Handbook of Satisfiability 2nd Edition A. Biere
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- 5. Handbook of Satisfiability 2nd Edition A. Biere Digital Instant Download Author(s): A. Biere, M. Heule, H. Van Maaren, T. Walsh ISBN(s): 9781643681603, 1643681605 Edition: 2 File Details: PDF, 11.25 MB Year: 2021 Language: english
- 9. Frontiers in Artificial Intelligence and Applications The book series Frontiers in Artificial Intelligence and Applications (FAIA) covers all aspects of theoretical and applied Artificial Intelligence research in the form of monographs, selected doctoral dissertations, handbooks and proceedings volumes. The FAIA series contains several sub-series, including ‘Information Modelling and Knowledge Bases’ and ‘Knowledge-Based Intelligent Engineering Systems’. It also includes the biennial European Conference on Artificial Intelligence (ECAI) proceedings volumes, and other EurAI (European Association for Artificial Intelligence, formerly ECCAI) sponsored publications. The series has become a highly visible platform for the publication and dissemination of original research in this field. Volumes are selected for inclusion by an international editorial board of well-known scholars in the field of AI. All contributions to the volumes in the series have been peer reviewed. The FAIA series is indexed in ACM Digital Library; DBLP; EI Compendex; Google Scholar; Scopus; Web of Science: Conference Proceedings Citation Index – Science (CPCI-S) and Book Citation Index – Science (BKCI-S); Zentralblatt MATH. Series Editors: Joost Breuker, Nicola Guarino, Pascal Hitzler, Joost N. Kok, Jiming Liu, Ramon López de Mántaras, Riichiro Mizoguchi, Mark Musen, Sankar K. Pal, Ning Zhong Volume 336 Recently published in this series Vol. 335. M. Nørskov, J. Seibt and O.S. Quick (Eds.), Culturally Sustainable Social Robotics – Proceedings of Robophilosophy 2020 – August 18–21, 2020, Aarhus University and online Vol. 334. S. Villata, J. Harašta and P. Křemen (Eds.), Legal Knowledge and Information Systems – JURIX 2020: The Thirty-third Annual Conference, Brno, Czech Republic, December 9–11, 2020 Vol. 333. M. Tropmann-Frick, B. Thalheim, H. Jaakkola, Y. Kiyokir and N. Yoshida (Eds.), Information Modelling and Knowledge Bases XXXII Vol. 332. A.J. Tallón-Ballesteros and C.-H. Chen (Eds.), Machine Learning and Artificial Intelligence – Proceedings of MLIS 2020 Vol. 331. A.J. Tallón-Ballesteros (Ed.), Fuzzy Systems and Data Mining VI – Proceedings of FSDM 2020 Vol. 330. B. Brodaric and F. Neuhaus (Eds.), Formal Ontology in Information Systems – Proceedings of the 11th International Conference (FOIS 2020) Vol. 329. A.J. Tallón-Ballesteros (Eds.), Modern Management based on Big Data I – Proceedings of MMBD 2020 ISSN 0922-6389 (print) ISSN 1879-8314 (online)
- 10. Handbook of Satisfiability Second Edition Edited by Armin Biere Johannes Kepler University, Linz, Austria Marijn Heule Carnegie Mellon University, Pittsburgh, USA Hans van Maaren TU Delft, The Netherlands, Delft and Toby Walsh University of New South Wales, Kensington, Australia Part 1/Part 2 Amsterdam Berlin Washington, DC
- 11. © 2021 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978-1-64368-160-3 (print) ISBN 978-1-64368-161-0 (online) Library of Congress Control Number: 2021931050 doi: 10.3233/FAIA336 Publisher IOS Press BV Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: order@iospress.nl For book sales in the USA and Canada: IOS Press, Inc. 6751 Tepper Drive Clifton, VA 20124 USA Tel.: +1 703 830 6300 Fax: +1 703 830 2300 sales@iospress.com LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN SLOVENIA
- 12. Preface First Edition Propositional logic has been recognized throughout the centuries as one of the corner stones of reasoning in philosophy and mathematics. During history, its formalization into Boolean algebra was gradually accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of these two roles, SAT has become a mature multi-faceted scientific discipline. Initiated by the work of Cook, who established its NP-complete status in 1971, SAT has become a reference problem for an enormous variety of complexity statements. Simultaneously, many real-world problems were formalized as SAT decision problems using different encoding techniques. This includes verification problems in hardware and software, planning, scheduling and combinatorial design. Due to the potential practical implications, an intensive search from the early days of computing has been underway of how one could solve SAT problems in an automated fashion. In 1957, Allen Newell and Herb Simon introduced one of the first AI programs, the Logic Theory Machine, to prove propositional theorems from Whitehead and Russell’s “Principia mathematica”. Shortly after in 1960, Martin Davis and Hillary Putnam introduced their now famous decision procedure for propositional satisfiability problems (a more space efficient version due to Martin Davis, George Logemann and Donald Loveland followed in 1962). Asked by the editors of this handbook as a witness of his role in this devel- opment Martin Davis wrote I felt delighted and honored when I was asked to write a foreword to this Hand- book. But when I examined the table of contents and especially, when I read the initial historical article, I concluded that it is an honor that I hardly deserve. When Hilary Putnam and I began our work on automated theorem proving half a century ago, we mainly thought of it as a way to get funding for work on our real passion, Hilbert’s tenth problem. We hardly imagined that SAT might have an independent importance aside from its role in automated deduction. It is wonderful to see what a flourishing area of research satisfiability has become. Of course what is regarded as the most important problem in theoretical computer science, P = ? NP lives right here. It is remarkable that we still don’t know whether or not there is a poly-time algorithm for SAT. I am in a tiny minority in being unconvinced that the answer must be “No”. I surely don’t expect anyone to find a really efficient uniform algorithm for SAT. But I find the heuristic arguments against the existence of a very inefficient algorithm for SAT that happens to run in poly-time quite unconvincing. The topics of the handbook span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algo- rithms, hard instances, randomized formulae, problem encodings, industrial ap- plications, solvers, simplifiers, tools, case studies and empirical results. SAT is
- 13. Preface First Edition interpreted in a rather broad sense. Besides propositional satisfiability it includes the domain of quantified Boolean formulae (QBF), constraints programming tech- niques (CSP) for word-level problems and their propositional encoding and par- ticularly satisfiability modulo theories (SMT). The handbook aims to capture the full breadth and depth of SAT and to bundle significant progress and advances in automated solving. It covers the main notions and techniques and introduces various formal extensions. Each area is dealt with in a survey-like style, where some details may be neglected in favor of coverage. The extensive bibliography concluding each chapter will help the interested reader to find his way to master necessary details. The intended audience of the handbook consists of researchers, graduate stu- dents, upper-year undergraduates, and practitioners who wish to learn about the state of the art in actual solving. Limited prior knowledge about the field is as- sumed. The handbook also aims to assist researchers from other fields in applying ideas and methods to their own work. We thus hope the handbook