title: John Churchill, 1st Duke of Marlborough

text: Since Walcourt, though, Marlborough's popularity at court had waned. William and Mary distrusted both Lord and Lady Marlborough's influence as confidants and supporters of Princess Anne (whose claim to the throne was stronger than William's). Sarah had supported Anne in a series of court disputes with the joint monarchs, infuriating Mary who included the Earl in her disfavour of his scheming wife. Yet for the moment the clash of tempers were over-shadowed by more pressing events in Ireland where James had landed in March 1689 in an attempt to regain his thrones. When William left for Ireland in June 1690 Marlborough became commander of all troops and militia in England, and was appointed a member of the Council of Nine to advise Mary on military matters in the King's absence; but she made scant effort to disguise her distaste at his appointment – "I can neither trust or esteem him", she wrote to William.


title: John Churchill, 1st Duke of Marlborough

text: William III's victory at the Battle of the Boyne on 1 July 1690 (O.S.) forced James II to abandon his army and flee back to France. In August Marlborough himself left for Ireland engaged upon his first independent command – a land/sea operation upon the southern ports of Cork and Kinsale. It was a bold, imaginative project aimed at disrupting Jacobite supply routes, and one which the Earl conceived and executed with outstanding success. Cork fell on 27 September (O.S.), and Kinsale followed in mid-October. Although the campaign did not end the war in Ireland as Marlborough hoped, it taught him the significance of the minutiae of logistics, and the importance of cooperation and tact when working alongside other senior Allied commanders. It would, however, be more than ten years before he once again took charge in the field.


title: John Churchill, 1st Duke of Marlborough

text: William III recognised Marlborough's qualities as a soldier and strategist, but the refusal of the Order of the Garter and failure to appoint him Master-General of the Ordnance rankled with the ambitious Earl; nor did Marlborough conceal his bitter disappointment behind his usual bland discretion. Using his influence in Parliament and the army, Marlborough aroused dissatisfaction concerning William's preferences for foreign commanders, an exercise designed to force the King's hand. Aware of this, William in turn began to speak openly of his distrust of Marlborough; the Elector of Brandenburg's envoy to London overheard the King remark that he had been treated – "so infamously by Marlborough that, had he not been King, he would have felt it necessary to challenge him to a duel".


title: John Churchill, 1st Duke of Marlborough

text: Since January 1691 Marlborough had been in contact with the exiled James II in Saint-Germain, anxious to obtain the erstwhile King's pardon for deserting him in 1688 – a pardon essential for the success of his future career in the not altogether unlikely event of a Jacobite restoration. James himself maintained contact with his supporters in England whose principal object was to re-establish him upon his throne. William was well aware of these contacts (as well as others such as Godolphin and the Duke of Shrewsbury), but their double-dealing was seen more in the nature of an insurance policy, rather than as an explicit commitment. Marlborough did not wish for a Jacobite restoration, but William was conscious of his military and political qualities, and the danger the Earl posed: "William was not prone to fear", wrote Thomas Macaulay, "but if there was anyone on earth that he feared, it was Marlborough".


title: John Churchill, 1st Duke of Marlborough

text: By the time William and Marlborough had returned from an uneventful campaign in the Spanish Netherlands in October 1691, their relationship had further deteriorated. In January 1692, the Queen, angered by Marlborough's intrigues in Parliament, the army, and even with Saint-Germain, ordered Anne to dismiss Sarah from her household – Anne refused. This personal dispute precipitated Marlborough's dismissal. On 30 January 1692 (20 January 1691 O.S.), the Earl of Nottingham, Secretary of State, ordered Marlborough to dispose of all his posts and offices, both civil and military, and consider himself dismissed from all appointments and forbidden the court. No reasons were given but Marlborough's chief associates were outraged: Shrewsbury voiced his disapproval and Godolphin threatened to retire from government. Admiral Russell, now commander-in-chief of the Navy, personally accused the King of ingratitude to the man who had "set the crown upon his head".


title: John Churchill, 1st Duke of Marlborough

text: The nadir of Marlborough's fortunes had not yet been reached. The spring of 1692 brought renewed threats of a French invasion and new accusations of Jacobite treachery. Acting on the testimony of one Robert Young, the Queen had arrested all the signatories to a letter purporting the restoration of James II and the seizure of William III. Marlborough, as one of these signatories, was sent to the Tower of London on 4 May (O.S.) where he languished for five weeks; his anguish compounded by the news of the death of his younger son Charles on 22 May (O.S.). Young's letters were eventually discredited as forgeries and Marlborough was released on 15 June (O.S.), but he continued his correspondence with James, leading to the celebrated incident of the "Camaret Bay letter" of 1694.


title: John Churchill, 1st Duke of Marlborough

text: For several months the Allies had been planning an attack on Brest, the French port in the West of Brittany. The French had received intelligence alerting them to the imminent assault, enabling Marshal Vauban to strengthen its defences and reinforce the garrison. Inevitably the attack on 18 June led by Thomas Tollemache ended in disaster; most of his men were killed or captured, and Tollemache himself died of his wounds shortly afterwards. Despite lacking evidence, Marlborough's detractors claimed that it was he who had alerted the enemy. Macaulay states that in a letter on 3 May 1694 Marlborough betrayed the Allied plans to James, thus ensuring that the landing failed and that Tollemache, a talented rival, was killed or discredited as a direct result. Historians such as John Paget and C. T. Atkinson conclude that he probably did write the letter, but did so only when he knew that it would be received too late for its information to be of any practical use (the plan of the attack on Brest was widely known, and the French had already begun to strengthen their defences in April). To Richard Holmes, the evidence linking Marlborough with the Camaret Bay letter (which no longer exists), is slender, concluding, "It is very hard to imagine a man as careful as Marlborough, only recently freed from suspicion of treason, writing a letter which would kill him if it fell into the wrong hands". However, David Chandler surmises that, "the whole episode is so obscure and inconclusive that it is still not possible to make a definite ruling. In sum, perhaps we should award Marlborough the benefit of the doubt".


title: John Churchill, 1st Duke of Marlborough

text: Mary's death on 28 December 1694 (O.S.) eventually led to a formal but cool reconciliation between William III and Anne, now heir to the throne. Marlborough hoped that the rapprochement would lead to his own return to office, but although he and Lady Marlborough were allowed to return to court, the Earl received no offer of employment.


title: John Churchill, 1st Duke of Marlborough

text: In 1696 Marlborough, together with Godolphin, Russell and Shrewsbury, was yet again implicated in a treasonous plot with James II, this time instigated by the Jacobite militant John Fenwick. The accusations were eventually dismissed as a fabrication and Fenwick executed – the King himself had remained incredulous – but it was not until 1698, a year after the Treaty of Ryswick brought an end to the Nine Years' War, that the corner was finally turned in William's and Marlborough's relationship. On the recommendation of Lord Sunderland (whose wife was a close friend of Lady Marlborough), William eventually offered Marlborough the post of governor to the Duke of Gloucester, Anne's eldest son; he was also restored to the Privy Council, together with his military rank. When William left for Holland in July, Marlborough was one of the Lords Justices left running the government in his absence; but striving to reconcile his close Tory connections with that of the dutiful royal servant was difficult, leading Marlborough to complain – "The King's coldness to me still continues".


title: John Churchill, 1st Duke of Marlborough

text: In the late 17th and early 18th centuries, the single most important theme in European politics was the rivalry between the House of Habsburg and the House of Bourbon. In 1665, the infirm and childless Habsburg Charles II became the King of Spain. Spain was no longer the dominant global power it once was but remained a vast global confederation, with possessions in Italy, the Spanish Netherlands, the Philippines and large parts of the Americas. It proved remarkably resilient; when Charles died in 1700, it was largely intact and had even expanded in areas like the Pacific. Its possession could change the balance of power in favour of either France or Austria.


title: John Churchill, 1st Duke of Marlborough

text: Attempts to partition the Empire between the French and Austrian candidates or install an alternative from the Bavarian Wittelsbach dynasty failed. When Charles died, he left his throne to Louis XIV's grandson who became Philip V of Spain on 16 November 1700. However, this was on condition Philip renounce his claim to the French throne; Louis' decision to ignore this once again threatened French domination over Europe and led to the Grand Alliance being reformed in 1701.


title: John Churchill, 1st Duke of Marlborough

text: With his health deteriorating, William III appointed Marlborough Ambassador-Extraordinary and commander of English forces to attend the conference at the Hague. On 7 September 1701, the Treaty of the Second Grand Alliance nominated Emperor Leopold I's second son Archduke Charles as King of Spain instead of Phillip. It was signed by England, the Dutch Republic and the Holy Roman Empire represented by Emperor Leopold I, head of the Austrian Habsburgs; however, the increasing independence of German states within the Empire meant Bavaria now allied itself with France.


title: John Churchill, 1st Duke of Marlborough

text: William III died on 8 March 1702 (O.S.) from injuries sustained in a riding accident and was succeeded by his sister-in-law Anne. While his death was expected, it deprived the Alliance of its most obvious leader although Marlborough's personal position was further strengthened by his close relationship with the new Queen. Anne appointed him Master-General of the Ordnance, a Knight of the Garter and Captain-General of her armies at home and abroad. Lady Marlborough was made Groom of the Stool, Mistress of the Robes and Keeper of the Privy Purse giving them a combined annual income of over £60,000 and unrivalled influence at court.


title: John Churchill, 1st Duke of Marlborough

text: On 4 May 1702 (O.S.) England formally declared war on France. Marlborough was given command of the English, Dutch, and hired German forces, but he had not as yet commanded a large army in the field, and had far less experience than a dozen Dutch and German generals who now had to work under him. His command had its limitations, however. As commander of Anglo-Dutch forces he had the power to give orders to Dutch generals only when their troops were in action with his own; at all other times he had to rely on his powers of tact and persuasion, and gain the consent of accompanying Dutch field deputies or political representatives of the States General. The Dutch generals and deputies were concerned by the threat of an invasion from a powerful enemy. Nevertheless, despite his Allies' initial lassitude the campaign in the Low Countries (the war's principal theatre) began well for Marlborough. After outmanoeuvring Marshal Boufflers, he captured Venlo, Roermond, Stevensweert and Liège, for which in December a grateful Queen publicly proclaimed Marlborough a duke.


