Political arithmetic is the one [subject] in which operations have the purpose of [making] discoveries which are useful to the art of governing peoples, such as the ones on the number of men who inhabit a country, on the quantity of food they need, on the work they are capable of doing, of the time they live, of the fertility of lands, of the frequency of shipwrecks, etc. It is evident that on the basis of these and of many other similar discoveries, acquired by a few calculations on the basis of some well grounded experiences, a skilled minister would draw many consequences for the excellence of agriculture, for interior as well as for foreign trade, for the colonies, for the circulation and the use of money, etc. But often, ministers (here I refrain from speaking without exceptions) often believe they have no need to go through combinations and sequels of arithmetic operations: many imagine they are endowed with a vast natural genius, which dispenses them of a process so slow and so troublesome, and this without taking into account that the nature of business almost never allows nor requires geometrical precision. However if the nature of business demanded and allowed for it, I don’t doubt that one would convince oneself that the political world, just like the physical world, in many respects may be regulated by weights, number and measure.

Sir Petty, [1] English, is the first to have published essays under this title. The first one is on the [demographical] increase of humanity; on the growth of the city of London, its degrees, its periods, its causes and its consequences. The second one [is] on the houses, the inhabitants, the deaths and the births of the city of Dublin. The third one is a comparison between the city of London and the city of Paris; Sir Petty strives to prove that the capital of England wins over that of France from all these aspects: Mr. Auzout [2] has attacked this essay by [making] several objections, to which Sir Petty has responded. The fourth [essay] tends to show that at the Hotel-Dieu of Paris three thousand sick [people] die each year because of bad administration. The fifth [essay] is divided into five parts: the first is a response to Mr. Auzout; the second one details the many points of comparison between London and Paris; the third one estimates at 696,000 the number of parishioners of 134 London parishes. The fourth one is a research on the inhabitants of London, Paris, Amsterdam, Venice, Rome, Dublin, Bristol and Rouen. The fifth is on the same subject, but relative to Holland and the rest of the United Provinces. The sixth deals with the expanse and the price of lands, the peoples, the houses, industry, economy, manufacture, commerce, fishing, craftsmen, sailors or seafarers, ground forces, public income, interests, taxes, profits, banks, companies, the cost of men, the increase of the navy and troops; residences, places, constructions of vessels, maritime forces, etc., relative to all countries in general, but particularly to England, Holland, the Netherlands and France. This essay is addressed to the King; it can on all accounts be said that the results are favorable to the English nation. It is the most important of all of Sir Petty’s essays; however it is extremely short, when compared with the large number and complexity of the topics. Sir Petty claims to have demonstrated in approximately one hundred small pages in twelve point, large character: 1. That a small country with a small number of inhabitants may be equivalent, for its location, its commerce and its policy, to a great country and to a great people compared either by their strength or by their wealth, and that there is nothing which tends more efficiently to reestablish this equality than the navy and maritime commerce. 2. That any regime of taxation and public taxes aims to increase rather than to weaken society and the public good. 3. That there are some natural and lasting obstacles to France becoming more powerful at sea than England or Holland: our Frenchmen will not favorably judge Sir Petty’s calculations regarding this proposal, and I believe that they will be right. 4. That by its resources and natural products, the people and the territory of England are more or less equal in wealth and in strength to the people and the territory of France. 5. That the obstacles countering the greatness of England are only contingencies and are not permanent. 6. That for forty years, the power and the wealth of England have greatly increased. 7. That the tenth part of all the expense of the King’s subjects would be sufficient to maintain one hundred thousand infantrymen, thirty thousand cavalrymen, forty thousand seamen, and to pay all other state expenditure, including ordinary and extraordinary [expenses], on the mere supposition that this tenth part be well imposed, well collected, and well used. 8. That there are more subjects without occupation than would be needed to earn the nation two million each year if they were suitably employed, and that these occupations are all ready and but await the workers. 9. That the nation has enough money to run its commerce. 10. Finally that the nation has the sufficient resources that it needs to embrace all the commerce in the universe, of whatever nature it might be.