will provide a means for cross fertilization. The start and completion of the underlying project would not have been possible without the support and encouragement of many people. As such, this handbook is a community effort and we take this opportunity to express our gratitude to this community as a whole, without addressing to all individual contributions. We are grateful to IOS Press Publishing Company because of their interest in materializing all these efforts into the book you are holding now. We are indebted to Martin Davis for his contribution to this preface and to Edmund Clarke for his support and recommendations which you may find at the back cover of this copy. Along with the completion of this handbook another similar project was started by Teofilo Gonzalez. The handbook on NP-Completeness, Theory and Applications, will be finished shortly and could be considered as a very welcome addition to those concepts which touch propositional proof complexity. These typically proof-system related issues are certainly not fully covered by us. And also there, various practical contributions on SAT solving will find updates which continue to be relevant as the discipline moves forward. Finally we take the opportunity to spend a few words on a particularly inspir- ing event who took place during the last SAT conferences: The SAT Competition. Started at the Cincinnati conference in 2002, Daniel Le Berre and Laurent Simon put an incredible amount of work in establishing the format of rules, benchmarks and solver-performance evaluations which made SAT a competitive area where especially young researchers feel triggered to contribute. As a consequence, one of the most frequently used references in this handbook undoubtedly is their competition web page. Arjen van Lith designed the cover of our Handbook. It is a challenge to rec- ognize various SAT research related patterns hidden there. Armin Biere Marijn Heule Hans van Maaren Toby Walsh vi
- 14. Preface Second Edition When the first edition of this handbook was published in 2009 advances in SAT were mostly only known to experts, and SAT was seen as a key technology only in certain applications. Since then the number of practical applications has ex- ploded, along with greater awareness of the usefulness of SAT in general: In the last century showing that a certain problem is as hard as SAT was the end of the story and trying to solve it directly seemed to be hopeless. Relying on the con- tinuing improvements made in practical SAT solving, it is now widely accepted that being able to encode a problem into SAT also is highly likely to lead to a practical solution. This “SAT Revolution” started at the end of the last century and continues to produce amazing new practical and theoretical results. Accordingly, this second edition contains several updates, including a com- pletely revamped Chapter 4 on conflict-driven clause learning. Half the chapters were updated or extended or both. Comments by Donald Knuth were also taken into account, collected while he was preparing the Section on Satisfiability in vol- ume 4 of the “The Art of Computer Programming”. This section appeared as fascicle 6a with more than 300 pages in 2015 and is a major milestone in the SAT literature that has appeared since the first edition of this Handbook. Three important topics, which were already in the first edition of the hand- book and deserve their own chapter, are now given enough space and discussed in detail: there is the new Chapter 7 on proof complexity, Chapter 9 on pre- processing, as well as the new Chapter 12 on automated configuration and solver selection. Additionally, the new Chapter 15 covers proofs of unsatisfiability, one of the main recent developments in practical SAT solving. These proofs are essential in solving long-standing mathematical problems. Beside these four completely new chapters, there are three new chapters which cover topics already discussed in the first edition. These three chapters focus on new aspects and new technology and are written by authors who made funda- mental contributions to change the state of the art. First, recent developments regarding quantified Boolean formulas including the discussion of proof systems are covered in the new Chapter 31. Second, the focus of the new Chapter 24 is on core-based methods for maximum satisfiability which have improved scalability considerably. Finally, the last new Chapter 26 covers a novel research direction on practical and approximate model counting with strong statistical guarantees. Research in SAT has established itself as a vibrant cross community effort. Beside the main SAT conference, other major conferences and journals in diverse fields from automated reasoning, verification, hardware to software engineering, complexity theory, even algorithms and of course artificial intelligence cover SAT
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- 16. was totally defeated, but, rallying his forces, he made a successful attack on the British baggage train, the loss of which forced them to retire. Ambate (Conquest of Peru). Fought 1532, between the two Peruvian chiefs Atahualpa and Huascar, in which the latter suffered a complete defeat. Ambracian Gulf. Fought B.C. 435, when a Corinthian fleet of 75 ships attempted the relief of Epidamnus, which was besieged by the Corcyreans, and was defeated with heavy loss by 80 Corcyrean triremes. Ambur. Fought 1749, between the army of Anwar-ud-din, Nawab of Arcot, 20,000 strong, and the combined forces of Muzuffer Jung and Chunda Sahib, aided by a French contingent under M. d'Auteil. Anwar-ud-din was defeated and slain, and Muzuffer Jung assumed the title of Subahdar of the Deccan, Chunda Sahib that of Nawab of Arcot. Ambur. This strong fortress was held by a garrison of 500 Sepoys, under Captain Calvert, and a detachment of Mysore troops under Mukhlis Khan. This man had assumed the status of an independent chief, but being suspected of intriguing with Hyder Ali, was arrested by Calvert. Hyder laid siege to the place November 10, 1767; but Calvert, now secure from treachery within, held out with his small garrison till December 6, when the approach of a relieving force obliged Hyder to raise the siege.
- 17. Amida (Persian Wars). This fortress, defended by a Roman garrison, was besieged, and after a vigorous defence taken by storm by the Persians under Sapor II in 359. The garrison and inhabitants were put to the sword. The siege, which lasted 73 days, cost the Persians 30,000 men, and so weakened Sapor that he was compelled to relinquish his designs upon the Eastern Empire. The fortress was again besieged by the Persians under Kobad in 503, being defended as before by a Roman garrison. After a defence of three months, which cost the besiegers 50,000 men, a weakly defended tower was surprised at night, and on the following day the Persians, headed by their King, scaled the walls, and massacred 80,000 of the garrison and inhabitants. Amiens (Franco-German War). Fought November 27, 1870, between the French under General Faure, and the Germans under Manteuffel. The French were compelled to abandon the city, but the Germans failed to secure a decisive victory. The French lost 1,383 killed and wounded, and 1,000 missing; the Germans, 76 officers and 1,216 men. Amoaful (Second Ashanti War). Fought January 31, 1874, when the British expeditionary force under Sir Garnet Wolseley defeated the Ashantis after a desperate resistance, which cost the assailants 16 officers and 174 men killed and wounded. The 42nd Regiment, which led the attack, lost 9 officers and 105 men. Amorium (Moslem Invasion of Asia Minor).