title: John Churchill, 1st Duke of Marlborough

text: On 9 February 1703 (O.S.), soon after the Marlboroughs' elevation, their daughter Elizabeth married Scroop Egerton, Earl of Bridgewater. This was followed in the summer by an engagement between Mary and John Montagu, heir to the Earl of, and later Duke of Montagu, (they later married on 20 March 1705 (O.S.)). Their two older daughters were already married: Henrietta to Godolphin's son Francis in April 1698, and Anne to the hot-headed and intemperate Charles Spencer, Earl of Sunderland in 1700. However, Marlborough's hopes of founding a great dynasty of his own reposed in his eldest and only surviving son, John, who, since his father's elevation, had borne the courtesy title of Marquess of Blandford. But while studying at Cambridge in early 1703, the 17-year-old was stricken with a severe strain of smallpox. His parents rushed to be by his side, but on Saturday morning, 20 February (O.S.), the boy died, plunging the duke into "the greatest sorrow in the world".


title: John Churchill, 1st Duke of Marlborough

text: Bearing his grief, and leaving Sarah to hers, the Duke returned to The Hague at the beginning of March. By now Marshal Villeroi had replaced Boufflers as commander in the Spanish Netherlands, but although Marlborough was able to take Bonn, Huy, and Limbourg in 1703, the "Great Design" – the Anglo-Dutch plan to secure Antwerp and thereby open the river lines into Flanders and Brabant – was left in ruins by Villeroi's initiative, poor Allied co-ordination, and by General Obdam's defeat at the Battle of Eckeren on 30 June. Domestically the Duke also encountered problems. The moderate Tory ministry of Marlborough, the Lord Treasurer Godolphin, and the Speaker of the House of Commons Robert Harley, were hampered by, and often at variance with, their High Tory colleagues whose strategic policy favoured the full employment of the Royal Navy in pursuit of trade advantages and colonial expansion overseas. To the Tories an action at sea was preferable to one ashore: rather than attack the enemy where they were strongest the Tories proposed to attack Louis XIV and Philip V where they were weakest – in their colonial empires and on the high seas. In contrast the Whigs, led by their Junto, enthusiastically supported the Ministry's Continental strategy of thrusting the army into the heart of France. This support wilted somewhat following the Allies' recent campaign, but the Duke, whose diplomatic tact had held together a very discordant Grand Alliance, was now a general of international repute, and the limited success of 1703 was soon eclipsed by the Blenheim campaign.


title: John Churchill, 1st Duke of Marlborough

text: Pressed by the French and Bavarians to the west and Hungarian rebels to the east, Austria faced the real possibility of being forced out of the war. Concerns over Vienna and the situation in southern Germany convinced Marlborough of the necessity of sending aid to the Danube; but the scheme of seizing the initiative from the enemy was extremely bold. From the start the Duke resolved to mislead the Dutch, who would never willingly permit any major weakening of Allied forces in the Spanish Netherlands. To this end, Marlborough moved his English troops to the Moselle (a plan approved of by The Hague), but once there he planned to slip the Dutch leash and march south to link up with Austrian forces in southern Germany.


title: John Churchill, 1st Duke of Marlborough

text: A combination of strategic deception and brilliant administration enabled Marlborough to achieve his purpose. After marching from the Low Countries, the Allies fought a series of engagements against the Franco-Bavarian forces ranged against them on the Danube. The first major encounter occurred on 2 July 1704 when Marlborough and Prince Louis of Baden stormed the Schellenberg heights at Donauwörth. However, the main event followed on 13 August when Marlborough – assisted by the Imperial commander, the able Prince Eugene of Savoy – delivered a crushing defeat on Marshal Tallard's and the Elector of Bavaria's army at the Battle of Blenheim. The whole campaign, which historian John A. Lynn describes as one of the greatest examples of marching and fighting before Napoleon, had been a model of planning, logistics, tactical and operational skill, the successful outcome of which had altered the course of the conflict – Bavaria was knocked out of the war, and Louis XIV's hopes of an early victory were destroyed. With the subsequent fall of Landau on the Rhine, and Trier and Trarbach on the Moselle, Marlborough now stood as the foremost soldier of the age. Even the Tories, who had declared that should he fail they would "break him up like hounds on a hare", could not entirely restrain their patriotic admiration.


title: John Churchill, 1st Duke of Marlborough

text: The Queen lavished upon her favourite the royal manor of Woodstock and the promise of a fine palace commemorative of his great victory at Blenheim; but since her accession her relationship with Sarah had become progressively distant. The Duke and Duchess had risen to greatness not least because of their intimacy with Anne, but the Duchess's relentless campaign against the Tories (Sarah was a firm Whig) isolated her from the Queen whose natural inclinations lay with the Tories, the staunch supporters of the Church of England. For her part, Anne, now Queen and no longer the timid adolescent so easily dominated by her more beautiful friend, had grown tired of Sarah's tactless political hectoring and increasingly haughty manner which, in the coming years, were to destroy their friendship and undermine the position of her husband.


title: John Churchill, 1st Duke of Marlborough

text: During the Duke's march to the Danube Emperor Leopold I offered to make Marlborough a prince of the Holy Roman Empire in the small principality of Mindelheim. The Queen enthusiastically agreed to this elevation, but after the successes of 1704, the campaign of 1705 brought little reason for satisfaction on the Continent. The planned invasion of France via the Moselle valley was frustrated by friend and foe alike, forcing the Duke to withdraw back towards the Low Countries. Although Marlborough penetrated the Lines of Brabant at Elixheim in July, Allied indecision and considerable Dutch hesitancy (concerned as they were for the security of their homeland), prevented the Duke from pressing his advantage. The French and the Tories in England dismissed arguments that only Dutch obstructionism had robbed Marlborough of a great victory in 1705, confirmed in their belief that Blenheim had been a chance occurrence and that Marlborough was a general not to be feared.


title: John Churchill, 1st Duke of Marlborough

text: The early months of 1706 also proved frustrating for the Duke as Louis XIV's generals gained early successes in Italy and Alsace. These setbacks thwarted Marlborough's original plans for the coming campaign, but he soon adjusted his schemes and marched into enemy territory. Louis XIV, equally determined to fight and avenge Blenheim, goaded his commander, Marshal Villeroi, to seek out "Monsieur Marlbrouck". The subsequent Battle of Ramillies, fought in the Spanish Netherlands on 23 May, was perhaps Marlborough's most successful action, and one in which he had himself characteristically drawn his sword at the pivotal moment. For the loss of fewer than 3,000 dead and wounded (far fewer than Blenheim), his victory had cost the enemy some 20,000 casualties, inflicting in the words of Marshal Villars, "the most shameful, humiliating and disastrous of routs". The campaign was an unsurpassed operational triumph for the English general. Town after town subsequently fell to the Allies. "It really looks more like a dream than truth", wrote Marlborough to Sarah.


title: John Churchill, 1st Duke of Marlborough

text: While Marlborough fought in the Low Countries, a series of personal and party rivalries instigated a general reversal of fortune. The Whigs, who were the main prop of the war, had been laying siege to Godolphin. As a price for supporting the government in the next parliamentary session, the Whigs demanded a share of public office with the appointment of a leading member of their Junto, the Earl of Sunderland (Marlborough's son-in-law), to the post of Secretary of State. The Queen, who loathed Sunderland and the Junto, and who refused to be dominated by any single party, bitterly opposed the move; but Godolphin, increasingly dependent on Whig support, had little room for manoeuvre. With Sarah's tactless, unsubtle backing, Godolphin relentlessly pressed the Queen to submit to Whig demands. In despair, Anne finally relented and Sunderland received the seals of office; but the special relationship between Godolphin, Sarah, and the Queen had taken a severe blow and she began to turn increasingly to a new favourite – Sarah's cousin, Abigail Masham. Anne also became ever more reliant on the advice of Harley, who, convinced that the duumvirate's policy of appeasing the Whig Junto was unnecessary, had set himself up as alternative source of advice to a sympathetic Queen.


title: John Churchill, 1st Duke of Marlborough

text: Following his victory at Ramillies, Marlborough returned to England and the acclamation of Parliament; his titles and estates were made perpetual upon his heirs, male or female, in order that "the memory of these deeds should never lack one of his name to bear it". However, the Allied successes were followed in 1707 with a resurgence in French arms in all fronts of the war, and a return to political squabbling and indecision within the Grand Alliance. The Great Northern War also threatened dire consequences. The French had hoped to entice King Charles XII of Sweden to attack the Empire regarding grievances over the Polish Succession. In a pre-campaign visit to the King's headquarters at Altranstädt, Marlborough's diplomacy helped placate Charles and prevent his interference regarding the Spanish Succession. Following the 1706 Treaty of Altranstädt, Tsar Peter the Great of Russia unsuccessfully offered the yet to be conquered Polish crown to Marlborough, among other candidates.


title: John Churchill, 1st Duke of Marlborough

text: In Altranstädt, Marlborough reportedly approached Carl Piper, the most favoured of the King's advisers. Allegedly, he offered Piper a pension in exchange for advising Charles XII to launch an invasion of Russia, as this would distract Charles from interfering in the War of the Spanish Succession. Carl Piper was accused of having accepted Marlborough's bribe, advising Charles to invade Russia. Carl Piper denied having accepted Marlborough's offer, but he did admit that Marlborough provided his wife, Christina Piper with a pair of valuable earrings which she accepted, and it was the habit of Carl to personally refuse bribes but allow his wife to accept them and then follow her advice.


title: John Churchill, 1st Duke of Marlborough

text: Nevertheless, major setbacks in Spain at Almansa and along the Rhine in Southern Germany, had caused Marlborough great anxiety. Prince Eugene's retreat from Toulon (Marlborough's major goal for 1707) ended any lingering hopes of a war-winning blow that year.


title: John Churchill, 1st Duke of Marlborough

text: Marlborough returned from these tribulations to a political storm as the Ministry's critics turned to attack the overall conduct of the war. The Duke and Godolphin had initially agreed to explore a "moderate scheme" with Harley and reconstruct the government, but they were incensed when Harley privately criticised the management of the war in Spain to the Queen, and his associate Henry St John, the Secretary at War, raised the issue in Parliament. Convinced of Harley's caballing, the duumvirs threatened the Queen with resignation unless she dismissed him. Anne fought stubbornly to keep her favourite minister, but when the Duke of Somerset and the Earl of Pembroke refused to act without "the General nor the Treasurer", Harley resigned: Henry Boyle replaced him as Secretary of State, and his fellow Whig, Robert Walpole, replaced St John as Secretary at War. The struggle had given Marlborough a final lease of power but it was a Whig victory, and he had to a large extent lost his hold on the Queen.


