addition

The passage around this formula

For most of the period in which Europeans kept parish records, the largest towns buried more people than they baptised. Population still rose, which means the arithmetic was closed from outside. The identity is trivial but it is worth writing down, because almost every disagreement in this field is a disagreement about one of its terms: $\Delta P = (B - D) + M$. Population change in a city equals natural increase, births minus deaths, plus net in-migration. The urban graveyard claim is the specific and testable assertion that for long stretches the first bracket was negative while the sum was positive: cities grew, and grew only because the countryside kept sending replacements.

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