat that has had its motor turned off and is now bobbing slightly in relatively calm and windless ocean waters; even though the boat randomly drifts to and fro, it stays in the same spot in the long term and makes no headway through the water. Accordingly, an atom that was precisely at absolute zero would not be "motionless", and yet, a statistically significant collection of such atoms would have zero net kinetic energy available to transfer to any other collection of atoms. This is because regardless of the kinetic temperature of the second collection of atoms, they too experience the effects of zero-point energy. Such are the consequences of statistical mechanics and the nature of thermodynamics.


title: Thermodynamic temperature

text: As mentioned above, there are other ways molecules can jiggle besides the three translational degrees of freedom that imbue substances with their kinetic temperature. As can be seen in the animation at right, molecules are complex objects; they are a population of atoms and thermal agitation can strain their internal chemical bonds in three different ways: via rotation, bond length, and bond angle movements; these are all types of "internal degrees of freedom". This makes molecules distinct from "monatomic" substances (consisting of individual atoms) like the noble gases helium and argon, which have only the three translational degrees of freedom (the X, Y, and Z axis). Kinetic energy is stored in molecules' internal degrees of freedom, which gives them an "internal temperature". Even though these motions are called "internal", the external portions of molecules still move—rather like the jiggling of a stationary water balloon. This permits the two-way exchange of kinetic energy between internal motions and translational motions with each molecular collision. Accordingly, as internal energy is removed from molecules, both their kinetic temperature (the kinetic energy of translational motion) and their internal temperature simultaneously diminish in equal proportions. This phenomenon is described by the equipartition theorem, which states that for any bulk quantity of a substance in equilibrium, the kinetic energy of particle motion is evenly distributed among all the active degrees of freedom available to the particles. Since the internal temperature of molecules are usually equal to their kinetic temperature, the distinction is usually of interest only in the detailed study of non-local thermodynamic equilibrium (LTE) phenomena such as combustion, the sublimation of solids, and the diffusion of hot gases in a partial vacuum.


title: Thermodynamic temperature

text: Thekinetic energy stored internally in molecules causes substances to contain more heat energy at any given temperature and to absorb additional internal energy for a given temperature increase. This is because any kinetic energy that is, at a given instant, bound in internal motions, is not contributing to the molecules' translational motions at that same instant . This extra kinetic energy simply increases the amount of internal energy that substance absorbs for a given temperature rise. This property is known as a substance's specific heat capacity.


title: Thermodynamic temperature

text: Different molecules absorb different amounts of internal energy for each incremental increase in temperature; that is, they have different specific heat capacities. High specific heat capacity arises, in part, because certain substances’ molecules possess more internal degrees of freedom than others do. For instance, room-temperature nitrogen, which is a diatomic molecule, has "five" active degrees of freedom: the three comprising translational motion plus two rotational degrees of freedom internally. Not surprisingly, in accordance with the equipartition theorem, nitrogen has five-thirds the specific heat capacity per mole (a specific number of molecules) as do the monatomic gases. Another example is gasoline (see table showing its specific heat capacity). Gasoline can absorb a large amount of heat energy per mole with only a modest temperature change because each molecule comprises an average of 21 atoms and therefore has many internal degrees of freedom. Even larger, more complex molecules can have dozens of internal degrees of freedom.


title: Thermodynamic temperature

text: "Heat conduction" is the diffusion of thermal energy from hot parts of a system to cold parts. A system can be either a single bulk entity or a plurality of discrete bulk entities. The term "bulk" in this context means a statistically significant quantity of particles (which can be a microscopic amount). Whenever thermal energy diffuses within an isolated system, temperature differences within the system decrease (and entropy increases).


title: Thermodynamic temperature

text: One particular heat conduction mechanism occurs when translational motion, the particle motion underlying temperature, transfers momentum from particle to particle in collisions. In gases, these translational motions are of the nature shown above in "Fig. 1". As can be seen in that animation, not only does momentum (heat) diffuse throughout the volume of the gas through serial collisions, but entire molecules or atoms can move forward into new territory, bringing their kinetic energy with them. Consequently, temperature differences equalize throughout gases very quickly—especially for light atoms or molecules; convection speeds this process even more.


title: Thermodynamic temperature

text: Translational motion in "solids", however, takes the form of "phonons" (see "Fig. 4" at right). Phonons are constrained, quantized wave packets that travel at the speed of sound of a given substance. The manner in which phonons interact within a solid determines a variety of its properties, including its thermal conductivity. In electrically insulating solids, phonon-based heat conduction is "usually" inefficient and such solids are considered "thermal insulators" (such as glass, plastic, rubber, ceramic, and rock). This is because in solids, atoms and molecules are locked into place relative to their neighbors and are not free to roam.


title: Thermodynamic temperature

text: Metals however, are not restricted to only phonon-based heat conduction. Thermal energy conducts through metals extraordinarily quickly because instead of direct molecule-to-molecule collisions, the vast majority of thermal energy is mediated via very light, mobile "conduction electrons". This is why there is a near-perfect correlation between metals' thermal conductivity and their electrical conductivity. Conduction electrons imbue metals with their extraordinary conductivity because they are "delocalized" (i.e., not tied to a specific atom) and behave rather like a sort of quantum gas due to the effects of "zero-point energy" (for more on ZPE, see "Note 1" below). Furthermore, electrons are relatively light with a rest mass only that of a proton. This is about the same ratio as a .22 Short bullet (29 grains or 1.88 g) compared to the rifle that shoots it. As Isaac Newton wrote with his third law of motion,


title: Thermodynamic temperature

text: However, a bullet accelerates faster than a rifle given an equal force. Since kinetic energy increases as the square of velocity, nearly all the kinetic energy goes into the bullet, not the rifle, even though both experience the same force from the expanding propellant gases. In the same manner, because they are much less massive, thermal energy is readily borne by mobile conduction electrons. Additionally, because they're delocalized and "very" fast, kinetic thermal energy conducts extremely quickly through metals with abundant conduction electrons.


title: Thermodynamic temperature

text: Thermal radiation is a byproduct of the collisions arising from various vibrational motions of atoms. These collisions cause the electrons of the atoms to emit thermal photons (known as black-body radiation). Photons are emitted anytime an electric charge is accelerated (as happens when electron clouds of two atoms collide). Even "individual molecules" with internal temperatures greater than absolute zero also emit black-body radiation from their atoms. In any bulk quantity of a substance at equilibrium, black-body photons are emitted across a range of wavelengths in a spectrum that has a bell curve-like shape called a Planck curve (see graph in "Fig. 5" at right). The top of a Planck curve (the peak emittance wavelength) is located in a particular part of the electromagnetic spectrum depending on the temperature of the black-body. Substances at extreme cryogenic temperatures emit at long radio wavelengths whereas extremely hot temperatures produce short gamma rays (see "Table of common temperatures").