title: John Churchill, 1st Duke of Marlborough

text: The military setbacks of 1707 continued through the opening months of 1708, with the defection of Bruges and Ghent to the French. Marlborough remained despondent about the general situation, but his optimism received a major boost with the arrival in theatre of Prince Eugene, his co-commander at Blenheim. Heartened by the Prince's robust confidence, Marlborough set about to regain the strategic initiative. After a forced march, the Allies crossed the river Schelde at Oudenaarde just as the French army, under Marshal Vendôme and the duc de Burgundy, was crossing farther north with the intent of besieging the place. Marlborough – with renewed self-assurance – moved decisively to engage them. His subsequent victory at the Battle of Oudenaarde on 11 July 1708 demoralised the French army in Flanders; his eye for ground, his sense of timing and his keen knowledge of the enemy were again amply demonstrated. The success, aided by the dissension of the two French commanders, restored the strategic initiative to the Allies, who now opted to besiege Lille, the strongest fortress in Europe. While the Duke commanded the covering force, Eugene oversaw the siege of the town, which surrendered on 22 October; however, it was not until 10 December that the resolute Boufflers yielded the citadel. Yet for all the difficulties of the winter siege, the campaign of 1708 had been a remarkable success, requiring superior logistical skill and organisation. The Allies re-took Brugge and Gent, and the French were driven out of almost all the Spanish Netherlands: "He who has not seen this", wrote Eugene, "has seen nothing".


title: John Churchill, 1st Duke of Marlborough

text: While Marlborough achieved honours on the battlefield, the Whigs, now in the ascendancy, drove the remaining Tories from the Cabinet. Marlborough and Godolphin, now distanced from Anne, would henceforth have to conform to the decisions of a Whig ministry, while the Tories, sullen and vengeful, looked forward to their former leaders' downfall. To compound his troubles, the Duchess, spurred on by her hatred of Harley and Abigail, had finally driven the Queen to distraction and wrecked what was left of their friendship. Sarah was retained in her court position out of necessity, as the price to be paid to keep her victorious husband at the head of the army.


title: John Churchill, 1st Duke of Marlborough

text: After the recent defeats and one of the worst winters in modern history, France was on the brink of collapse. However, Allied demands at the peace talks in The Hague in April 1709 (principally concerning Article 37 that bound Louis XIV to hand over Spain within two months or face the renewal of the war), were rejected by the French in June. The Whigs, the Dutch, Marlborough and Eugene failed for personal and political reasons to secure a favourable peace, adhering to the uncompromising slogan "No peace without Spain" without any clear knowledge of how to accomplish it. All the while Harley, maintained up the backstairs by Abigail, rallied the moderates to his side, ready to play an ambitious and powerful middle part.


title: John Churchill, 1st Duke of Marlborough

text: Marlborough returned to campaigning in the Low Countries in June 1709. After outwitting Marshal Villars to take the town of Tournai on 3 September (a major and bloody operation), the Allies turned their attention upon Mons, determined to maintain the ceaseless pressure on the French. With direct orders from the increasingly desperate Louis XIV to save the city, Villars advanced on the tiny village of Malplaquet on 9 September 1709 and entrenched his position. Two days later the opposing forces clashed in battle. On the Allied left flank the Prince of Orange led his Dutch infantry in desperate charges only to have it cut to pieces. On the other flank, Eugene attacked and suffered almost as severely. Nevertheless, sustained pressure on his extremities forced Villars to weaken his centre, enabling Marlborough to break through and claim victory. Yet the cost was high: the allied casualty figures were approximately double that of the enemy (sources vary), leading Marlborough to admit – "The French have defended themselves better in this action than in any battle I've seen". A rumour among the French about Marlborough's death in this battle lead to the burlesque lament "Marlbrough s'en va-t-en guerre", (Marlborough has left for the war). The Duke proceeded to take Mons on 20 October, but on his return to England his enemies used the Malplaquet casualty figures to sully his reputation. Harley, now master of the Tory party, did all he could to persuade his colleagues that the pro-war Whigs – and by their apparent concord with Whig policy, Marlborough and Godolphin – were bent on leading the country to ruin.


title: John Churchill, 1st Duke of Marlborough

text: The Allies had confidently expected that victory in a major set-piece battle would compel Louis XIV to accept peace on Allied terms, but after Malplaquet (the bloodiest battle of the war), that strategy had lost its validity: Villars had only to avoid defeat for a compromise peace settlement to become inevitable. In March 1710, fresh peace talks re-opened at Geertruidenberg, but again Louis XIV would not concede Whig demands to force his grandson, Philip V, from Spain. Publicly Marlborough toed the government line, but privately he had real doubts about pressing the French into accepting such a dishonourable course.


title: John Churchill, 1st Duke of Marlborough

text: Although the Duke was only an observer at Geertruidenberg, the failed negotiations gave credence to his detractors that he was deliberately prolonging the war for his own profit. Yet it was with reluctance that he returned to campaigning in the spring, capturing Douai in June, before taking Béthune, and Saint-Venant, followed in November by Aire-sur-la-Lys. Nevertheless, support for the pro-war policy of the Whigs had, by this time, ebbed away. The Cabinet had long lacked cohesion and mutual trust (particularly following the Sacheverell affair) when in the summer the plan to break it up, prepared by Harley, was brought into action by the Queen. Sunderland was dismissed in June, followed by Godolphin (who had refused to sever his ties with Sarah) in August. Others followed. The result of the general election in October was a Tory landslide and a victory for the peace policy. Marlborough remained at the head of the army, however. The defeated Junto, the Dutch, Eugene and the Emperor, implored him to stand by the common cause, while the new ministers, knowing they had to fight another campaign, required him to maintain the pressure on the enemy until they had made their own arrangements for the peace.


title: John Churchill, 1st Duke of Marlborough

text: The Duke, "much thinner and greatly altered", returned to England in November. His relationship with Anne had suffered further setbacks in recent months (she had refused to grant him his requested appointment of Captain-General for life, and had interfered in military appointments). The damage done to Marlborough's general standing was substantial because it was so visible. For now, though, the central issue was the Duchess whose growing resentment of Harley and Abigail had finally persuaded the Queen to be rid of her. Marlborough visited Anne on 17 January 1711 (O.S.) in a last attempt to save his wife, but she was not to be swayed, and demanded Sarah give up her Gold Key (the symbol of her office) within two days, warning, "I will talk of no other business till I have the key."


title: John Churchill, 1st Duke of Marlborough

text: Notwithstanding all this turmoil – and his declining health – Marlborough returned to The Hague in late February to prepare for what was to be his last campaign, and one of his greatest. Once again Marlborough and Villars formed against each other in line of battle, this time along the Avesnes-le-Comte–Arras sector of the Lines of "Ne Plus Ultra". Expecting another onslaught on the scale of Malplaquet, the allied generals surmised that their commander, distressed from domestic turmoil, was leading them to an appalling slaughter. By an exercise of brilliant psychological deception, and a secretive night march covering nearly 40 miles in 18 hours, the Allies penetrated the allegedly impregnable lines without losing a single man; Marlborough was now in position to besiege the fortress of Bouchain. Villars, deceived and outmanoeuvred, was helpless to intervene, compelling the fortress's unconditional surrender on 12 September. Chandler writes – "The pure military artistry with which he repeatedly deceived Villars during the first part of the campaign has few equals in the annals of military history ... the subsequent siege of Bouchain with all its technical complexities, was an equally fine demonstration of martial superiority".


title: John Churchill, 1st Duke of Marlborough

text: For Marlborough, though, time had run out. His strategic gains in 1711 made it virtually certain that the Allies would march on Paris the following year, but Harley had no intention of letting the war progress that far and risk jeopardising the favourable terms secured from the secret Anglo-French talks (based on the idea that Philip V would remain on the Spanish throne) that had proceeded throughout the year. Marlborough had long had doubts about the Whig policy of "No Peace Without Spain", but he was reluctant to abandon his allies (including the Elector of Hanover, Anne's heir presumptive), and sided with the Whigs in opposing the peace preliminaries. Personal entreaties from the Queen (who had long tired of the war), failed to persuade the Duke. The Elector made it clear that he too was against the proposals, and publicly sided with the Whigs. Nevertheless, Anne remained resolute, and on 7 December 1711 (O.S.) she was able to announce that – "notwithstanding those who delight in the arts of war" – a sneer towards Marlborough – "both time and place are appointed for opening the treaty of a general peace".


title: John Churchill, 1st Duke of Marlborough

text: To prevent the serious renewal of warfare in the spring, it was considered essential to replace Marlborough with a general more in touch with the Queen's ministers and less in touch with their allies. To do this, Harley (newly created Earl of Oxford) and St John first needed to bring charges of corruption against the Duke, completing the anti-Whig, anti-war picture that Jonathan Swift was already presenting to a credulous public through his pamphleteering, notably in his "Conduct of the Allies" (1711).


title: John Churchill, 1st Duke of Marlborough

text: Two main charges were brought to the House of Commons against Marlborough: first, an assertion that over nine years he had illegally received more than £63,000 from the bread and transport contractors in the Netherlands; second, that he had taken 2.5% from the pay of the foreign troops in English pay, amounting to £280,000. Despite Marlborough's refutations (claiming ancient precedent for the first allegation, and, for the second, producing a warrant signed by the Queen in 1702 authorising him to make the deductions in lieu of secret-service money for the war), the findings were enough for Harley to persuade the Queen to release her Captain-General. On 29 December 1711 (O.S.), before the charges had been examined, Anne, who owed to him the success and glory of her reign, sent her letter of dismissal: "I am sorry for your own sake the reasons are become so public which makes it necessary for me to let you know you have render'd it impracticable for you to continue yet longer in my service". The Tory-dominated Parliament concluded by a substantial majority that "the taking of several sums of money annually by the Duke of Marlborough from the contractor for foraging the bread and wagons ... was unwarrantable and illegal", and that the 2.5% deducted from the pay of foreign troops "is public money and ought to be accounted for". When his successor, the Duke of Ormonde, left London for The Hague to take command of British forces he went, noted Bishop Burnet, with "the same allowances that had been lately voted criminal in the Duke of Marlborough".


