from πόλις "a city," signifies any thing that relates to policy or civil government.

POLITICAL Arithmetic, is the art of reasoning by figures upon matters relating to government, such as the revenues, number of people, extent and value of land, taxes, trade, &c. in any nation.

These calculations are generally made with a view to ascertain the comparative strength, prosperity, &c. of any two or more nations. With this view, Sir William Petty, in his Political Arithmetic, p. 74, &c. computes the land of Holland and Zealand to be about 1,000,000 acres, and that of France to be 8,000,000; and yet the former is one-third part as rich and strong as the latter. The shipping of Europe he computes to be about 2,000,000, of which Britain has 500,000; Holland 900,000; France 100,000; Hamburg, Denmark, Sweden, and Dantzig 250,000; and Spain, Portugal, Italy, &c. the rest. The exports of France he computes at L. 5,000,000, of which one-fourth came to Britain; of Holland L. 18,000,000, of which L. 300,000 came to Britain. The money raised yearly by the king of France was about L. 6,500,000 Sterling; that of all the Dutch provinces L. 3,000,000, of which 2,100,000 was raised in Holland and Zealand. The number of people in England he computed to be six millions, and their expenses, at L. 7 per annum a head, L. 42,000,000; the rent of land L. 8,000,000; and the interests, &c. of personal estates as much, the rents of houses L. 4,000,000, and the profits of labour L. 26,000,000. The people of Ireland he reckoned 1,200,000. The corn spent in England, at 5s. a bushel for wheat, and 2s. 6d. for barley, amounts to L. 10,000,000 a-year. The navy of England then required 36,000 men to man it, and other trade and shipping 48,000. In France, to manage the whole shipping trade, there were then required only 1500 men. The whole people of France were 13,500,000; and those of England, Scotland, and Ireland, about 9,500,000. In the three kingdoms are about 20,000 churchmen, and in France more than 270,000. In the dominions of England were above 40,000 freemen, and in France not more than 10,000. In England, Scotland, and Ireland, and all their dependencies, there was then about 60,000 tons of shipping, worth about 4,500,000 in money. The sea-line round England, Scotland, and Ireland, and the adjacent isles, is about 3800 miles. In the whole world he reckoned about 350,000,000 of people; and those with whom the English and Dutch have any commerce, not more than eighty millions; and the value of commodities commodities annually traded for in the whole not above L. 45,000,000. That the manufactures exported from England amounted to about L. 5,000,000 per annum; lead, tin, and coals, to L. 500,000 per annum. The value of the French commodities then brought into England did not exceed L. 1,200,000 per annum; and the whole cask of England in current money was then about L. 6,000,000 Sterling.

With these calculations Dr Davenant was dissatisfied; and therefore, from the observations of Mr Greg. King, he advanced others of his own. He reckons the land of England 39 millions of acres; the number of people 5 millions and a half, increasing 9000 a year, making allowance for wars, plagues, and other accidents. He reckons the inhabitants of London 530,000; of other cities and market-towns in England 870,000; and those of villages, &c. 4,100,000. The yearly rent of land he reckons L. 10,000,000; of houes, &c. 2,000,000; the produce of all kinds of grain in a tolerable year L. 9,075,000; the annual rent of corn lands L. 2,200,000, and their net produce L. 9,000,000; the rent of pasture, meadows, woods, forests, commons, heaths, &c. L. 7,000,000; the annual produce by cattle in butter, cheese, and milk, about L. 2,500,000; the value of the wool yearly thorn about L. 2,000,000; of horsef yearly bred about L. 250,000; of the flesh yearly spent as food about L. 3,500,000; of the tallow and hides about L. 600,000; of the hay yearly consumed by horses about L. 1,300,000; of the hay consumed by other cattle L. 1,000,000; of the timber yearly felled for building L. 500,000; and of the wood yearly spent in firing, &c. about L. 500,000. The proportion of the land of England to its inhabitants is now about 7½ acres per head; the value of the wheat, rye, and barley, necessary for the sustenance of England, amounts to at least L. 6,000,000 Sterling per annum; of the woollen manufacture about L. 8,000,000 per annum; and exports of all kinds of the woollen manufacture amount to above L. 2,000,000 per annum; the annual income of England, on which the whole people subsist, and out of which all taxes are paid, is reckoned to be about L. 4,300,000, that of France L. 81,000,000, and of Holland L. 18,250,000. See Davenant's Essay on Trade, in vol. vi. of his works. For calculations respecting mortality, see Major Grant's Observations on the Bills of Mortality, and our article Bills of Mortality.

In Vol. XLIX. of the Philosophical Transactions we have an estimate of the number of people in England by Dr Brakenridge, from considering the number of houes and quantity of bread consumed. On the former principle he computes the number of people to be 6,257,418 of all ages, counting in England and Wales 911,310 houes, and allowing six persons to a house. From a survey of the window-lights after the year 1750, the number of houes charged in England and Wales were 690,000, besides 200,000 cottages that pay nothing; the whole number therefore was 890,000, and the number of people, allowing six to a house, 5,340,000. On the latter principle, he estimates the number of quarters of wheat consumed at home to be 2,426,100; and allowing a quarter for three persons in a year, or seven ounces a day for each person, he concludes the number of people to be 6,078,300. Of this number, according to Dr Halley's rule, he supposes about 1,500,000 men able to carry arms. The country he supposes capable of supporting one-half more inhabitants, or 9,000,000; for, according to Mr Templeman's survey, England contains 49,450 square miles, that is, 31,648,000 acres, of which 25,300,000 acres are proper to be cultivated; and allowing three acres, well manured, for the maintenance of one person, there will be maintenance in England for 8,430,000 people; to which add the produce of fishing, and it will enable the country to support 9,000,000. In Ireland, Mr Templeman reckons 17,536,000 acres, of which Dr Brakenridge thinks 12,000,000 are capable of cultivation; and allowing four acres to each person, and the number of inhabitants to be only 1,000,000, Ireland could maintain 2,000,000 more people than it has now. In Scotland, containing 1,100,000 people, and 17,728,000 acres of land, of which there are 11,000,000 good acres, allowing five for each person, he supposes there may be provision for 2,200,000 people, or for 700,000 more than there are at present. Hence he infers, that were both the British isles properly cultivated, there is a provision for 6,000,000 inhabitants beyond the present number. Extending his survey to the whole globe, he supposes the whole surface to be to the quantity of land as 8 to 3, i.e., as 197,819,550 to 74,182,331 square miles; out of which, deducting one-third for waste-ground, there will be 49,154,887 square miles, or 31,651,127,680 good acres. And stating the whole number of inhabitants on the globe to be 400,000,000, there will be 70 good acres to each person. See Dr Halley's Calculations on the same subject, and Dr Price's (for a list of whose works see his life at the word PRICE), and King on the National Debt.