- 18. Fought 838, between the Moslems under the Caliph Motassem, and the Greeks under Theophilus. Thirty thousand Persian horsemen, serving under the Emperor, succeeded in breaking the Moslem line, but the Greeks themselves were overthrown by the Moslems, and the day ended in a complete rout of the Imperial army. Motassem then laid siege to Amorium, and after a defence of 55 days, which cost the besiegers 70,000 men, the gates were opened by treachery, and 30,000 Christians were massacred. Amphipolis (Peloponnesian War). Fought March 422 B.C. between 1,500 Athenians, with a contingent of allies under Cleon, and the Spartans, 2,000 hoplites, besides light armed troops, under Brasidas. Cleon advanced to attack Amphipolis, but finding the garrison preparing for a sortie, wheeled about and commenced to retreat, He was at once assailed by Brasidas, and his left fled without striking a blow. The Athenian right and centre offered some resistance, but in the end were routed with heavy loss. Both Brasidas and Cleon fell, the latter while fleeing from the field. Amstetten (Campaign of the Danube). Fought November 5, 1805, when the Russians retiring on Vienna fought a rear-guard action against Murat's cavalry and a portion of Lannes' corps, in which they were defeated with a loss of 1,000 killed, wounded, and prisoners. Añaquito (Conquest of Peru). Fought January 8, 1546, between the troops of the Viceroy, Blasco Nuñez, and those of Gonzalo Pizarro. Pizarro gained a signal victory, the Viceroy being among the slain, and in consequence the Government of Peru fell into Pizarro's hands.
- 19. Ancona (Unification of Italy). This place was attacked, September, 1860, by the Piedmontese fleet of 13 warships under Admiral Persano, and the army of General Cialdini. It was defended by a small Papal garrison under La Moricière, and after a resistance of over a week, at the end of which time Persano forced the boom guarding the harbour, La Moricière capitulated. Ancrum Moor (Scottish Wars). Fought February 17, 1545, between the English under Sir Ralph Evans, and the Scots under the Earl of Angus. The Borderers who had joined the English deserted during the action, with the result that the Scots were completely victorious. Ancyræ. Fought B.C. 242, between the Syrians under Seleucus Callinicus, and the rebels under his brother Hierax, aided by a large contingent of Gauls. After a desperate struggle, in which Hierax nearly lost his life at the hands of his barbarian auxiliaries, Seleucus was utterly routed. Angora (Tartar Invasion of Asia Minor). Fought June 30, 1402, between the Tartars under Tamerlane, and the Turks under Bajazet I. The numbers engaged are variously estimated at from one to two millions, Tamerlane, it is said, having at least 800,000 men in the field. The Turks were totally defeated, Bajazet and one of his sons being captured, while another son was killed. Angostura (Americo-Mexican War).
- 20. Fought February 21, 1847, between the Mexicans under Santa Anna and the Americans under General Scott, when the Mexicans were totally defeated. Angostura (Paraguayan War). Fought December 22 to 27, 1868, between the Paraguayans under Lopez, and the allied armies of the Argentine Republic, Brazil, and Uruguay. Lopez held his position for six days against the greatly superior forces of the allies, but was then compelled to retire, leaving in the hands of the enemy 1,000 prisoners and 6 guns. Antietam (American Civil War). Fought September 17, 1862, between the main Confederate army under General Lee, and the Federals under General M’Clellan. On the morning of the 17th Lee had only 35,000 men on the ground against M’Clellan's 95,000. The Federals strongly attacked Lee's left, and after a stubborn fight drove it back, but reinforcements arriving, Lee resumed the offensive, and recovered his lost positions. On the following day neither side was disposed to resume the struggle, and the battle was therefore indecisive. The Federals lost 12,460 men; the Confederates about 9,000. Antioch. Fought B.C. 244, between the Syrians under Seleucus Callinicus and the Egyptians under Ptolemy Energetes. Seleucus was routed and compelled to take refuge within the walls of Antioch. Antioch (Aurelian's Expedition to Palmyra). Fought B.C. 272, between the Palmyrenians under Zenobia, and the Romans under the Emperor Aurelian. Zenobia's heavy cavalry
- 21. defeated and drove from the field the Roman horse, but her infantry was unable to withstand the charge of the legionaries, and she was totally defeated. Antioch (First Crusade). The city was besieged, October 21, 1097, by the Crusaders under Godefroi de Bouillon, and defended by a Saracen garrison under Baghasian. The siege was unskilfully conducted, and provisions and munitions ran short in the Christian camp, with the result that the place held out till June 3, 1098, when it was taken by stratagem. An indiscriminate massacre followed, in which 10,000 of the defenders perished. On the 28th of the same month the Crusading army was attacked outside Antioch a force of Saracens under Kirboga. Kirboga concentrated his attack against one wing of the Christians, and outflanked it, but was then assailed by the main body, and driven off with heavy loss. Antium (War of Chiozza). Fought May 30, 1378, when Vittorio Pisani, with 14 Venetian galleys, defeated the Genoese fleet under Fieschi. The Genoese lost 6 ships, and Fieschi was taken prisoner. Antwerp (Netherlands War of Independence). This city was sacked by the Spaniards, November 4, 1576. It was defended by 6,000 troops, mostly Walloons, who offered little resistance to the 5,600 Spaniards under Sancho d'Avila, who formed the attacking force. Having effected an entrance, the Spaniards proceeded to massacre the inhabitants, of whom 8,000 are said to have perished. This event is known as the Spanish Fury.
- 22. Antwerp (Liberation of Belgium). When Holland refused to recognize the London Protocol creating Belgium into an independent State, the French laid siege to Antwerp, November, 1832. The city, which was defended by Chassé, held out till December 23, when, the citadel being demolished by the French fire, it was forced to capitulate. Aong (Indian Mutiny). Fought July 15, 1857, between the British relieving force under Havelock and the mutineers who were opposing their advance on Cawnpore. The rebels were defeated and driven from their entrenchments. Aquae Sextiae (Cimbric War). Fought B.C. 102, when the Teutones under the king Teutobod, were totally routed by the Romans under Marius. Aquidaban (Paraguayan War). The last stand of the Paraguayans against the allied armies of the Argentine Republic, Brazil, and Uruguay, May 1, 1870. Lopez, with a small force of Paraguayans and 5,000 Indians, met the attack of the allies under General Camera on the banks of the Aquidaban, and after a sanguinary engagement, in which he and the Vice-President Sanchez fell, his army was cut to pieces, and the war ended. During the war the population of Paraguay was reduced from 1,500,000 to 221,000, of whom only 29,000 were males over fifteen years of age. Aquileia (Eugenius' Usurpation).