title: John Churchill, 1st Duke of Marlborough

text: The Allies were stunned by Marlborough's dismissal. The French, however, rejoiced at the removal of the main obstacle to the Anglo-French talks. Oxford (i.e. Harley) and St John had no intention of letting Britain's new Captain-General undertake any action, and issued Ormonde his "restraining orders" in May, forbidding him to use British troops in action against the French – an infamous step that ultimately ruined Eugene's campaign in Flanders. Marlborough continued to make his views known, but he was in trouble: attacked by his enemies and the government press; with his fortune in peril and Blenheim Palace still unfinished and running out of money; and with England split between Hanoverian and Jacobite factions, Marlborough thought it wise to leave the country. After attending Godolphin's funeral on 7 October (O.S.), he went into voluntary exile to the Continent on 1 December 1712 (O.S.).


title: John Churchill, 1st Duke of Marlborough

text: Marlborough was welcomed and fêted by the people and courts of Europe, where he was not only respected as a great general but also as a prince of the Holy Roman Empire. Sarah joined him in February 1713, and was delighted when on reaching Frankfurt in the middle of May to see that the troops under Eugene's command paid her lord "all the respects as if he had been at his old post".


title: John Churchill, 1st Duke of Marlborough

text: Throughout his travels Marlborough remained in close contact with the Electoral court of Hanover, determined to ensure a bloodless Hanoverian succession on Anne's death. He also maintained correspondence with the Jacobites. The spirit of the age saw little wrong in Marlborough's continuing friendship with his nephew, the Duke of Berwick, James II's illegitimate son with Arabella. But these assurances against a Jacobite restoration (which he had been taking out since the early years of William III, no matter how insincere), stirred Hanoverian suspicions, and perhaps prevented him from holding the first place in the counsels of the future George I.


title: John Churchill, 1st Duke of Marlborough

text: The representatives of France, Great Britain, and the Dutch Republic signed the Treaty of Utrecht on 11 April 1713 (N.S.) – the Emperor and his German allies, including the Elector of Hanover, continued with the war before finally accepting the general settlement the following year. The Treaty marked Britain's emergence as a great power. Domestically, however, the country remained divided between Whig and Tory, Jacobite and Hanoverian factions. By now Oxford and St John (Viscount Bolingbroke since 1712) – absorbed entirely by their mutual enmity and political squabbling – had effectively wrecked the Tory administration. Marlborough had been kept well informed of events while in exile and had remained a powerful figure on the political scene, not least because of the personal attachment the Queen still retained for him. After the death of his daughter Elizabeth from smallpox in March 1714, Marlborough contacted the Queen. Although the contents of the letter are unknown, it is possible that Anne may have summoned him home. Either way, it seems that an agreement was reached to reinstate the Duke in his former offices.


title: John Churchill, 1st Duke of Marlborough

text: Oxford's period of predominance was now at an end, and Anne turned to Bolingbroke and Marlborough to assume the reins of government and ensure a smooth succession. But beneath the weight of hostility the Queen's health, already fragile, rapidly deteriorated, and on 1 August 1714 (O.S.) – the day the Marlboroughs returned to England – she died. The Privy Council immediately proclaimed the Elector of Hanover King George I of Great Britain. The Jacobites had proved incapable of action; what Daniel Defoe called the "solidity of the constitution" had triumphed, and the regents chosen by George prepared for his arrival.


title: John Churchill, 1st Duke of Marlborough

text: The Duke's return to favour under the House of Hanover enabled him to preside over the defeat of the 1715 Jacobite rising from London (although it was his former assistant, Cadogan, who directed the operations). But his health was fading, and on 28 May 1716 (O.S.), shortly after the death of his daughter Anne, Countess of Sunderland, he suffered a paralytic stroke at Holywell House. This was followed by another, more severe stroke in November, this time at a house on the Blenheim estate. The Duke recovered somewhat, but while his speech had become impaired his mind remained clear, recovering enough to ride out to watch the builders at work on Blenheim Palace and attend the Lords to vote for Oxford's impeachment.


title: John Churchill, 1st Duke of Marlborough

text: In 1719 the Duke and Duchess were able to move into the east wing of the unfinished palace, but Marlborough had only three years to enjoy it. While living at Windsor Lodge he suffered another stroke in June 1722, not long after his 72nd birthday. Finally, at 4 a.m on 16 June (O.S.), in the presence of his wife and two surviving daughters Henrietta Godolphin and Mary Montagu, the 1st Duke of Marlborough died. He was initially buried on 9 August (O.S.) in the vault at the east end of Henry VII's chapel in Westminster Abbey, but following instructions left by Sarah, who died in 1744, Marlborough was moved to be by her side lying in the vault beneath the chapel at Blenheim.


title: John Churchill, 1st Duke of Marlborough

text: Marlborough's place as one of the finest soldiers Britain ever produced is well deserved. He possessed the personal courage, imagination, common sense, self-control, and quick wits that mark the best battlefield commanders. He had an unerring ability to sense an enemy's weaknesses and the ability to use stratagems to throw his enemy off balance... It was in the realm of strategy, however, where Marlborough really shone. As commander-in-chief of a coalition army, he had the ability to tolerate politicians, allies, and fools gladly. He also saw the potential of the recently introduced combination of flintlock and socket bayonet to restore the offensive...to warfare in an age when extensive fortifications, magazines, and the defensive dominated military thinking. Marlborough's attention to logistics allowed him to break free of the bonds of the magazine system and ensured that his soldiers were fed, clothed, and paid, earning him the loyalty of his troops and the nickname "Corporal John".


title: John Churchill, 1st Duke of Marlborough

text: in the ten campaigns he made against [the French]; during all which time it cannot be said that he ever slipped an opportunity of fighting, when there was any probability of coming at his enemy: and upon all occasions he concerted matters with so much judgement and forecast, that he never fought a battle which he did not gain, nor laid siege to a town which he did not take.


title: John Churchill, 1st Duke of Marlborough

text: To military historians David Chandler and Richard Holmes, Marlborough is the greatest British commander in history, an assessment that is shared by others, including the Duke of Wellington who could "conceive nothing greater than Marlborough at the head of an English army". However, the 19th century Whig historian, Thomas Macaulay, denigrates Marlborough throughout the pages of his "The History of England from the Accession of James the Second" who, in the words of historian John Wilson Croker, pursues the Duke with "more than the ferocity, and much less than the sagacity, of a bloodhound". According to historian George Trevelyan, Macaulay "instinctively desired to make Marlborough's genius stand out bright against the background of his villainy". It was in response to Macaulay's "History" that a descendant, Winston Churchill, wrote his laudatory biography, "" (4 vol. 1933–1938).


title: John Churchill, 1st Duke of Marlborough

text: Marlborough was ruthlessly ambitious, relentless in the pursuit of wealth, power and social advancement, earning him a reputation for avarice and miserliness. These traits may have been exaggerated for the purposes of party faction but, notes Trevelyan, nearly all other statesmen of the day were engaged in founding families and amassing estates at the public expense; Marlborough only differed in that he gave the public much more value for their money. In his quest for fame and personal interests he could be unscrupulous, as his desertion of James II testifies. To Macaulay this is regarded as a piece of selfish treachery against his patron; an analysis shared by G. K. Chesterton, a devout Catholic: "Churchill, as if to add something ideal to his imitation of Iscariot, went to James with wanton professions of love and loyalty ... and then calmly handed over the army to the invader. To the finish of this work of art but few could aspire, but in their degree all the politicians of the Revolution were upon this ethical pattern". To Trevelyan, Marlborough's behaviour during the 1688 revolution was a sign of his "devotion to the liberties of England and the Protestant religion". However, his continuing correspondence with Saint-Germain was not noble. Although Marlborough did not wish for a Jacobite restoration his double-dealing ensured that William III and George I would never be fully disposed to trust him.


title: John Churchill, 1st Duke of Marlborough

text: Marlborough's weakness during Anne's reign lay in the English political scene. His determination to preserve the independence of the Queen's administration from control of party faction initially enjoyed full support, but once royal favour turned elsewhere, the Duke, like his key ally Godolphin, found himself isolated; first becoming little more than a servant of the Whigs, then a victim of the Tories. Nonetheless he has been consistently ranked as one of the greatest military commanders of the modern Era.


title: John Churchill, 1st Duke of Marlborough

text: On the grand strategic level Marlborough had a rare grasp of the broad issues involved, and was able from the start of the Spanish Succession war to see the conflict in its entirety. He was one of the few influences working towards genuine unity within the Grand Alliance, but the extension of the war aims to include the replacement of Philip V as King of Spain was a fatal mistake. Marlborough stands accused – possibly for political and diplomatic reasons – of not pressing his private doubts about reinforcing failure. Spain proved a continuous drain of men and resources, and ultimately hampered his chances of complete success in Flanders, the war's main theatre. The Allies did come close to a complete victory on several occasions, but the increasingly severe conditions imposed upon Louis XIV forestalled an early end to hostilities. Although the Duke lost his political influence in the latter stages of the war he still possessed vast prestige abroad, yet his failure to communicate his innermost convictions to his allies or political masters means he must bear some responsibility for the continuance of the war beyond its logical conclusion.


title: John Churchill, 1st Duke of Marlborough

text: As a commander Marlborough preferred battle over slow moving siege warfare. Aided by an expert staff (particularly his carefully selected "aides-de-camp" such as Cadogan), as well as enjoying a close personal relationship with the talented Imperial commander, Prince Eugene, Marlborough proved far-sighted, often far ahead of his contemporaries in his conceptions, and was a master at assessing his enemy's characteristics in battle. Marlborough was more likely to manoeuvre than his opponents, and was better at maintaining operational tempo at critical times, yet the Duke qualifies more as a great practitioner within the constraints of early 18th century warfare, rather than as a great innovator who radically redefined military theory. Nevertheless, his predilection for fire, movement, and co-ordinated all-arms attacks, lay at the root of his great battlefield successes.