Note how we see some very excessive pretention: but whatever they might be, the reader would do well to carefully examine in Sir Petty’s work the reasoning and the experiences he draws on: in [implementing] such an analysis, it will be necessary not to forget that revolutions, for good and for evil, change in a moment the face of states, and modify and even annihilate the suppositions, and that calculations and their results are no less variable than events. The work of Sir Petty was written before 1699. According to this author, although Holland and the Netherlands have no more than 1,000,000 acres of land, while France has at least 8,000,000, the first of these countries has only a third of the wealth and the force of the latter. The revenues of lands in Holland are proportionate to those of France to the measure of 7 or 8 to 1. (It should be noted that under discussion here is the state of Europe in 1699, and that all of Sir Petty’s calculations, accurate or otherwise, are referred to this year). The citizens of Amsterdam number two-thirds those of Paris or of London; and the difference between the latter two cities is, according to the author, but about a twentieth part. The tonnage of all the ships of Europe amounts to about two million tons, of which the English have 500,000, the Dutch 900,000, the French 100,000, the Hamburghers, Danes, Swedish, and the citizens of Danzig 250,000; Spain, Portugal, Italy etc., have more or less the same. The value of the goods leaving France each year for the use of various countries amounts altogether to 5,000,000 pounds sterling; i.e., four times as much as that which enters England alone. The goods leaving Holland for England are worth 300,000 pounds sterling, and those leaving that country to be distributed all over the rest of the world are worth 18,000,000 pounds sterling. The money that the King of France raises yearly in times of peace is roughly of 6 1/2 million sterling. The sums raised in Holland and in the Netherlands are around 2,100,000 pounds sterling, and those coming from the whole United Provinces are, all together, roughly 3,000,000 pounds sterling. The inhabitants of England are approximately 6,000,000, and their spending, at the rate of 7 pounds sterling each per year, amounts to 42,000,000 pounds sterling or to 80,000 pounds sterling per week. The revenues of lands in England is of roughly 8 million pounds sterling and the interests and profits of personal properties is about the same. The revenue of houses in England amounts to 4,000,000 pounds sterling. The profit of the labor of all the inhabitants amounts to 26,000,000 pounds sterling per year. The inhabitants of Ireland are 1,200,000. The wheat consumed annually in England, counting the wheat at 5 shillings the woody, and the barley at 2 1/2 [shillings], amounts to ten million sterling. The Navy of England in 1699, i.e. at the time of Sir Petty or at the end of the last century, needed 36,000 men for its war vessels and 48,000 for commercial and other vessels; for the entire Navy of France only 15,000 men were needed. There are about thirteen and a half million people in France, and approximately nine and a half million in England, Scotland and Ireland. In the three kingdoms of England, Scotland and Ireland, there are roughly 20,000 clergymen and in France there are more than 270,000. The Kingdom of England has more than 40,000 seamen, while France has no more than 10,000. In England, Scotland, Ireland and in the countries which depend on them, their vessels have a tonnage which roughly amounts to 60,000 tons, which is worth more or less four and a half million pounds sterling. The maritime line around England, Scotland, Ireland, and the adjacent islands, is roughly of 3,800 miles. There are in the world roughly 300 million people, of which there are but roughly 80 million with whom the English and the Dutch trade. The value of the bills of exchange in their entirety do not exceed 45 million sterling. The manufactures of England leaving the kingdom roughly amount annually to 5 million sterling. Lead, tin and coal, to 500,000 pounds sterling per year. The value of the goods of France which enter England does not exceed 1,200,000 pounds sterling per year. Finally in England there are approximately six million pounds sterling of cash in circulation. All these calculations, as we have said, are relative to the year 1699 and surely must have changed since.

Mr. Davenant, [3] another author of political arithmetic , proves that one must not rely entirely on several of the calculations of our dear Petty: he gives others which he himself has made and which are based on the observations of Mr. King. [4] Here are some of them.

