PETTY, William
Several essays in political arithmetick. London, ClavelMortlock, 1699. 4, 276 lap.
/80.434/
William Petty (1623 – 1687) took an interest in mathematics and mechanics and by the age of
twelve he had some competence in Latin and was studying Greek. He was greatly interested
in, and showed some aptitude for, the work of craftsmen, producing artefacts such as clocks
and furniture. In 1636 he became cabin boy on a merchant ship and during ten months at sea
studied navigation. However, he broke his leg and was put ashore in France by his shipmates
who were allegedly envious of his precocious learning. He enrolled in the Jesuit College at
Caen, supporting himself by teaching English and navigation. then returned to England and
joined the navy. In 1643 he abandoned his naval career and returned to the Continent to study
medicine at Utrecht, Amsterdam and then at Leiden. He subsequently went to Paris to study
anatomy. Back in England in 1646 he worked in his father’s business on the mechanical
aspects of textile manufacture. He met Samuel HARTLIB, under whose guidance he wrote a
tract on education (1647). In it he proposed the formation of a society for ‘the advancement of
mechanical arts and manufactures’ which helped to stimulate the founding of the Royal
Society. He moved to Oxford to continue his medical studies and took a doctorate in physick
in 1650. He became professor of Anatomy (1651). He also taught chemistry at Oxford and
was a Professor of Music at Gresham College.
He resigned from these posts on his appointment in 1652 as physician-general to Cromwell’s
army in Ireland, where he later lived from 1667 until 1673. He was a Fellow of the Royal
Society from its incorporation in 1662, on which occasion he was knighted. He was later
Vice-President of the Society. He was one of the few members to retain his interest in medical
research and the organization of medical treatment. At this time medicine was in such a bad
state that most members concentrated on the physical and biological sciences, and Petty
himself published work in these fields. He was an enthusiastic Baconian showing much
interest in practical applications of mechanics and mathematics, and in collecting facts, which
led to his enormous contributions to statistics, demography and economics.
He was highly praised by James II, although the king eventually rejected his plan for
reforming the administration. He was a Protestant and Parliamentarian during the civil war,
and a firm ally of the Cromwell family. It does not seem that Petty’s work in the physical
sciences had much influence. By far his most influential work was in the social sciences,
especially in the application to them of quantitative and mathematical methods. His
contributions to economics, demography and statistics were particularly fruitful. He dealt with
these matters in a number of essays on ‘political arithmetic’ and in his book Political
Arithmetick, published in 1690.
Petty was a pioneer in adopting a scientific approach to economics
His book Political Arithmetick was general and polemical rather than scientific. It was largely
concerned with the defence of English politics and the economy.
The principal conclusions of his treatise were as follows:
CHAP. I. that a small country, and few people, may by their situation, trade, and policy, be
equivalent in wealth and strength, to far greater people, and territory. and particularly, how
conveniences for shipping, and water carriage, do most eminently, and fundamentally,
conduce thereunto.
Chap. II. that some kind of taxes, and public levies, may rather increase than diminish the
common wealth.
Chap. III. That France cannot by reason of natural and perpetual impediments, be more
powerful at sea, than the English, or Hollanders.
Chap. IV. that the people, and territories of the king of England, are naturally near as
considerable, for wealth, and strength, as those of France.
Chap. V. That the impediments of Englands greatness, are but contingent and removeable.
Chap. VI. That the power and wealth of England, have increased above this forty years.
Chap. VII. That one tenth part, of the whole expence, of the King of England's subjects; is
sufficient to maintain one hundred thousand soldiers, thirty thousand horse(men), and forty
thousand men at sea, and to defray all other charges, of the Government: both ordinary and
extraordinary, if the same were regularly taxed and raised.
Chap. VIII. That there are spare hands enough among the King of England's subjects, to earn
two Millions per annum, more than they now do, and there are employments, ready, proper,
and sufficient, for that purpose.
Chap. IX. That there is money sufficient to drive the trade of the Nation.
Chap. X. That the King of England's subjects, have stock, competent, and convenient to drive
the trade of the whole commercial World.
The author explains the need for his study providing a very sad image of the state of the
Kingdom as follows: the rents of lands have fallen, and therefore, as well as for many other
reasons, the whole Kingdom grows every day poorer and poorer; there is a great scarcity both
of gold and silver; there is no trade nor employment for the people, and yet the land is underpeopled; taxes have been many and great; that Ireland and the plantations in America and
other additions to the Crown are a burthen to England; Scotland is of no advantage; trade in
general diminishes; the Hollanders are at our heels in the race of Naval Power; the French
grow too fast upon both, and appear so rich and potent, that it is but their clemency that they
do not devour their neighbors.
It was important for this work, as well as for his later work on the surveying and redistribution
of land in Ireland, that Petty find ways of estimating populations and their growth. In his
Essay on Political Arithmetick of 1683 on the growth of London he assumed that the
population was proportional to the number of burials in years of normal health. However, he
found that this led to anomalies, so in the second of his Five Essays of 1687 he proposed three
independent methods. These depended (1) on estimating the number of houses, which itself
depended on three subsidiary methods; (2) on using the number of burials and the death rates;
and (3) on using the proportion of plague deaths to survivals in plague years. Petty found the
figures so obtained to agree fairly well with one another.
In later Essays Petty worked on the populations of Paris, Amsterdam, Venice, Rome, Dublin,
Bristol and Rouen.