title: John Churchill, 1st Duke of Marlborough

text: As an administrator Marlborough was also without peer; his attention to detail meant his troops rarely went short of supply – when his army arrived at its destination it was intact and in a fit state to fight. This concern for the welfare of the common soldier together with his ability to inspire trust and confidence, and his willingness to share the dangers of battle, often earned him adulation from his men – "The known world could not produce a man of more humanity", observed Corporal Matthew Bishop. It was this range of abilities that makes Marlborough outstanding. Even his old adversaries recognised the Duke's qualities. In his "Letters on the Study of History" (1752), Bolingbroke declared – "I take with pleasure this opportunity of doing justice to that great man ... [whose memory] as the greatest general, and as the greatest minister that our country, or perhaps any other has produced, I honour". His success was made possible because of his enormous reserves of stamina, willpower and self-discipline; his ability to hold together the Alliance against France, made possible by his victories, can hardly be overestimated.


title: Luby's shooting

text: The Luby's shooting was a mass shooting that took place on October 16, 1991, at a Luby's Cafeteria in Killeen, Texas. The perpetrator, George Hennard, drove his pickup truck through the front window of the restaurant. He shot and killed 23 people, and wounded 27 others. He had a brief shootout with police, refused their orders to surrender, and fatally shot himself.


title: Luby's shooting

text: At the time, the shooting was the deadliest mass shooting by a lone gunman in U.S. history, being surpassed 16 years later by the Virginia Tech shooting.


title: Luby's shooting

text: On October 16, 1991, 35-year-old George Hennard, an unemployed former merchant seaman, drove a blue 1987 Ford Ranger pickup truck through the plate-glass front window of a Luby's Cafeteria in Killeen, Texas, at 12:39 p.m. October 16 was Boss's Day, and the cafeteria was unusually crowded with around 150 people. Hennard then began firing from inside the truck while holding Glock 17 and Ruger P89 pistols; the first victim was veterinarian Michael Griffith. Hennard exited the truck and yelled, "All women of Killeen and Belton are vipers! This is what you've done to me and my family! This is what Bell County did to me ... this is payback day!" He then opened fire on the patrons and staff with both pistols. Hennard then circled around the cafeteria, selectively picking his victims. Hennard said "You bitch" to a woman before fatally shooting her.


title: Luby's shooting

text: Hennard saw another woman hiding underneath a bench near the serving line and said "Hiding from me, bitch?" before shooting her dead. Hennard then approached Steve Ernst who was hiding underneath a table before shooting him. Steve then rolled over, holding his stomach. The shooter then approached a baby and a woman. He barked at the woman, saying, "You with the baby. Get out before I change my mind". The woman ran out, holding the baby in her arms. After the woman left, Hennard shot Ernst's wife in the arm which went clean through and instead killed 70-year-old Venice Ellen Henehan, Ernst's mother-in-law. During a brief lull in the shooting, Hennard approached the table of 28-year-old Tommy Vaughan in the rear of the cafeteria. Huddled on the floor beside a window, Vaughn threw himself through the window, creating an escape route for others. Dozens of people pushed, shoved, and knocked each other down as they made their escape. When police arrived a few minutes later, a third of the victims had managed to escape.


title: Luby's shooting

text: Hennard reloaded at least three times before police arrived and engaged in a brief shootout. Wounded, he retreated to an area between the two bathrooms (people were hiding in these bathrooms and had blocked their doors). Police repeatedly ordered Hennard to surrender, but he refused, saying he was going to kill more people. Hennard was shot twice more by police, in the abdomen. Having depleted ammunition for one of his weapons and his injuries growing more severe, he shot himself in the head with the final bullet. He had shot and killed 23 people—10 of whom with single shots to the head at point blank range—and wounded another 27.


title: Luby's shooting

text: George Pierre Hennard was born on October 15, 1956, in Sayre, Pennsylvania, in a wealthy family. Hennard was the son of a Swiss-born surgeon and a homemaker. He had two younger siblings, brother Alan and sister Desiree. Since the age of 5, Hennard and his family moved across the country as his father worked at several army hospitals. Hennard's family later moved to New Mexico, where his father worked at the White Sands Missile Range near Las Cruces. After graduating from Mayfield High School in 1974, he enlisted in the U.S. Navy and served for three years, until he was honorably discharged. Hennard later worked as a merchant mariner, but was dismissed for drug use. Several months later, Hennard enrolled in a drug treatment program in Houston.


title: Luby's shooting

text: Early in the investigation of the massacre, the Killeen police chief said that Hennard "had an evident problem with women for some reason". After his parents divorced in 1983, his father moved to Houston, and his mother moved to Henderson, Nevada. The Glock 17 and Ruger P89 9mm pistols which Hennard used were purchased in February 1991 at Mike's Gun House, a gun shop in the town of Henderson, Nevada.


title: Luby's shooting

text: Hennard had begun to work at several different jobs, including construction crews in South Dakota and Killeen while living part-time in Henderson, Nevada, with his mother in a redbrick colonial home in Belton that his family had purchased in 1980 shortly after moving to Fort Hood.


title: Luby's shooting

text: Hennard had stalked two sisters, 23-year-old Jill Fritz and 19-year-old Jana Jemigan who lived two blocks away from him in his neighborhood. He sent them a five-page letter in June, part of which said: "Please give me the satisfaction of some day laughing in the face of all those mostly white treacherous female vipers from those two towns [Killeen and Belton] who tried to destroy me and my family" and “You think the three of us can get together some day?” He also wrote that he was "truly flattered knowing I have two teenage groupie fans".


title: Luby's shooting

text: Hennard was described as reclusive and belligerent, with an explosive temper. He was discharged from the Merchant Marine on May 11, 1989 for possession of marijuana and racial incidents. That same month, Hennard's seaman papers were suspended after he had a racial argument with another shipmate. Numerous reports included accounts of Hennard's expressed hatred of women. An ex-roommate of his said, "He hated blacks, Hispanics, and gays. He said women were snakes and always had derogatory remarks about them, especially after fights with his mother." Survivors of the shootings later said Hennard had passed over men to shoot women. Fourteen of the twenty three people killed were women, as were many of the wounded. He called two of the victims a "bitch" before shooting them.


title: Luby's shooting

text: In 1990, Hennard called Isaiah (Ike) R. Williams, a port agent for the national maritime union in Wilmington, California, stating that he needed a letter of recommendation in order to regain his papers and rejoin the Merchant Marine. "I don't recall having given him one," Williams claimed. Hennard had learned in mid-February that his attempt to be reinstated had been denied. Several months later, Hennard entered a drug treatment program in Houston.


title: Luby's shooting

text: Around two months before the shooting, Hennard entered a convenience store in Belton to buy breakfast. Mead, the clerk of the store, claimed that Hennard had leaned over the counter and said, "I want you to tell everybody, if they don't quit messing around my house something awful is going to happen."


title: Luby's shooting

text: A week and a half before the shooting, Hennard collected his paycheck at a cement company in Copperas Cove and announced he was quitting. Hennard also wondered aloud what would happen if he killed someone. “He got to talking about some of the people in Belton and certain women that had given him problems,” a coworker Bubba Hawkins claimed. “And he kept saying, ‘Watch and see, watch and see.’ "


title: Luby's shooting

text: On his 35th birthday, October 15, 1991, Hennard spoke with his mother on the phone. Later that evening, while eating a cheeseburger and french fries outside of Belton, Hennard had a sudden outburst of rage as he watched television coverage of Clarence Thomas's confirmation hearings. “When an interview with Anita Hill came on, he just went off,” Bill Stringer, a manager, said. "He started screaming, 'You dumb bitch! You bastards opened the door for all the women!'"


title: Luby's shooting

text: An anti-crime bill was scheduled for a vote in the U.S. House of Representatives the day after the massacre. Some of the Hennard victims had been constituents of Rep. Chet Edwards, and in response he abandoned his opposition to a gun control provision that was part of the bill. The provision, which did not pass, would have banned some weapons and magazines like one used by Hennard.


title: Luby's shooting

text: Families of deceased victims, survivors, and policemen received counseling for grief, shock and stress.


title: Luby's shooting

text: The Texas State Rifle Association and others preferred that the state allow its citizens to carry concealed weapons. Democratic governor Ann Richards vetoed such bills, but in 1995 her Republican successor, George W. Bush, signed one into force. The law had been campaigned for by Suzanna Hupp, who was present at the massacre; both of her parents, Alphonse "Al" Gratia and Ursula "Suzy" Gratia, were killed by Hennard. She later testified that she would have liked to have had her .38 revolver, but said, "It was a hundred feet away in my car." (She had feared that if she was caught carrying it she might lose her chiropractor's license.) Hupp testified across the country in support of concealed handgun laws, and was elected to the Texas House of Representatives in 1996.


title: Luby's shooting

text: A pink granite memorial stands behind the Killeen Community Center with the date of the event and the names of those killed.


title: Luby's shooting

text: The restaurant reopened five months after the massacre, but closed permanently on September 9, 2000. As of 2020, a buffet called "Yank Sing" located on 1705 E Central Texas Expressway, currently occupies the location.


title: Geometric mean

text: In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the th root of the product of numbers, i.e., for a set of numbers , the geometric mean is defined as


title: Geometric mean

text: For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, formula_3. As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, formula_4. The geometric mean applies only to positive numbers.


title: Geometric mean

text: The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or interest rates of a financial investment over time. It also applies to benchmarking, where it is particularly useful for computing means of speedup ratios: since the mean of 0.5x (half as fast) and 2x (twice as fast) will be 1 (i.e., no speedup overall).


title: Geometric mean

text: The geometric mean can be understood in terms of geometry. The geometric mean of two numbers, formula_5 and formula_6, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths formula_5 and formula_6. Similarly, the geometric mean of three numbers, formula_5, formula_6, and formula_11, is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers.


title: Geometric mean

text: The geometric mean is one of the three classical Pythagorean means, together with the arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between (see Inequality of arithmetic and geometric means.)


title: Geometric mean

text: The above figure uses capital pi notation to show a series of multiplications. Each side of the equal sign shows that a set of values is multiplied in succession (the number of values is represented by "n") to give a total product of the set, and then the "n"th root of the total product is taken to give the geometric mean of the original set. For example, in a set of four numbers formula_14, the product of formula_15 is formula_16, and the geometric mean is the fourth root of 24, or ~ 2.213. The exponent formula_17 on the left side is equivalent to the taking "n"th root. For example, formula_18.


title: Geometric mean

text: The geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal. This allows the definition of the arithmetic-geometric mean, an intersection of the two which always lies in between.