- 23. Fought September 6 and 7, 394, between Theodosius, Emperor of the East, and Eugenius, the usurping Emperor of the West, whose army was commanded by Arbogastes. The first day's fighting went against Theodosius, who was only saved by darkness from a severe reverse, but during the night a force sent by Arbogastes to secure the passes in Theodosius' rear, deserted to his standard, and thus reinforced and aided by a dust storm which blew in the faces of his antagonists and disordered their ranks, he on the following day gained a signal victory. Aras (First Mahratta War). Fought May 18, 1775, between Raghunath Rao, the claimant to the Peshwaship, with 20,000 Mahrattas, and 2,500 British troops under Colonel Keating, and the army of the Mahratta chieftains, 25,000 strong under Hari Pant Phunhay. Raghunath's undisciplined levies fled, and threw the British line into confusion; but they rallied, and after hard fighting repulsed the Mahrattas with heavy loss. The British lost 222, including 11 officers. Arausio (Fourth Gallic Invasion). Fought B.C. 105, when the Gauls under Boiorix totally routed two consular armies under Cæpio and Cn. Mallius Maximus. It is said that 80,000 Romans fell. Arbela (Alexander's Asiatic Campaign). Fought October 31, 331 B.C., between 47,000 Macedonians under Alexander the Great, and the Persian army, three or four times as numerous, under Darius Codomannus. Alexander, who led the Macedonian right wing, forced a passage between the Persian left and centre, and attacked the centre on the flank. After a stubborn resistance, and though meanwhile the Macedonian left had been
- 24. hard pressed, the Persians gave way, and Darius taking to flight, the whole army fled in confusion, and was routed with enormous loss, especially at the passage of the Lycas, which barred their retreat. This victory made Alexander master of Asia. Arcis-sur-Aube (Allied Invasion of France). Fought March 21, 1814, between 23,000 French under Napoleon, and 60,000 allies under Schwartzenberg. The French made a gallant stand against superior numbers, and in the end effected an orderly retreat, with a loss of about 2,000. The allies' losses were considerably heavier. Arcola (Napoleon's Italian Campaigns). Fought November 15, 16, and 17, 1796, between the main Austrian army under Alvinzi, and the French under Napoleon. Napoleon's object was to drive back Alvinzi before he could effect a junction with Davidowich, who was descending from the Tyrol. The village of Arcola was occupied on the 15th, after severe fighting, in which Napoleon was in great personal danger on the bridge, but it was evacuated during the night. On the 16th Napoleon again attacked the village, but the Austrians held their ground. On the 17th he turned the position, and Davidowich still remaining inactive, Alvinzi was driven back, with losses variously estimated at from 8,000 to 18,000. The French also lost heavily. Arcot. This fortress was captured by Clive, with a force of 200 Europeans and 300 Sepoys, in August, 1751. The garrison, 1,100 strong, offered no resistance, but marched out on Clive's approach. In the course of the autumn Arcot was beleaguered by an army of 10,000 natives, and 150 Frenchmen under Chunda Sahib, the French
- 25. nominee for the Nawabship of Arcot. Against this overwhelming force, Clive, whose garrison had been reduced by sickness to 120 Europeans, and less than 200 Sepoys, held out for seven weeks, till the approach of a Mahratta army forced Chunda Sahib to raise the siege. The garrison had 45 Europeans and 30 Sepoys killed. Argaum (Second Mahratta War). Fought November 28, 1803, between the British under Wellesley (the Duke of Wellington) and the forces of the Rajah of Berar, under Sindhia of Gwalior. Three of Wellesley's battalions, which had previously fought well, on this occasion broke and fled, and the situation was at one time very serious. Wellesley, however, succeeded in rallying them, and in the end defeated the Mahrattas, with the loss of all their guns and baggage. The British lost 346 killed and wounded. This victory ended the Second Mahratta War. Argentaria (Invasion of the Alemanni). Fought May, 378, between the Romans under Gratianus and the Alemanni under Priarius. The Alemanni were overwhelmed by the Roman legionaries, though they stood their ground bravely, and only 5,000 escaped from the field. Priarius was slain. Argentoratum. Fought August, 357, between 13,000 Romans under Julian, and a vastly superior army of Alemanni under Chnodomar. The Romans attacked the German lines shortly before night-fall, after a long march, and though the right wing, under Julian, was at first driven in, they were rallied by their general, and the left and centre pressing on, the Alemanni were totally routed, with a loss of 6,000, in addition to those who fell in the flight. The Romans lost 4 tribunes and 243 soldiers only. Chnodomar was taken prisoner.
- 26. Arginusæ (Peloponnesian War). Fought B.C. 406, between 150 Athenian triremes under Thrasyllus and other generals, and 120 Peloponnesian ships under Callicratidas. The Peloponnesians were routed, with a loss of 70 vessels, sunk or taken, and Callicratidas slain. The Athenians lost 25 ships with their crews, and the generals were brought to trial for not having taken proper steps to rescue the men of the disabled ships. They were convicted, and six of them, including Thrasyllus, executed. This victory temporarily restored to Athens the command of the sea. Argos (Roman Invasion of Greece). Fought B.C. 195, between Nabis of Sparta, with 15,000 men, and 50,000 Romans and Macedonians under Flaminius. Nabis was totally defeated, and though allowed to retain Sparta, was compelled to restore to the Achæan league all his foreign possessions. Arikera (Second Mysore War). Fought May 13, 1791, between the British under Lord Cornwallis, and the forces of Tippu Sahib. The latter was encamped between Arikera and Seringapatam, and was attacked by Cornwallis, who attempted to surprise him by a night march, but was foiled by heavy rain. A frontal attack on Tippu's position was, however, successful, and, aided by a flank movement under Maxwell, resulted in the total defeat of the Mysore troops, with a loss of over 2,000. The British loss amounted to 500. This is also known as the battle of Carigat. Arius, The. Fought B.C. 214, between the Syrians under Antiochus the Great, and the Parthians and Bactrians under Arsaces III, and Euthydemus.
