Hadrian gave up Mesopotamia within months and fixed the frontiers in stone. The climate had been warm and stable for three centuries; grain crossed the Mediterranean on a scale Europe would not see again until the 1700s. The army was paid in good silver and led by Roman officers; the Senate's sons still commanded legions.

Three things began to change within a single lifetime. Around 150 the Roman Climate Optimum ended. In 165 soldiers returning from Persia brought the Antonine Plague. In 166 Germanic peoples crossed the Danube and besieged Aquileia, inside Italy. From here on every emperor would fight on two fronts with fewer people and worse weather.

The crisis of the third century is the number in its purest form: from 235 to 284 at least twenty-six men were recognised as emperor, an average reign of under two years. The empire split into three. It was reunited by Aurelian and rebuilt by Diocletian, but the cure changed the patient. Provinces were doubled, taxes assessed on every head and acre, town councillors chained to their duties, the army pushed toward half a million men.

Civil war never stopped. Mursa (351), Frigidus (394) and the usurpations of 406–413 each destroyed a field army — at exactly the moments barbarian peoples were walking into the provinces. A state that spends its soldiers on itself has none left for the frontier.

In 439 Gaiseric took Carthage by surprise. Six years later a law of Valentinian III admitted that the treasury could no longer meet army pay from an "exhausted" revenue. Rome tried three times to get Africa back. In 441 the Eastern fleet turned home when Attila attacked the Balkans. In 460 Majorian's 300 ships were betrayed and captured before they sailed. In 468 the two empires gathered everything they had.

The Cape Bon expedition — some 1,100 ships, 50,000 men, and by the lowest estimate 64,000 pounds of gold — was destroyed by Vandal fireships in a single night off Carthage. The East hovered near bankruptcy for thirty years. The West had nothing left to spend, and eight years later it had no emperor.

On 4 September 476 Odoacer, commander of the federate army in Italy, deposed the teenage Romulus Augustulus and did not replace him. He sent the imperial regalia to Constantinople with a message: Italy no longer needed an emperor of its own. Zeno accepted him as patrician while insisting that Julius Nepos, exiled in Dalmatia, was the lawful Western emperor. Nepos was murdered by his own retainers in 480.

Nobody in 476 thought the world had ended. Theodoric's Goths kept the Senate, the consuls and Roman law; the bishops of Rome inherited its grain dole. What the archaeology shows is a different kind of ending: within a century, mass-produced pottery, roof tiles and coins vanish from Britain, cattle shrink, and the economic complexity of the Roman West collapses to levels not seen since before the conquest.

Charlemagne was crowned Roman emperor in 800, Otto in 962; the Holy Roman Empire outlived its name until 1806. Russia's tsars and Turkey's sultans both claimed the inheritance of Constantinople. Gibbon fixed the question in the modern mind in 1776 and blamed barbarism and religion; Rostovtzeff blamed class war; Piganiol said Rome was assassinated; Peter Brown said it did not fall at all. Heather, Ward-Perkins and Harper, in our own century, have put the barbarians, the balance sheet and the climate back at the centre.

Every age finds in the fall of Rome the thing it fears for itself. That is why the question is still asked, and why the numbers matter more than the moral.