title: Geometric mean

text: The geometric mean is also the arithmetic-harmonic mean in the sense that if two sequences (formula_19) and (formula_20) are defined:


title: Geometric mean

text: where formula_23 is the harmonic mean of the previous values of the two sequences, then formula_19 and formula_20 will converge to the geometric mean of formula_26 and formula_27. The sequences converge to a common limit, and the geometric mean is preserved:


title: Geometric mean

text: Replacing the arithmetic and harmonic mean by a pair of generalized means of opposite, finite exponents yields the same result.


title: Geometric mean

text: The geometric mean can also be expressed as the exponential of the arithmetic mean of logarithms. By using logarithmic identities to transform the formula, the multiplications can be expressed as a sum and the power as a multiplication:


title: Geometric mean

text: This is sometimes called the log-average (not to be confused with the logarithmic average). It is simply computing the arithmetic mean of the logarithm-transformed values of formula_32 (i.e., the arithmetic mean on the log scale) and then using the exponentiation to return the computation to the original scale, i.e., it is the generalised f-mean with formula_35. For example, the geometric mean of 2 and 8 can be calculated as the following, where formula_6 is any base of a logarithm (commonly 2, formula_37 or 10):


title: Geometric mean

text: Related to the above, it can be seen that for a given sample of points formula_39, the geometric mean is the minimizer of


title: Geometric mean

text: Thus, the geometric mean provides a summary of the samples whose exponent best matches the exponents of the samples (in the least squares sense).


title: Geometric mean

text: The log form of the geometric mean is generally the preferred alternative for implementation in computer languages because calculating the product of many numbers can lead to an arithmetic overflow or arithmetic underflow. This is less likely to occur with the sum of the logarithms for each number.


title: Geometric mean

text: The geometric mean of a non-empty data set of (positive) numbers is always at most their arithmetic mean. Equality is only obtained when all numbers in the data set are equal; otherwise, the geometric mean is smaller. For example, the geometric mean of 2 and 3 is 2.45, while their arithmetic mean is 2.5. In particular, this means that when a set of non-identical numbers is subjected to a mean-preserving spread — that is, the elements of the set are "spread apart" more from each other while leaving the arithmetic mean unchanged — their geometric mean decreases.


title: Geometric mean

text: In many cases the geometric mean is the best measure to determine the average growth rate of some quantity. (For example, if in one year sales increases by 80% and the next year by 25%, the end result is the same as that of a constant growth rate of 50%, since the geometric mean of 1.80 and 1.25 is 1.50.) In order to determine the average growth rate, it is not necessary to take the product of the measured growth rates at every step. Let the quantity be given as the sequence formula_42, where formula_43 is the number of steps from the initial to final state. The growth rate between successive measurements formula_44 and formula_45 is formula_46. The geometric mean of these growth rates is then just:


title: Geometric mean

text: The fundamental property of the geometric mean, which does not hold for any other mean, is that for two sequences formula_48 and formula_49 of equal length,


title: Geometric mean

text: This makes the geometric mean the only correct mean when averaging "normalized" results; that is, results that are presented as ratios to reference values. This is the case when presenting computer performance with respect to a reference computer, or when computing a single average index from several heterogeneous sources (for example, life expectancy, education years, and infant mortality). In this scenario, using the arithmetic or harmonic mean would change the ranking of the results depending on what is used as a reference. For example, take the following comparison of execution time of computer programs:


title: Geometric mean

text: The arithmetic and geometric means "agree" that computer C is the fastest. However, by presenting appropriately normalized values "and" using the arithmetic mean, we can show either of the other two computers to be the fastest. Normalizing by A's result gives A as the fastest computer according to the arithmetic mean:


title: Geometric mean

text: while normalizing by B's result gives B as the fastest computer according to the arithmetic mean but A as the fastest according to the harmonic mean:


title: Geometric mean

text: and normalizing by C's result gives C as the fastest computer according to the arithmetic mean but A as the fastest according to the harmonic mean:


title: Geometric mean

text: In all cases, the ranking given by the geometric mean stays the same as the one obtained with unnormalized values.


title: Geometric mean

text: Giving consistent results is not always equal to giving the correct results. In general, it is more rigorous to assign weights to each of the programs, calculate the average weighted execution time (using the arithmetic mean), and then normalize that result to one of the computers. The three tables above just give a different weight to each of the programs, explaining the inconsistent results of the arithmetic and harmonic means (Table 4 gives equal weight to both programs, the Table 2 gives a weight of 1/1000 to the second program, and the Table 3 gives a weight of 1/100 to the second program and 1/10 to the first one). The use of the geometric mean for aggregating performance numbers should be avoided if possible, because multiplying execution times has no physical meaning, in contrast to adding times as in the arithmetic mean. Metrics that are inversely proportional to time (speedup, IPC) should be averaged using the harmonic mean.


title: Geometric mean

text: The geometric mean can be derived from the generalized mean as its limit as formula_51 goes to zero. Similarly, this is possible for the weighted geometric mean.


title: Geometric mean

text: If formula_52 is a positive continuous real-valued function, its geometric mean over this interval is


title: Geometric mean

text: For instance, taking the identity function formula_54 over the unit interval shows that the geometric mean of the positive numbers between 0 and 1 is equal to formula_55.


title: Geometric mean

text: The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.


title: Geometric mean

text: Suppose an orange tree yields 100 oranges one year and then 180, 210 and 300 the following years, so the growth is 80%, 16.6666% and 42.8571% for each year respectively. Using the arithmetic mean calculates a (linear) average growth of 46.5079% (80% + 16.6666% + 42.8571%, that sum then divided by 3). However, if we start with 100 oranges and let it grow 46.5079% each year, the result is 314 oranges, not 300, so the linear average "over"-states the year-on-year growth.


title: Geometric mean

text: Instead, we can use the geometric mean. Growing with 80% corresponds to multiplying with 1.80, so we take the geometric mean of 1.80, 1.166666 and 1.428571, i.e. formula_56; thus the "average" growth per year is 44.2249%. If we start with 100 oranges and let the number grow with 44.2249% each year, the result is 300 oranges.


title: Geometric mean

text: The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean. It is also used in the recently introduced "RPIJ" measure of inflation in the United Kingdom and in the European Union.


title: Geometric mean

text: Although the geometric mean has been relatively rare in computing social statistics, starting from 2010 the United Nations Human Development Index did switch to this mode of calculation, on the grounds that it better reflected the non-substitutable nature of the statistics being compiled and compared:


title: Geometric mean

text: Not all values used to compute the HDI (Human Development Index) are normalized; some of them instead have the form formula_57. This makes the choice of the geometric mean less obvious than one would expect from the "Properties" section above.


title: Geometric mean

text: The equally distributed welfare equivalent income associated with an Atkinson Index with an inequality aversion parameter of 1.0 is simply the geometric mean of incomes. For values other than one, the equivalent value is an Lp norm divided by the number of elements, with p equal to one minus the inequality aversion parameter.


title: Geometric mean

text: In the case of a right triangle, its altitude is the length of a line extending perpendicularly from the hypotenuse to its 90° vertex. Imagining that this line splits the hypotenuse into two segments, the geometric mean of these segment lengths is the length of the altitude. This property is known as the geometric mean theorem.


title: Geometric mean

text: In an ellipse, the semi-minor axis is the geometric mean of the maximum and minimum distances of the ellipse from a focus; it is also the geometric mean of the semi-major axis and the semi-latus rectum. The semi-major axis of an ellipse is the geometric mean of the distance from the center to either focus and the distance from the center to either directrix.


title: Geometric mean

text: Consider a circle with radius formula_58. Now take two diametrically opposite points on the circle and apply pressure from both ends to deform it into an ellipse with semi-major and semi-minor axes of lengths formula_5 and formula_6.


title: Geometric mean

text: The radius of the circle is the geometric mean of the semi-major and the semi-minor axes of the ellipse formed by deforming the circle.


title: Geometric mean

text: Distance to the horizon of a sphere is approximately equal to the geometric mean of the distance to the closest point of the sphere and the distance to the farthest point of the sphere when the distance to the closest point of the sphere is small.


title: Geometric mean

text: Both in the approximation of squaring the circle according to S.A. Ramanujan (1914) and in the construction of the Heptadecagon according to ""sent by T. P. Stowell, credited to Leybourn's Math. Repository, 1818"", the geometric mean is employed.


title: Geometric mean

text: The geometric mean has been used in choosing a compromise aspect ratio in film and video: given two aspect ratios, the geometric mean of them provides a compromise between them, distorting or cropping both in some sense equally. Concretely, two equal area rectangles (with the same center and parallel sides) of different aspect ratios intersect in a rectangle whose aspect ratio is the geometric mean, and their hull (smallest rectangle which contains both of them) likewise has the aspect ratio of their geometric mean.


title: Geometric mean

text: In aspect ratio by the SMPTE, balancing 2.35 and 4:3, the geometric mean is formula_62, and thus formula_63... was chosen. This was discovered empirically by Kerns Powers, who cut out rectangles with equal areas and shaped them to match each of the popular aspect ratios. When overlapped with their center points aligned, he found that all of those aspect ratio rectangles fit within an outer rectangle with an aspect ratio of 1.77:1 and all of them also covered a smaller common inner rectangle with the same aspect ratio 1.77:1. The value found by Powers is exactly the geometric mean of the extreme aspect ratios, (1.33:1) and CinemaScope(2.35:1), which is coincidentally close to formula_64 (formula_65). The intermediate ratios have no effect on the result, only the two extreme ratios.


title: Geometric mean

text: Applying the same geometric mean technique to 16:9 and 4:3 approximately yields the (formula_66...) aspect ratio, which is likewise used as a compromise between these ratios. In this case 14:9 is exactly the "arithmetic mean" of formula_64 and formula_68, since 14 is the average of 16 and 12, while the precise "geometric mean" is formula_69 but the two different "means", arithmetic and geometric, are approximately equal because both numbers are sufficiently close to each other (a difference of less than 2%).


title: Geometric mean

text: The geometric mean is also used to calculate B and C series paper formats. The formula_70 format has an area which is the geometric mean of the areas of formula_71 and formula_72. For example, the area of a B1 paper is formula_73, because it is the geometric mean of the areas of an A0 (formula_74) and an A1 (formula_75) paper (formula_76).


