The hearth-money was not altogether a safe basis of reckoning, for the reason that many were excused it on account of their poverty by certificate from the magistrates, and that hamlets in the hills, perhaps those which held their lands in rungale or joint-lease, often compounded with the collectors for a fixed sum; so that cabins might multiply and no more hearth-tax be paid[460]. It is probable that a considerable increase had taken place which was not represented in the books of the tax-collectors; for in 1788, only three years from the last date given, the number of hearths suddenly leapt up to the round figure of 650,000 (from 474,322), giving a population of 3,900,000, at the rate of six persons to a cabin or house. But it is undoubted that a new impulse was given to population in the last twenty years of the 18th century, firstly by the bounties on Irish corn exported, dating from 1780, which caused much grazing land to be brought under the plough, and secondly by the gradual removal, after 1791, of various penalties and disabilities which had rested on the Roman Catholics since the reign of Anne, affecting their tenure of land, and serving in various ways to repress the multiplication of families. Accordingly we find the hearths rated in 1791 at the number of 701,102, equal to a population of 4,206,612. The estimates or enumerations from 1788, to the census of 1831, show an increase as follows: Year Persons 1788 3,900,000 1791 4,206,612 1805 5,395,456 1812 5,937,856 1821 6,801,827 1831 7,784,539