England contains, he says, 39 million acres of land. The inhabitants, according to his computations, are more or less in the range of 5,545,000 souls and this number increases each year by about 9,000, less those who may die because of plague, illness, war, the sea, etc. and those who go to the colonies. He counts 530,000 inhabitants in the city of London; in the other cities and in the country towns of England 870,000, and in the villages and hamlets 4,100,000. He estimates the annual revenue of the lands at 10 million sterling; that of the houses and of the buildings at two million per year; the product of all the kinds of grain, in a tolerably abundant year, at 9,075,000 pounds sterling; the annual revenue of the land in wheat, at 2 million, and their net production above 9 million sterling; the revenue of pasture grounds, of meadows, of woods, of forests, of downs, etc. at 7 million sterling; the annual product of cattle, in butter, cheese and milk can increase, according to him, to roughly 2 1/2 million sterling. He estimates the annual value of sheared wool at roughly 2 million sterling: the value of the horses that we breed every year at approximately 250,000 pounds sterling; the annual consumption of meat for food at approximately 3,350,000 pounds sterling: and tallow and leather at approximately 600,000 pounds sterling: those of hay for the annual nurture of the horses, at roughly 1,300,000 pounds sterling, and for that of other cattle, one million sterling: the wood for buildings annually cut, 500,000 pound sterling. The wood to burn, etc. roughly 500,000 pounds sterling. If all the lands of England were equally distributed among all the inhabitants, each one would have for his share roughly 7 1/4 acres. The value of wheat, of rye, and barley, necessary for the subsistence of England, amounts to at least 6 million sterling per year. The value of the goods from wool manufactured in England is of roughly 8 million per year; and all the woolen goods which yearly leave England are above the value of 2 million sterling. The annual revenue of England, on which all the inhabitants feed and maintain themselves, and pay all the tariffs and taxes, amounts, according to him, to roughly 43 million: that of France to 81 million, and that of Holland to 18,250,000 pounds sterling.

Major Grant, [5] in his observations on the bills of mortality , counts that there are in England 39,000 square miles of land; that there are in England and in the principality of Wales 4,600,000 people; that the inhabitants of the city of London more or less number 640,000, i.e. the fourteenth part of all the inhabitants of England; that in England and in the Welsh lands there are roughly 10,000 parishes; that there are 25 million acres of land in England and in the countries of Wales, i.e. roughly 4 acres per inhabitant; that out of 100 born children, 64 of them reach the age of 6 years; that in 100, there are but 40 in life at the end of 16 years; that out of 100, there are only 25 who pass the age of 26; that there are 16 who live 36 years accomplished, and only 10 out of 100 live up to the end of their 46th year; and in the same number, that there are not but 6 who will reach 56 accomplished years; that 3 out of 100 reach the end of 66 years; and that out of 100, there is but one who is alive at the end of 76 years; and that the inhabitants of the city of London have changed twice in the course of about 64 years. See Life, etc. Messrs. de Moivre, Bernoulli, de Montmort, and de Parcieux have frequently dealt with the subject of political arithmetic: la doctrine des hasards of Mr. de Moivre can be consulted; l’art de conjecturer , by Mr. Bernoulli; l’analyse des jeux de hasard , of Mr. de Montmort; the work sur les rentes viageres et les tontines , etc. of Mr. de Parcieux and some memories of Mr. Halley, scattered in the Transactions philosophiques , along with the articles of our dictionary, Chance, Game, Probability, Combination, Absent, Life, Death, Birth, Annuity, Revenue, Tontine, etc.

Notes

1. [Sir William Petty (1624–1687) was a prominent English economist, scientist and philosopher. His essays on political arithmetic were among the first important works of modern statistics. Above all, his Political Arithmetic , published posthumously in 1690, was at the time considered a path-breaking contribution to this field of study.]

2. [Adrien Auzout (1622–1629) was a French astronomer and a mathematician who took part in the debates on political arithmetic by contesting Petty’s comparison between the cities of London and Paris.]

3. [Charles Davenant (1656–1714) was an English economic arithmetician, a civil servant and also a politician. His most interesting contribution to the development of political arithmetic are the Discourses on the Publick Revenues and on the Trade in England , published between 1697 and 1698.]

4. [Gregory King (1648–1712) was an English genealogist, civil servant and economist. Among his most important works are Of the Naval Trade of England written in 1688 and the Natural and Political Observations and Conclusions upon the State and Condition of England , written 1696.]

5. [A London merchant, John Graunt (1620–1674) was also a successful amateur scientist who concentrated on vital statistics. His most famous work is Natural and Political Observations made upon the Bills of Mortality , published in 1662.]