title: Geometric mean

text: The same principle applies with the C series, whose area is the geometric mean of the A and B series. For example, the C4 format has an area which is the geometric mean of the areas of A4 and B4.


title: Geometric mean

text: An advantage that comes from this relationship is that an A4 paper fits inside a C4 envelope, and both fit inside a B4 envelope.


title: Dacia

text: Dacia (, ; ) was the land inhabited by the Dacians, its core in Transylvania, stretching to the Danube in the south, the Black Sea in the east, and the Tisza in the west. The Carpathian Mountains were located in the middle of Dacia. It thus roughly corresponds to the present-day countries of Romania, as well as parts of Moldova, Bulgaria, Serbia, Hungary, Slovakia, and Ukraine.


title: Dacia

text: A Dacian Kingdom of variable size existed between 82 BC until the Roman conquest in AD 106, reaching its height under King Burebista. As a result of the two wars with Emperor Trajan, the population was dispersed and the central city, Sarmizegetusa Regia, was destroyed by the Romans, but was rebuilt by the latter to serve as the capital of the Roman province of Dacia. The Free Dacians, living the territory of modern-day Northern Romania disappeared with the start of the Migration Period.


title: Dacia

text: The Dacians are first mentioned in the writings of the Ancient Greeks, in Herodotus ("Histories" Book IV XCIII: "[Getae] the noblest as well as the most just of all the Thracian tribes") and Thucydides ("Peloponnesian Wars", Book II: "[Getae] border on the Scythians and are armed in the same manner, being all mounted archers"). Some historians argue that Daxia (mentioned in 3rd century BC) was the previous home of Indo-Iranian nomads who later came to form the Geto-Dacian people.


title: Dacia

text: The Dacia of King Burebista (82–44 BC) stretched from the Black Sea to the source of the river Tisza and from the Balkan Mountains to Bohemia. During that period, the Getae and Dacians conquered a wider territory and Dacia extended from the Middle Danube to the Black Sea littoral (between Apollonia and Pontic Olbia) and from the Northern Carpathians to the Balkan Mountains. In 53 BC, Julius Caesar stated that the lands of the Dacians started on the eastern edge of the Hercynian (Black) Forest. After Burebista's death, his kingdom fell apart.


title: Dacia

text: ″As for the southern part of Germany beyond the Albis, the portion which is just contiguous to that river is occupied by the Suevi; then immediately adjoining this is the land of the Getae, which, though narrow at first, stretching as it does along the Ister [Danube] on its southern side and on the opposite side along the mountain-side of the Hercynian [Black] Forest (for the land of the Getae also embraces a part of the mountains), afterwards broadens out towards the north as far as the Tyregetae; but I cannot tell the precise boundaries″


title: Dacia

text: On this basis, Lengyel and Radan (1980), Hoddinott (1981) and Mountain (1998) consider that the Geto-Dacians inhabited both sides of the Tisza river prior to the rise of the Celtic Boii, and again after the latter were defeated by the Dacians. The hold of the Dacians between the Danube and Tisza was tenuous. However, the archaeologist Parducz argued a Dacian presence west of the Tisa dating from the time of Burebista. According to Tacitus (AD 56–117) Dacians bordered Germania in the south-east, while Sarmatians bordered it in the east.


title: Dacia

text: In the 1st century AD, the Iazyges settled West of Dacia, on the plain between the Danube and the Tisa rivers, according to the scholars' interpretation of Pliny's text: "The higher parts between the Danube and the Hercynian Forest (Black Forest) as far as the winter quarters of Pannonia at Carnutum and the plains and level country of the German frontiers there are occupied by the Sarmatian Iazyges, while the Dacians whom they have driven out hold the mountains and forests as far as the river Theiss".


title: Dacia

text: Written a few decades after Emperor Trajan's Roman conquest of parts of Dacia in AD 105–106, Ptolemy's "Geographia" included the boundaries of Dacia. According to the scholars' interpretation of Ptolemy (Hrushevskyi 1997, Bunbury 1879, Mocsy 1974, Bărbulescu 2005) Dacia was the region between the rivers Tisza, Danube, upper Dniester, and Siret. Mainstream historians accept this interpretation: Avery (1972) Berenger (1994) Fol (1996) Mountain (1998), Waldman Mason (2006).


title: Dacia

text: Ptolemy also provided a couple of Dacian toponyms in south Poland in the Upper Vistula (Polish: Wisla) river basin: Susudava and Setidava (with a manuscript variant Getidava). This could have been an "echo" of Burebista's expansion. It seems that this northern expansion of the Dacian language, as far as the Vistula river, lasted until AD 170–180 when the migration of the Vandal Hasdingi pushed out this northern Dacian group. This Dacian group, possibly the Costoboci/Lipița culture, is associated by Gudmund Schütte with towns having the specific Dacian language ending "dava" i.e. Setidava.


title: Dacia

text: The Roman province "Dacia Traiana", established by the victors of the Dacian Wars during AD 101–106, initially comprised only the regions known today as Banat, Oltenia, Transylvania, and was subsequently gradually extended to southern parts of Moldavia, while Dobruja and Budjak belonged to the Roman province of Moesia.


title: Dacia

text: In the 2nd century AD, after the Roman conquest, Ptolemy puts the eastern boundary of "Dacia Traiana" (the Roman province) as far east as the "Hierasus" (Siret) river, in the middle of modern Romania. Roman rule extended to the south-western area of the Dacian Kingdom (but not to what later became known as Maramureş), to parts of the later Principality of Moldavia east of the Siret and north of the Upper Trajan Wall, and to areas in modern Muntenia and Ukraine, except the Black Sea shore.


title: Dacia

text: After the Marcomannic Wars (AD 166–180), Dacian groups from outside Roman Dacia had been set in motion. So were the 12,000 Dacians "from the neighbourhood of Roman Dacia sent away from their own country". Their native country could have been the Upper Tisa region, but other places cannot be excluded.


title: Dacia

text: The later Roman province "Dacia Aureliana", was organized inside former Moesia Superior after the retreat of the Roman army from Dacia, during the reign of emperor Aurelian during AD 271–275. It was reorganized as Dacia Ripensis (as a military province) and Dacia Mediterranea (as a civil province).


title: Dacia

text: Ptolemy gives a list of 43 names of towns in Dacia, out of which arguably 33 were of Dacian origin. Most of the latter included the added suffix "dava" (meaning settlement, village). But, other Dacian names from his list lack the suffix (e.g. Zarmisegethusa regia = Zermizirga). In addition, nine other names of Dacian origin seem to have been Latinised.


title: Dacia

text: The cities of the Dacians were known as "-dava", "-deva", -δαυα ("-dawa" or "-dava", Anc. Gk.), -δεβα ("-deva", Byz. Gk.) or -δαβα ("-dava", Byz. Gk.), etc. .


title: Dacia

text: Geto-Dacians inhabited both sides of the Tisa river prior to the rise of the Celtic Boii and again after the latter were defeated by the Dacians under the king Burebista. It seems likely that the Dacian state arose as a tribal confederacy, which was united only by charismatic leadership in both military-political and ideological-religious domains. At the beginning of the 2nd century BC, under the rule of Rubobostes, a Dacian king in present-day Transylvania, the Dacians' power in the Carpathian basin increased after they defeated the Celts, who previously held power in the region.


title: Dacia

text: A kingdom of Dacia also existed as early as the first half of the 2nd century BC under King Oroles. Conflicts with the Bastarnae and the Romans (112–109 BC, 74 BC), against whom they had assisted the Scordisci and Dardani, greatly weakened the resources of the Dacians.


title: Dacia

text: Burebista (Boerebista), a contemporary of Julius Caesar, ruled Geto-Dacian tribes between 82 BC and 44 BC. He thoroughly reorganised the army and attempted to raise the moral standard and obedience of the people by persuading them to cut their vines and give up drinking wine. During his reign, the limits of the Dacian Kingdom were extended to their maximum. The Bastarnae and Boii were conquered, and even the Greek towns of Olbia and Apollonia on the Black Sea ("Pontus Euxinus") recognized Burebista's authority. In 53 BC, Caesar stated that the Dacian territory was on the eastern border of the Hercynian Forest.


title: Dacia

text: Burebista suppressed the indigenous minting of coinages by four major tribal groups, adopting imported or copied Roman denarii as a monetary standard. During his reign, Burebista transferred Geto-Dacians capital from Argedava to Sarmizegetusa Regia. For at least one and a half centuries, Sarmizegetusa was the Dacians' capital and reached its peak under King Decebalus. The Dacians appeared so formidable that Caesar contemplated an expedition against them, which his death in 44 BC prevented. In the same year, Burebista was murdered, and the kingdom was divided into four (later five) parts under separate rulers.


title: Dacia

text: One of these entities was Cotiso's state, to whom Augustus betrothed his own five-year-old daughter Julia. He is well known from the line in Horace ("Occidit Daci Cotisonis agmen", Odes, III. 8. 18).


title: Dacia

text: The Dacians are often mentioned under Augustus, according to whom they were compelled to recognize Roman supremacy. However they were by no means subdued, and in later times to maintain their independence they seized every opportunity to cross the frozen Danube during the winter and ravaging the Roman cities in the province of Moesia, which was under Roman occupation.


title: Dacia

text: Strabo testified: "although the Getae and Daci once attained to very great power, so that they actually could send forth an expedition of two hundred thousand men, they now find themselves reduced to as few as forty thousand, and they have come close to the point of yielding obedience to the Romans, though as yet they are not absolutely submissive, because of the hopes which they base on the Germans, who are enemies to the Romans."


title: Dacia

text: In fact, this occurred because Burebista's empire split after his death into four and later five smaller states, as Strabo explains, "only recently, when Augustus Caesar sent an expedition against them, the number of parts into which the empire had been divided was five, though at the time of the insurrection it had been four. Such divisions, to be sure, are only temporary and vary with the times".


title: Dacia

text: Decebalus ruled the Dacians between AD 87 and 106. The frontiers of Decebal's Dacia were marked by the Tisa River to the west, by the trans-Carpathians to the north and by the Dniester River to the east. His name translates into ""strong as ten men"".


title: Dacia

text: When Trajan turned his attention to Dacia, it had been on the Roman agenda since before the days of Julius Caesar when a Roman army had been beaten at the Battle of Histria.


