The Roman Empire (Latin: Imperium Rōmānum, Classical Latin: (ɪmˈpɛ. ri. ũː roːˈmaː. nũː); Koine and Medieval Greek: Βασιλεία τῶν Ῥωμαίων, tr. Basileia tōn Rhōmaiōn) was the post-Roman Republic period of the ancient Roman civilization, with a government headed by emperors and large territorial holdings around the Mediterranean Sea in Europe, Africa and Asia. The city of Rome was the largest city in the world c. 100 BC -- c. AD 400, with Constantinople (New Rome) becoming the largest around AD 500, and the Empire's population grew to an estimated 50 to 90 million inhabitants (roughly 20% of the world's population at the time). The 500 - year - old republic which preceded it had been severely destabilized in a series of civil wars and political conflict, during which Julius Caesar was appointed as perpetual dictator and then assassinated in 44 BC. Civil wars and executions continued, culminating in the victory of Octavian, Caesar's adopted son, over Mark Antony and Cleopatra at the Battle of Actium in 31 BC and the annexation of Egypt. Octavian's power was then unassailable and in 27 BC the Roman Senate formally granted him overarching power and the new title Augustus, effectively marking the end of the Roman Republic.
The precise start and end of the Industrial Revolution is still debated among historians, as is the pace of economic and social changes. Eric Hobsbawm held that the Industrial Revolution began in Britain in the 1780s and was not fully felt until the 1830s or 1840s, while T.S. Ashton held that it occurred roughly between 1760 and 1830. Rapid industrialization first began in Britain, starting with mechanized spinning in the 1780s, with high rates of growth in steam power and iron production occurring after 1800. Mechanized textile production spread from Great Britain to continental Europe and the United States in the early 19th century, with important centres of textiles, iron and coal emerging in Belgium and the United States and later textiles in France.
Hiberni (Ireland), Pictish (northern Britain) and Britons (southern Britain) tribes, all speaking Insular Celtic, inhabited the islands at the beginning of the 1st millennium AD. Much of Brittonic-controlled Britain was conquered by the Roman Empire from AD 43. The first Anglo-Saxons arrived as Roman power waned in the 5th century and eventually dominated the bulk of what is now England. Viking invasions began in the 9th century, followed by more permanent settlements and political change—particularly in England. The subsequent Norman conquest of England in 1066 and the later Angevin partial conquest of Ireland from 1169 led to the imposition of a new Norman ruling elite across much of Britain and parts of Ireland. By the Late Middle Ages, Great Britain was separated into the Kingdoms of England and Scotland, while control in Ireland fluxed between Gaelic kingdoms, Hiberno-Norman lords and the English-dominated Lordship of Ireland, soon restricted only to The Pale. The 1603 Union of the Crowns, Acts of Union 1707 and Acts of Union 1800 attempted to consolidate Britain and Ireland into a single political unit, the United Kingdom of Great Britain and Ireland, with the Isle of Man and the Channel Islands remaining as Crown Dependencies. The expansion of the British Empire and migrations following the Irish Famine and Highland Clearances resulted in the distribution of the islands' population and culture throughout the world and a rapid de-population of Ireland in the second half of the 19th century. Most of Ireland seceded from the United Kingdom after the Irish War of Independence and the subsequent Anglo-Irish Treaty (1919–1922), with six counties remaining in the UK as Northern Ireland.

Question: What was the beginning and end date of the empire that conquered the country where the industrial revolution started?
Answer: c. 100 BC -- c. AD 400