- 27. Antiochus was severely wounded, but remained at the head of his troops, and completely routed the enemy with enormous loss. Arkenholm (Douglas Rebellion). Fought May 12, 1455, between the troops of James II of Scotland and the rebels under the Douglas brothers. The rebels were completely defeated. Archibald Douglas was killed, Hugh captured, and James, Earl of Douglas, forced to take refuge in England. Arklow (Irish Rebellion). Fought 1798, when General Needham, with about 1,400 Militia and Volunteers, defended the town from the attack of 27,000 rebels led by Father John Murphy. The rebels were beaten off with great slaughter, and their intended advance on Dublin prevented. Armada, The Invincible. The fight with the Spanish Armada in the Channel began on Sunday, July 21, 1588, and lasted with intervals until the 30th. The Armada consisted of 130 ships, many of large size, under the command of the Duke of Medina Sidonia. The English fleet numbered 197 in all, but only 34 were Queen's ships, and of these but 8 were over 600 tons burden. Lord Howard of Effingham commanded, with Drake and Hawkins as his lieutenants. The English vessels hung on to the flanks of the Spanish ships as they sailed up channel, harassing them in every way, and doing considerable damage, until the Armada anchored in Calais roads. Here many of their finest vessels were captured or destroyed by fire-ships, and finally on the 30th, Medina Sidonia decided to attempt to escape northwards. His fleet was scattered by storms, and many wrecked on the Scotch and Irish coasts, and in the end only about one-half of the Armada returned to Spain.
- 28. Arnee. Fought 1751, shortly after the relief of Arcot, between 900 British troops, under Clive, with 600 Mahratta horse under Basin Rao, and a French force of 4,800, including 300 Europeans, who were in charge of a convoy of treasure. Clive took up a position in swampy ground, crossed by a causeway along which the convoy must pass. The French were thrown into disorder, and forced to retreat, but night saved them from complete destruction. The treasure was captured. Arnee (First Mysore War). An indecisive action fought June 7, 1782, between the British under Sir Eyre Coote, and the Mysore troops under Hyder Ali. Arques (Eighth Civil War). Fought September 23, 1589, between 5,000 Huguenots under Henri IV, and 30,000 Leaguers under the Duc de Mayenne. Henri had taken up a strong position, defended by marshy ground, and of such a nature that Mayenne could only bring against the king 5,000 troops at a time, thus neutralizing the disparity of numbers. He repulsed attack after attack, with heavy loss to the assailants, and eventually Mayenne was forced to withdraw, with the loss of about half his army. Arrah (Indian Mutiny). A house in Arrah was, in 1857, defended by Mr. Boyle, with 16 Englishmen and 60 Sikh police, against the attacks of three revolted native regiments, led by a Zemindar named Kur Singh. This small garrison held out from July 25 till August 3, when they were relieved by a small field force under Major Vincent Eyre.
- 29. Arras (Wars of Louis XIV). This place, held by a French garrison, was besieged August, 1654, by the Spaniards under the Great Condé. On the 24th a relieving army under Turenne attacked the Spanish lines, and totally routed them with a loss of 3,000 men. Condé succeeded in rallying the remainder of his army, and made a masterly retreat to Cambray. Arretium (Etruscan War). Fought B.C. 283, when the consular army of L. Cæcilius Metellus, marching to the relief of Arretium, which the Etruscans were besieging, met with a disastrous defeat. Thirteen thousand, including Metellus, were slain, and the rest made prisoners. Arroyo Grande (Uruguayan War of Independence). Fought 1842, between the Argentine troops under Oribe, and the Uruguayans under Ribera. Ribera was totally defeated, and Oribe proceeded to lay siege to Montevideo. Arsouf (Third Crusade). Fought 1192, between the English Crusaders under Richard Cœur de Lion, and the Saracens, 300,000 strong under Saladin. The Saracens made a desperate onslaught on the English, and both their wings gave way, but the centre under the king stood firm and finally drove back the Moslems in great disorder, with a loss of 40,000 men. Ascalon (First Crusade). Fought August 19, 1099, between the Crusaders under Godefroi de Bouillon, and the Saracens under Kilidj Arslan. The Crusaders
- 30. gained a signal victory, and for a time the Moslem resistance to the Christian occupation of the Holy Land came to an end. Asculum (Pyrrhus' Invasion of Italy). Fought B.C. 279, between 45,000 Romans under Sulpicius Saverrio and P. Decius Mus, and the Epirots, with their Italian allies, in about equal force. The Romans fought to raise the siege of Asculum, but were finally routed by the Epirot cavalry and elephants, and driven back to their camp with a loss of 6,000. The Epirots lost 3,000. Asculum (Social War). Fought B.C. 89, between 75,000 Romans under Strabo, who was besieging the town, and 60,000 Italians under Judacilius, who had marched to its relief. The Romans were victorious, but Judacilius succeeded in throwing a considerable portion of his army into the beleaguered city. Ashdown (Danish Invasion). Fought 871, between the West Saxons under Æthelred and the Danes under Bag Secg and Halfdene. Largely owing to the brilliant leading of Alfred (the Great), who commanded one of the wings, the Danes, after a desperate conflict, which lasted throughout the day, were finally put to flight, having lost one of their kings and five jarls. Ashtee (Third Mahratta War). Fought February 19, 1818, between the army of the Peshwá, Baji Rao, under Gokla, and the British under General Smith. The Peshwá fled before the action began, and Gokla, charging at the head of his cavalry, was killed, whereupon the Mahrattas broke and fled in confusion.