title: Dacia

text: In AD 85, the Dacians had swarmed over the Danube and pillaged Moesia. In AD 87, the Roman troops sent by the Emperor Domitian against them under Cornelius Fuscus, were defeated and Cornelius Fuscus was killed by the Dacians by authority of their ruler, Diurpaneus. After this victory, Diurpaneus took the name of "Decebalus", but the Romans were victorious in the Battle of Tapae in AD 88 and a truce was drawn up. The next year, AD 88, new Roman troops under Tettius Julianus, gained a significant advantage, but were obligated to make peace following the defeat of Domitian by the Marcomanni, leaving the Dacians effectively independent. Decebalus was given the status of "king client to Rome", receiving military instructors, craftsmen and money from Rome. To Rome, Domitian brought Italian peasants in Dacian clothing because he couldn't take slaves in the war.


title: Dacia

text: To increase the glory of his reign, restore the finances of Rome, and end a treaty perceived as humiliating, Trajan resolved on the conquest of Dacia, the capture of the famous Treasure of Decebalus, and control over the Dacian gold mines of Transylvania. The result of his first campaign (101–102) was the siege of the Dacian capital Sarmizegethusa and the occupation of part of the country. Emperor Trajan recommenced hostilities against Dacia and, following an uncertain number of battles, and with Trajan's troops pressing towards the Dacian capital Sarmizegethusa, Decebalus once more sought terms.


title: Dacia

text: Decebalus rebuilt his power over the following years and attacked Roman garrisons again in AD 105. In response Trajan again marched into Dacia, attacking the Dacian capital in the Siege of Sarmizegethusa, and razing it to the ground; the defeated Dacian king Decebalus committed suicide to avoid capture. With part of Dacia quelled as the Roman province Dacia Traiana. Trajan subsequently invaded the Parthian empire to the east. His conquests brought the Roman Empire to its greatest extent. Rome's borders in the east were governed indirectly in this period, through a system of client states, which led to less direct campaigning than in the west.


title: Dacia

text: Some of the history of the war is given by Cassius Dio. Trajan erected the Column of Trajan in Rome to commemorate his victory.


title: Dacia

text: Although the Romans conquered and destroyed the ancient Kingdom of Dacia, a large remainder of the land remained outside of Roman Imperial authority. Additionally, the conquest changed the balance of power in the region and was the catalyst for a renewed alliance of Germanic and Celtic tribes and kingdoms against the Roman Empire. However, the material advantages of the Roman Imperial system was attractive to the surviving aristocracy. Afterwards, many of the Dacians became Romanised (see also Origin of Romanians). In AD 183, war broke out in Dacia: few details are available, but it appears two future contenders for the throne of emperor Commodus, Clodius Albinus and Pescennius Niger, both distinguished themselves in the campaign.


title: Dacia

text: According to Lactantius, the Roman emperor Decius (AD 249–251) had to restore Roman Dacia from the Carpo-Dacians of Zosimus "having undertaken an expedition against the Carpi, who had then possessed themselves of Dacia and Moesia".


title: Dacia

text: Even so, the Germanic and Celtic kingdoms, particularly the Gothic tribes, slowly moved toward the Dacian borders, and within a generation were making assaults on the province. Ultimately, the Goths succeeded in dislodging the Romans and restoring the "independence" of Dacia following Emperor Aurelian's withdrawal, in 275.


title: Dacia

text: In AD 268–269, at Naissus, Claudius II (Gothicus Maximus) obtained a decisive victory over the Goths. Since at that time Romans were still occupying Roman Dacia it is assumed that the Goths didn't cross the Danube from the Roman province. The Goths who survived their defeat didn't even attempt to escape through Dacia, but through Thrace. At the boundaries of Roman Dacia, Carpi (Free Dacians) were still strong enough to sustain five battles in eight years against the Romans from AD 301–308. Roman Dacia was left in AD 275 by the Romans, to the Carpi again, and not to the Goths. There were still Dacians in AD 336, against whom Constantine the Great fought.


title: Dacia

text: The province was abandoned by Roman troops, and, according to the "Breviarium historiae Romanae" by Eutropius, Roman citizens "from the towns and lands of Dacia" were resettled to the interior of Moesia. Under Diocletian, c. AD 296, in order to defend the Roman border, fortifications were erected by the Romans on both banks of the Danube.


title: Dacia

text: In 328 the emperor Constantine the Great inaugurated the Constantine's Bridge (Danube) at Sucidava, (today Celei in Romania) in hopes of reconquering Dacia, a province that had been abandoned under Aurelian. In the late winter of 332, Constantine campaigned with the Sarmatians against the Goths. The weather and lack of food cost the Goths dearly: reportedly, nearly one hundred thousand died before they submitted to Rome. In celebration of this victory Constantine took the title "Gothicus Maximus" and claimed the subjugated territory as the new province of Gothia. In 334, after Sarmatian commoners had overthrown their leaders, Constantine led a campaign against the tribe. He won a victory in the war and extended his control over the region, as remains of camps and fortifications in the region indicate. Constantine resettled some Sarmatian exiles as farmers in Illyrian and Roman districts, and conscripted the rest into the army. The new frontier in Dacia was along the Brazda lui Novac line supported by Castra of Hinova, Rusidava and Castra of Pietroasele. The limes passed to the north of Castra of Tirighina-Bărboși and ended at Sasyk Lagoon near the Dniester River. Constantine took the title "Dacicus maximus" in 336. Some Roman territories north of the Danube resisted until Justinian.


title: Dacia

text: Victohali, Taifals, and Thervingians are tribes mentioned for inhabiting Dacia in 350, after the Romans left. Archeological evidence suggests that Gepids were disputing Transylvania with Taifals and Tervingians. Taifals, once independent from Gothia became federati of the Romans, from whom they obtained the right to settle Oltenia.


title: Dacia

text: In 376 the region was conquered by Huns, who kept it until the death of Attila in 453. The Gepid tribe, ruled by Ardaric, used it as their base, until in 566 it was destroyed by Lombards. Lombards abandoned the country and the Avars (second half of the 6th century) dominated the region for 230 years, until their kingdom was destroyed by Charlemagne in 791. At the same time, Slavic people arrived.


title: Ergot

text: The most prominent member of this group is "Claviceps purpurea" ("rye ergot fungus"). This fungus grows on rye and related plants, and produces alkaloids that can cause ergotism in humans and other mammals who consume grains contaminated with its fruiting structure (called "ergot sclerotium").


title: Ergot

text: "Claviceps" includes about 50 known species, mostly in the tropical regions. Economically significant species include "C. purpurea" (parasitic on grasses and cereals), "C. fusiformis" (on pearl millet, buffel grass), "C. paspali" (on dallis grass), "C. africana" (on sorghum), and "C. lutea" (on paspalum). "C. purpurea" most commonly affects outcrossing species such as rye (its most common host), as well as triticale, wheat, and barley. It affects oats only rarely.


title: Ergot

text: An ergot kernel, called a "sclerotium", develops when a spore of fungal species of the genus "Claviceps" infects a floret of flowering grass or cereal. The infection process mimics a pollen grain growing into an ovary during fertilization. Infection requires that the fungal spore have access to the stigma; consequently, plants infected by "Claviceps" are mainly outcrossing species with open flowers, such as rye ("Secale cereale") and ryegrasses (genus "Lolium"). The proliferating fungal mycelium then destroys the plant ovary and connects with the vascular bundle originally intended for seed nutrition. The first stage of ergot infection manifests itself as a white soft tissue (known as "sphacelia") producing sugary honeydew, which often drops out of the infected grass florets. This honeydew contains millions of asexual spores (conidia), which insects disperse to other florets. Later, the sphacelia convert into a hard dry sclerotium inside the husk of the floret. At this stage, alkaloids and lipids accumulate in the sclerotium.


title: Ergot

text: "Claviceps " species from tropic and subtropic regions produce macro- and microconidia in their honeydew. Macroconidia differ in shape and size between the species, whereas microconidia are rather uniform, oval to globose (5×3 μm). Macroconidia are able to produce secondary conidia. A germ tube emerges from a macroconidium through the surface of a honeydew drop and a secondary conidium of an oval to pearlike shape is formed, to which the contents of the original macroconidium migrates. Secondary conidia form a white, frost-like surface on honeydew drops and spread via the wind. No such process occurs in "Claviceps purpurea", "Claviceps grohii", "Claviceps nigricans", and "Claviceps zizaniae", all from northern temperate regions.


title: Ergot

text: When a mature sclerotium drops to the ground, the fungus remains dormant until proper conditions (such as the onset of spring or a rain period) trigger its fruiting phase. It germinates, forming one or several fruiting bodies with heads and stipes, variously coloured (resembling a tiny mushroom). In the head, threadlike sexual spores form, which are ejected simultaneously when suitable grass hosts are flowering.


title: Ergot

text: Ergot infection causes a reduction in the yield and quality of grain and hay, and if livestock eat infected grain or hay it may cause a disease called ergotism. Black and protruding sclerotia of "C. purpurea" are well known. However, many tropical ergots have brown or greyish sclerotia, mimicking the shape of the host seed. For this reason, the infection is often overlooked.


title: Ergot

text: Insects, including flies and moths, carry conidia of "Claviceps" species, but it is unknown whether insects play a role in spreading the fungus from infected to healthy plants.


title: Ergot

text: The evolution of plant parasitism in the Clavicipitaceae dates back at least 100 million years, to the early-mid Cretaceous. An amber fossil discovered in 2014 preserves a grass spikelet and an ergot-like parasitic fungus. The fossil shows that the original hosts of the Clavicipitaceae could have been grasses. The discovery also establishes a minimum time for the conceivable presence of psychotropic compounds in fungi.


title: Ergot

text: Several evolutionary processes have acted to diversify the array of ergot alkaloids produced by fungi; these differences in enzyme activities are evident at the levels of substrate specificity (LpsA), product specification (EasA, CloA) or both (EasG and possibly CloA). The "old yellow enzyme", EasA, presents an outstanding example. This enzyme catalyzes reduction of the C8=C9 double-bond in chanoclavine I, but EasA isoforms differ in whether they subsequently catalyze reoxidation of C8–C9 after rotation. This difference distinguishes most Clavicipitaceae from Trichocomaceae, but in Clavicipitaceae it is also the key difference dividing the branch of classical ergot alkaloids from dihydroergot alkaloids, the latter often being preferred for pharmaceuticals due to their relatively few side effects.