, in Optics, an oblique kind of prospective glass, contrived for the seeing of objects that do not lie directly before the eye. It was invented by Hevelius, in 1637, and is the same as Opera Glass; which see.

POLITICAL Arithmetic, the application of arithmetical calculations to political uses and subjects; such as the public revenues, the number of people, the extent and value of lands, taxes, trade, commerce, or whatever relates to the power, strength, riches, &c, of a nation or commonwealth. Or, as Davenant concisely defines it, the art of reasoning by figures, upon things relating to government.

The chief authors who have attempted calculations of this kind, are, Sir William Petty, Major Graunt, Dr. Halley, Dr. Davenant, Mr. King, and Dr. Price.

Sir William Petty, among many other articles, states that, in his time, the people in England were about six millions, and their annual expence about 7l. each; that the rent of the lands was about eight millions, and the interests and profits of the personal estates as much; that the rent of the houses in England was four millions, and the profits of the labour of all the people twenty-six millions yearly; that the corn used in England, at 5s. the bushel for wheat, and 2s. 6d. for barley, amounts to ten millions per annum; that the navy of England required 36,000 men to man it, and the trade and other shipping about 48,000; that the whole people in England, Scotland, and Ireland, together, were about nine millions and a half; and those in France about thirteen millions and a half; and in the whole world about 350 millions; also that the whole cash of England, in current money, was then about six millions sterling. See his Political Arith. p. 74, &c.

Mr. Davenant gives some good reasons why many of Sir W. Petty's numbers are not to be entirely depended on; and advances others of his own, founded on the observations of Mr. Greg. King. Some of the particulars are, that the land of England is thirty-nine millions of acres; that the number of people in London was about 530,000, and in all England five millions and 2 half, increasing 9000 annually, or about the 600th part; the yearly rent of the lands ten millions, and that of the houses two millions; the produce of all kinds of grain 9 millions. Davenant's Essay upon the probable methods &c, in his works, vol. 6.

Major Graunt, in his observations on the bills of mortality, computes, that there are 39,000 square miles of land in England, or 25 million acres in England and Wales, and 4,600,000 persons, making about 5 acres and a half to each person; that the people of London were 640,000; and states the several numbers of persons living at the different ages.

Sir William Petty, in his discourse about duplicate proportion, farther states, that it is found by experience, that there are more persons living between 16 and 26 than of any other age; and from thence he infers, that the square roots of every number of men's ages under 16, whose root is 4, shew the proportion of the probability of such persons reaching the age of 70 years: thus, the probability of reaching that age by persons of the

ages of16,9,4,and 1,
are as4,3,2,1,respectively.
Also that the probabilities of their order of dying, at ages above that, are as the square-roots of the ages: thus, the probabilities of the order of dying first,
of the ages16,25,36,&c,
are as the roots4,5,6,&c.
that is, the odds are 5 to 4 that a person of 25 dies before one of 16, and so on, declining up to 70 years of age.

Dr. Halley has made a very exact estimation of the degrees of mortality of mankind, from a curious table of the births and burials, at the city of Bre<*>lau, in Silesia; with an attempt to ascertain the price of annuities upon lives, and many other curious particulars. See the Philos. Trans. vol. 17, pa. 596. Another table of this kind is given by Mr. Simpson, for the city of London; and several by Dr. Price, for many different places.

Mr. Kerseboom, of Holland, has many and curious calculations and tables of the same kind. From his observations on the births of the people in England, it appears, that the number of males born, is in proportion to that of the females, as 18 to 17; and that the inhabitants living in Holland are in the same pro. portion.

Dr. Brackenridge has given an estimate of the number of people in England, formed both from the number of houses, and also from the quantity of bread consumed. Upon the former principle, he finds the number of houses in England and Wales to be about 900,000; and, allowing 6 persons to each house, the number of people near 5 millions and a half. And upon the latter principle, estimating the quantity of corn consumed at home at 2 millions of quarters, and 3 persons to every quarter of corn, makes the number of people 6 millions. See Philos. Trans. vol. 49, art. 45 and 113.

Dr. Derham, from a great number of registers of places, finds the proportions of the marriages to the births and burials; and Dr. Price has done the same for still more places; the mediums of all which are,

Marriages to Births, as
Dr. Derham1 to 4.7
Dr. Price1 to 3.9

See Philos. Trans. Abr. vol. 7, part 4, pa. 46; also Dr. Price's Observations on Reversionary Payments; and the articles of this Dictionary, Expectation of| Life, Life-Annuities, Mortality, Population, &c.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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