- 31. Asirghur (Third Mahratta War). This fortress, held by Jeswunt Rao, with a strong Mahratta garrison, was besieged by a British force under Sir John Malcolm and General Doveton, March 18, 1819. On the 21st the garrison was driven into the upper fort, and after a continuous bombardment, Jeswunt Rao surrendered April 7. The British loss during the siege was 313 killed and wounded; that of the garrison somewhat less. Askultsik (Ottoman Wars). Fought 1828, between 30,000 Turks and the Russians, 17,000 strong, under General Paskiewitch. The Turks were routed, and their camp, with all artillery and baggage, captured. Paskiewitch then laid siege to the town, which was defended by a garrison of 50,000 men, and after a siege of three weeks, carried it by storm, August 28. Aspendus. Fought B.C. 191, between the Syrian fleet of Antiochus the Great, under Hannibal, and a Rhodian squadron under Eudamus. Though Hannibal was in superior force, he suffered a severe defeat. Aspern (Campaign of Wagram). Fought May 21 and 22, 1809, between 36,000 French under Napoleon, and 70,000 Austrians under the Archduke Charles. The battle commenced about four p.m. on the 21st by an attack on the French position at Aspern, and at nightfall the Austrians had established a lodgment in the village. On the 22nd, both armies having been reinforced during the night, the combat was renewed round Aspern, which was taken and retaken ten times, while Essling was the scene of an equally desperate conflict. Towards evening the bridge by which Napoleon had crossed the Danube was swept away,
- 32. and Napoleon was compelled to retire. Each side lost about 20,000 men, and both claimed the victory. Among the French who fell were Marshal Lannes and General St. Hilaire. Aspromonte (Garibaldi's Rising). Fought August 29, 1862, between a small force of "Red Shirts" under Garibaldi, and the royal troops under General Pallavicini. After a short engagement, in which Garibaldi was wounded, the "Red Shirts," largely outnumbered and surrounded, laid down their arms. Assandun (Danish Invasion). The last of the five battles fought in 1016 between the English under Edmund Ironside and the Danish invaders under Knut. Owing to the treachery of Ædric, who crossed over with the Hereford men in the course of the battle, the English were defeated, and shortly afterwards Knut was proclaimed King of England. Assaye (First Mahratta War). Fought September 23, 1803, when General Wellesley (the Duke of Wellington) with 4,500 British and native troops routed the army of Sindhia of Gwalior, over 30,000 strong. All the camp equipment and 100 guns were taken. The Duke always considered this the bloodiest action, for the numbers engaged, that he ever witnessed. The British loss amounted to 1,566, or more than one-third of Wellesley's entire force. Astrakhan. Siege was laid to this town, 1569, by the Turks under Selim II, who required it as a base for his projected invasion of Persia. It was held by a small Russian garrison, which made an obstinate defence,
- 33. and was finally relieved by an army despatched to its assistance by Ivan the Terrible, which attacked the Turkish lines, and utterly routed them. Atahualpa (Conquest of Peru). Fought 1531, between 160 Spaniards under Pizarro, and 30,000 Peruvians, forming the escort of the Inca, Manco-Capac. The battle was nothing but a butchery, Pizarro, who had invited the Inca to visit him, falling upon the unsuspecting Peruvians, seizing Manco-Capac, and slaughtering 4,000 men, without the loss of a single Spaniard. Atbara (Soudan Campaigns). Fought April 8, 1898, between the British and Egyptian army, 14,000 strong, under Sir Herbert Kitchener, and 18,000 Mahdists under Mahmad. The Mahdists occupied an entrenched zareeba on the Atbara, where they were attacked and utterly routed, with a loss in the zareeba of 5,000 killed and 1,000 prisoners, while many more fell in the pursuit. Mahmad was captured. The Anglo-Egyptian losses were 570 killed and wounded, including 29 British officers. Athenry (Conquest of Ireland). Fought 1316 between the English under William de Burgh and Richard de Bermingham, and the O'Connors under their chieftain, Feidlim. The O'Connors were defeated, 11,000 of the sept falling in the battle. This is the last appearance of the O'Connors as a clan in Irish history. Atherton Moor. See Adwalton Moor.
- 34. Auerstadt. See Jena. Augsburg. Fought 900, between the Germans and the invading Hungarians. The Christians fought gallantly, but were overwhelmed by the numbers of the barbarian cavalry, and in the end suffered a signal defeat. Auldearn (Civil War). Fought May 9, 1645, when Montrose and his Highlanders defeated a largely superior force of Covenanters under Sir John Hurry, who was marching northward to raid the lands of the Gordons. Auray. Fought September 27, 1364, between the partisans of John de Montfort, and those of Charles of Blois, the rival claimants to the Dukedom of Brittany. The English party, under Sir John Chandos, were besieging Auray, when they were attacked by the French, who were led by Bertrand du Guesclin. Chandos' position, however, was very strong, and the French were unable to make any impression upon it. Meanwhile they were thrown into utter confusion by an attack on their flank, and were ultimately routed, with heavy loss, Charles of Blois being among the slain. Bertrand du Guesclin was captured. De Montfort was shortly afterwards acknowledged by Charles V of France as Duke of Brittany. Aussig (Hussite War).
- 35. Fought 1426, between the Germans under the Emperor Sigismund, and the Taborites, the extreme section of the Hussites, under John Zisca. The Germans were signally defeated. Austerlitz (Campaign of the Danube). Fought December 2, 1805, between 50,000 Russians and 25,000 Austrians under Kutusoff, and 75,000 French under Napoleon. An attempt to turn the French flank failed, and led to the left of the allies being entirely cut off from their centre. Their left and centre were thus beaten in detail, and the right, which had at first held its own, was surrounded, and driven in disorder across a partially frozen lake, where many perished. The allies lost 20,000 killed, wounded, and prisoners, and a large number of guns. The French lost about 5,000. The battle is called the Battle of the Three Emperors, those of Russia, Austria, and France being all present with their respective armies. Avaricum (Gallic War). This place was made the headquarters of the revolted Gauls under Vercingetorix, B.C. 53, and was besieged by Cæsar, with 50,000 Romans. The place was strongly defended, but supplies ran short, and Vercingetorix attempted to withdraw his troops. In this he was unsuccessful, and the Romans, delivering a vigorous assault, took possession of the town, and massacred the garrison and inhabitants. Avus (Second Macedonian War). Fought B.C. 198, between 20,000 Macedonians under Philip, and two Roman legions under T. Quinctius Flamininus. A force of 4,000 legionaries penetrated to the rear of Philip's camp, and when Flamininus attacked in front, they fell upon the Macedonian rear, and completely routed them, with a loss of 2,000.
- 36. Axarquia (War of Granada). Fought March 20, 1483, between a Spanish force of 3,000 knights, and about 2,000 infantry, under the Marquis of Cadiz, and a strong Moorish force under Abul Hasan. The Spaniards were marching through the defile of Axarquia, on their way to attack Malaga, when they were assailed in front and flank, and totally routed, losing 800 killed and 1,600 prisoners. Among the killed were 400 men of rank. Ayacucho (South American War of Independence). Fought December 9, 1824, between the South American patriots, 5,780 strong, under Sucre, and the Spaniards, 9,310 in number, under Laserna. The latter were routed with a loss of 2,100 killed and wounded, and over 3,500 prisoners, including Laserna, in addition to 15 guns. The Patriots lost 979. This engagement, which is also known as the Battle of Candorcanqui, practically decided the question of South American independence. Aylesford (Jutish Invasion). Fought 456, between the Jutes under Hengist and Horsa, and the Britons under Vortigern. Horsa was slain in the battle, but the Jutes were victorious. Azimghur (Indian Mutiny). Fought April 15, 1858, between a British column, composed of three regiments of infantry and three of Sikh cavalry, under Sir Edward Layard, and the Dinapur mutineers, about 5,000 strong, under Kur Singh. The rebels were routed and dispersed, Kur Singh falling mortally wounded. Azores.
- 37. In 1591, a fleet of 7 ships under Lord Thomas Howard was driven from Floris by the Spanish fleet under Don Alfonso Bassano. The action was chiefly remarkable for the gallant fight made by Sir Richard Grenville in the Revenge, which maintained an unequal struggle for nine hours, when her gallant commander was mortally wounded, and she surrendered at daybreak.
- 38. B Badajos (Peninsular War). On March 17, 1812, this fortress, held by a garrison of French, Hessians and Spaniards, 5,000 strong, under Phillipon, was invested by Wellington. The breaches were declared to be practicable on April 5, and an assault was ordered. After terrible slaughter, the town was taken, with a loss to the assailants of 3,500, the total British losses during the siege exceeding 5,000. Fearful excesses were committed after the assault, and for two days the troops were completely out of hand. Baduli-ki-Serai (Indian Mutiny). Fought June 8, 1857, when a British force, under Sir Henry Barnard, defeated a large body of mutineers, who were opposing their march to Delhi. All the rebels' guns were captured. Bagdad (Tartar Invasion of Mesopotamia). This city was captured by the Tartars under Tamerlane, July 23, 1401. Bagradas (Civil War of Cæsar and Pompey). Fought B.C. 49, between the Cæsareans under Curio and the Numidians under Juba and Saburra, who adhered to the fortunes of
- 39. Pompey. The Roman cavalry was cut to pieces, before the legionaries could come to its assistance, and eventually the Romans were surrounded, and cut down to a man, Curio being amongst the slain. This victory left the Pompeians masters of Africa. Bahur (Seven Years' War). Fought August, 1752, between the French, numbering 2,500, including natives, under M. Kirkjean, and 2,000 British troops, with 4,000 of Mohammed Ali's levies, under Major Lawrence. The French were totally defeated, losing heavily in men, guns and stores. This victory determined the Mahrattas, who were wavering, to throw in their lot with the British. Balaclava (Crimean War). Fought October 25, 1854, between 30,000 Russians under Prince Mentschikoff, and the British under Lord Raglan. The Russians, having driven the Turks from their redoubts at Kadikoi, entered the valley of Balaclava, where they were encountered and driven back by the Heavy Cavalry Brigade under General Scarlett. Later in the day, acting under a mistaken order, Lord Cardigan at the head of the Light Brigade, charged the Russian guns at the head of the valley, and captured their batteries. Being, however, shelled from all sides, he was compelled to retire with heavy loss. Of this famous feat of arms, General Pelissier is reported to have said, "C’est magnifique, mais ce n’est pas la guerre." Another feature of this singular battle was the repulse by the Highland Brigade, in line, of a charge of the Russian cavalry. The British losses were small, except in the case of the Light Brigade, whose casualties amounted to 272 out of 673 who took part in the charge. Balls Bluff (American Civil War).
- 40. Fought October 21, 1861, between the Federals under General Stone, and the Confederates under General Evans. The Federals crossed the Potomac to attack the Southern position, but were repulsed, and driven back over the river in confusion losing 1,100 killed and wounded, 700 prisoners and the only three guns which they had succeeded in taking across. The Confederates lost 155 only. Ballymore (Irish Rebellion). Fought June 3, 1798, when Colonel Walpole, with 500 Royal troops, on the march to Enniscorthy, was surprised and overpowered by a body of rebels under Father Murphy. Walpole and the majority of his force were cut to pieces. Baltimore (Second American War). This city was attacked September 11, 1814, by a British fleet of ten sail, under Admiral Sir Alexander Cochrane, and a land force of 3,270 under General Ross, who fell during the action. The Americans, 17,000 strong, under General Winder, were defeated, but the British retired on the evening of the 13th. The British lost 46 killed and 300 wounded, the Americans, 20 killed, 90 wounded, and 200 prisoners. Bamian (Tartar Invasion of Kharismia). This city was invested by the Mongols under Genghiz Khan in 1221, and after an obstinate defence, lasting several months, was taken by storm. Genghiz, who had seen a favourite grandson killed during the progress of the siege, gave orders that neither woman nor child was to be spared, and the whole city with its inhabitants was wiped out.
- 41. Banda (Indian Mutiny). Fought April 19, 1858, between a force of rather over 1,000 British troops under General Whitlock, and 7,000 mutineers under the Nawab of Banda. After an obstinate conflict the rebels were totally routed. Banda Islands (Wars of the French Revolution). These islands, forming part of the Dutch East Indian possessions, were captured March 8, 1796, by a British squadron under Admiral Peter Rainier. Bands, The (Danish Invasion). Fought 961, between the Scots under their king, Indulph, and the Danish pirates. The Danes were defeated, but Indulph fell in the battle. Bangalore (Second Mysore War). This place was besieged by the British under Lord Cornwallis, March 5, 1791, and notwithstanding numerous efforts to relieve it on the part of Tippu Sahib, it was taken by storm on the night of the 21st, Tippu's final attempt being beaten off by the reserve with heavy loss. The British casualties were few. Bannockburn (Scottish Wars). Fought June 24, 1314, between the Scots under Robert Bruce, and the English invaders under Edward II. Bruce's position was partly covered by a marsh, and further strengthened by pitfalls, in which the English cavalry were entrapped, and defeated with great loss. The king escaped with difficulty and the invasion was abandoned.
- 42. Bapaume (Franco-German War). Fought January 3, 1871, between the French under General Faidherbe, and the Germans under Von Goeben. The result was indecisive, and though the French gained some tactical successes, the result strategically was an advantage to the Germans, as General Faidherbe was compelled to desist from his attempt to raise the siege of Péronne. The Germans lost 52 officers and 698 men; the French 53 officers and 1516 men killed and wounded, and 550 prisoners. Barbosthenian Mountains (Wars of the Achæan League). Fought 192 B.C. between the Spartans under Narbis, and the Achæan League under Philopœmen. Nabis was totally routed, with the loss of three-fourths of his troops. Barcelona (War of the Spanish Succession). This city, which was held for Philip V of Spain by a Spanish garrison, was besieged September 14, 1705, by the British under the Earl of Peterborough. After a short bombardment, the place surrendered, October 9. Barnet (Wars of the Roses). Fought April 14, 1471, between the Yorkists under Edward IV, and the Lancastrians under the Earl of Warwick. Warwick prepared to attack the king as he issued from Barnet, but Edward came out during the night and took up a position opposite Warwick unseen. The left of the Yorkists was outflanked and beaten, but their right outflanked and defeated the Lancastrian left, and then fell upon and routed the centre. Warwick was slain. The losses on the two sides are said to have amounted in all to 1,000 killed.
- 43. Barosa (Peninsular War). In the course of the operations for the relief of Cadiz, General Graham, with 4,000 British troops, defeated Marshal Victor with 9,000 French, March 5, 1811. The French lost 2,000 killed and wounded, including two generals, 6 guns, 2 eagles, and 400 prisoners. The British losses amounted to 50 officers and 1,160 rank and file. A large Spanish force under La Peña stood idly by, and took no part in the action. Barquisimeto (South American War of Independence). Fought 1813, between the Colombian patriots under Simon Bolivar, and the Spanish Royalists, Bolivar gaining a complete victory. Basing (Danish Invasion). A victory of the Danish invaders in 871 over the West Saxons. Bassano (Napoleon's Italian Campaigns). Fought September 8, 1796, when Napoleon, who had on the previous day destroyed the Austrian vanguard at Primolano, fell upon the main body of Wurmser's army. The assault on the town of Bassano was delivered by Augereau's division on the right, and Masséna's on the left, and the French utterly routed the Austrians, Wurmser narrowly escaping capture. Six thousand men laid down their arms, and when Wurmser collected his scattered forces, he had but 16,000 left out of the 60,000 with which he had commenced the campaign. Bassein (First Mahratta War).
- 44. This place, held by a Mahratta garrison, was besieged by a British force under General Goddard, November 13, 1780. A serious attempt was made to relieve the garrison, but the defeat of the relieving force by Colonel Hartley at Dugaar, on December 10, completely discouraged the defenders, and they surrendered on the following day. Bassorah (Arab Revolt). Fought in 665 between the Caliph Ali, at the head of 29,000 Moslems, and the rebel Arabs in superior force, under Telha and Zobin. The rebels were defeated with heavy loss, Telha and Zobin being slain, and Ayesha, the widow of the prophet, who had espoused their cause, captured. This victory is known to Moslems as the Day of the Camel, 70 men, who in succession held the bridle of the camel on which Ayesha was mounted, being killed in the fight which raged round her. Batavia (Napoleonic Wars). This town was captured by the British under Sir Samuel Auchmuty, with 10,000 troops, August 26, 1811. The French and Dutch garrison had abandoned the town, and occupied a strong position at Fort Cornelius, in the immediate neighbourhood. The British stormed the entrenchments, with a loss of 872 killed and wounded, whereupon the survivors of the garrison laid down their arms. Batoche (Riel's Second Rebellion). Fought May 9 to 12, 1885, when 750 Canadians under General Middleton gradually drove back and finally defeated Riel's force of half-breeds and Indians, with a loss of 224. The Canadians lost only 54 killed and wounded. Riel surrendered on the 15th.
- 45. Batowitz. Fought 1653 between 40,000 Poles under John II, and the Wallachians under Bogdan. The Poles, who were waiting to intercept the passage of the Wallachians, were thrown into disorder by a furious charge headed by Bogdan in person, and almost completely annihilated. Bautzen (Campaign of Leipzic). Fought May 20 and 21, 1813, between 150,000 French under Napoleon, and the Prussians and Russians, 100,000 strong, under Blucher and Count Wittgenstein. The allies were strongly posted in and around Bautzen, while their front was protected by the Spree. On the 20th Napoleon forced the passage of the Spree, and seized Bautzen after severe fighting, driving the allies from their first line of defence. On the 22nd he attacked the second line, while a flank march of Ney's corps drove in their right flank, and captured all their positions. The allies retired in good order, lack of cavalry preventing Napoleon from pushing his advantage. The allies lost 15,000 killed and wounded in the two days; the French, 1,300. Bavay (Gallic War). Fought B.C. 57 between the Romans, 50,000 strong, under Cæsar, and a large force of Gauls, drawn from the Nervii, Viromandui, Atrebates and other tribes. The Gauls attacked as the Romans were pitching their camp on the banks of the Sambre, but, although surprised, the legionaries stood their ground, and utterly routed their assailants. The Nervii, in particular, were practically annihilated. Baylen (Peninsular War).
- 46. Fought July 19, 1808, between 15,000 Spaniards under Castaños, and 20,000 French under Dupont. The French were totally defeated with a loss of over 2,000 men, and Dupont surrendered with his whole army. Baza (War of Granada). This fortress, one of the outposts of Granada, was besieged by Ferdinand, with 95,000 Spaniards, in June 1489, and was defended by a strong Moorish garrison under Sidi Yahye. The town was very strong, and was gallantly defended, and the siege lasted until December, when the place was surrendered on honourable terms. Beachy Head (War of the Revolution). A naval action fought June 30, 1690, between a combined English and Dutch fleet of 73 sail under Torrington, and a French fleet of 78 ships under de Tourville, which had been despatched to create a diversion in favour of James II in Ireland. The allies were defeated, the Dutch losing six and the British one ship. Beaugé (Hundred Years' War). Fought March 22, 1421, between the English under the Duke of Clarence, and the Armagnacs, aided by the Scottish mercenaries, resulting in one of the few defeats sustained by the English during the French wars. The Duke and his immediate following, charging ahead of his troops, vigorously attacked the Scottish outposts, and, becoming separated from the main body, was surrounded and slain, all his gentlemen being either killed or captured. The bodies were afterwards recovered by the English archers, but the defeat was complete.
- 47. Beaumont (Franco-German War). Fought August 30, 1870, between the Fifth French Corps d'Armée under General de Failly, and the Fourth and Twelfth German Army Corps under the Crown Prince of Saxony. The French were surprised in their cantonments, and were driven back upon Monzon, with a loss of 4,800 men and 42 guns. The Germans lost about 3,500. Beaune-la-Rolande (Franco-German War). Fought November 28, 1870, between 9,000 Germans under the Grand Duke of Mecklenburg, and 60,000 French under General Crouzat. The French assailed the German position, but, notwithstanding the disparity of numbers, the Germans succeeded in maintaining their ground, after a desperate encounter, driving off their assailants with a loss of 8,000 men. The Germans lost 37 officers and 817 men only. Beauséjour (Seven Years' War). This fort in Nova Scotia, held by a garrison of 460 men under Duchambon de Vergor, was invested June 4, 1755, by 2,000 Massachusetts volunteers and a small force of regulars under Colonel Monckton. On the 14th the besiegers opened fire, and on the 16th the garrison surrendered. Beaver's Dam Creek. See Seven Days' Battle. Bedr (Mohammed's War with the Koreish). Fought in 623, and notable as the first military exploit of Mohammed, who, with only 313 followers, routed a force of 950
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