Sir William, a man eminently distinguished for his learning, mechanical ingenuity, and political writings, was the eldest son of Antony Petty, a clothier at Rumsey, in Hampshire, where he was born on the 16th of May 1623. Petty, when a boy, was noted for the pleasure he took in observing mechanics at work, and the facility with which he comprehended the nature of their employments and the use of their tools. He received the rudiments of his education at the grammar-school of Rumsey, where, before the age of fifteen, he had acquired a competent knowledge of the Latin, Greek, and French languages, and made himself master of the common rules of arithmetic, as well as of the elements of geometry, dialling, and navigation. He then removed to the University of Caen, in Normandy, taking with him a small stock of merchandise, which he disposed of to so much advantage, that he maintained himself out of the profits of his traffic, and at the same time perfected himself in Latin and French, acquired enough of Greek "to serve his turn," studied the arts, and extended his knowledge of the mathematics. Even at this early period the prevailing bias of his mind displayed itself; and in the student of Caen we discover the father of the man who, holding that there are few ways in which a person may be more harmlessly employed than in getting money, afterwards realized a very great fortune. On his return from France, he was appointed to the navy, though in what capacity is not known. In this situation he remained for some time, and having saved about L60, he determined to bid adieu to the navy, and travel for further improvement. Having made choice of physic as a profession, he, in 1643, visited Leyden, Utrecht, and Paris, where he studied anatomy, and read Vesalius with Hobbes, whom he in turn assisted by drawing diagrams for the philosopher, who was then writing on optics. Whilst at Paris he appears to have been reduced to great straits from want of money; but his ingenuity and industry extricated him from all his difficulties; and, in 1646, he returned home a richer man than when he had set out, although he had maintained his brother Antony as well as himself.

Petty was not a man to remain inactive or slothful. It appears indeed that, on the 6th of March 1647, a patent was granted him by parliament for an invention which would now be termed a copying-machine, but which he calls an instrument for double writing. In an advertisement prefixed to his Advice to Mr Samuel Hartlib, he describes it as an instrument of small bulk and price, easily made, and very durable, by means of which "any man, even at the first sight and handling, may write two resembling copies of the same thing at once, as serviceable and as fast as by the ordinary way;" and Rushworth informs us that it might be learned in an hour's practice, and was calculated to be of great advantage to lawyers, scriveners, merchants, scholars, registrars, clerks, and others, by saving the labour of examination, and discovering or preventing falsification. But this machine having been found not to promote expedition in writing, the principal advantage proposed to be attained by it, Petty did not reap much profit by his invention; but, although it failed of its object in this respect, it served to make him acquainted with the leading men of the times. His next production was a pamphlet entitled Advice to Mr Hartlib for the Advancement of Learning, containing some sensible remarks on national education, particularly in so far as regards the more useful branches of knowledge, which he justly conceived were too much neglected. In 1648 he went to Oxford, where he gave instructions in anatomy as a private teacher; became assistant to Dr Clayton, the professor of anatomy, who had an insurmountable aversion to the sight of a mangled corpse; and also practised physic with considerable success. Here he acquired such reputation, that the philosophical meetings which led to the institution of the Royal Society were for the most part held at his lodgings; and, by a parliamentary recommendation, he obtained a fellowship in Brazen-nose College, and was created doctor of physic on the 7th of March 1649. In June 1650, he was admitted a member of the College of Physicians; and the same year he was concerned in the recovery of a woman, named Anne Green, who had been hanged at Oxford for the supposed murder of her bastard child. In the beginning of 1651, he was appointed professor of anatomy, and soon afterwards professor of music, at Gresham College; and in 1652, he went to Ireland as physician to the army in that country, where he served under three successive lords-lieutenant, namely, Lambert, Fleetwood, and Henry Cromwell.

Some time after his settlement in Ireland, Dr Petty observing that the forfeited lands adjudged to the soldiers, after the suppression of the rebellion of 1641, were very inaccurately measured, represented the matter to the persons then in power; and a contract, dated the 11th of December 1654, was in consequence granted him, by which he was authorized to make the admeasurements anew, a duty which he appears to have discharged with exactness and fidelity. By this contract he gained a very considerable sum of money; for, besides the twenty shillings a day which he received during its performance, he had also, by agreement with the soldiers, a penny an acre for the lands measured by him; and by an order of government, dated the 19th of March 1655, it appears that he had then surveyed 2,008,000 acres, which, at the rate stipulated, must have yielded him about £8,400 sterling. He was likewise one of the commissioners for allocating the lands to the soldiers after they had been surveyed. In 1655, Henry Cromwell assumed the lord-lieutenancy of Ireland, and soon afterwards appointed Dr Petty his secretary; in 1657, the viceroy further appointed him clerk of the council, and got him elected to serve as burgess for West Love, in Cornwall, in Richard Cromwell's parliament, which assembled on the 27th of January 1658. But this last honour speedily involved him in trouble. On the 28th of March following he was impeached of high crimes and misdemeanours in the execution of his office, and obliged to proceed to England. On the 19th of April he appeared in the House of Commons, and answered to the charge on the 21st; the prosecutors then replied, after which the matter was adjourned, and never came to an issue, as the parliament was suddenly dissolved the next day. He soon afterwards returned to Ireland, where, some further attempts being made to bring on a prosecution, he published two pamphlets; the one giving an account of the proceedings in the impeachment, and the other containing reflections on some persons and things in Ireland. Finding the latter country getting too hot for him, he crossed over to England, provided with a warm application in his favour by the lord-lieutenant; but, notwithstanding this intercession, he was in June removed from all his employments.

The charges brought against him were six in number. He was accused of having received or taken great bribes; of having made a trade of buying debentures, contrary to the statute; of having obtained by fraud large sums of money and extensive tracts of land; of having employed many foul practices, as surveying and setting out lands; of having, along with his fellow-commissioners, placed some debentures in better situations than they could claim, and denied right to others; and, lastly, he and his fellow-commissioners were accused of having totally disposed of the army's security for payment, whilst the debt still remained chargeable on the state. Petty's answer to these charges is abundantly curious. Instead of trying to refute them in detail, he labours to show that, without ever interfering with the surveys of the Irish lands, he might have acquired as large a fortune by other means; and, certainly, whatever may be thought of such a defence to specific charges of malversation and fraud, the statement itself must be allowed the praise of ingenuity.

In 1659, the republican spirit not being yet extinct in Petty, he became a member of the Rota Club, which met at Miles's coffee-house, in New Palace-yard, Westminster. This club received its name from the strange practice it was intended to support, namely, that all officers of state should be chosen by ballot, that the time for holding their places should be limited, and that a certain number of members of parliament should be annually changed by rotation. But the star of the commonwealth was now waxing dim, and, not long after Christmas, Petty went to Ireland. At the Restoration, however, he came back to England, where he was graciously received by Charles II., and, having resigned his professorship at Gresham College, was appointed one of the commissioners of the Court of Claims. In April 1661, he received the honour of knighthood, with the grant of a new patent constituting him surveyor-general of Ireland; and he was at the same time chosen a member of the Irish parliament. Being one of the founders of the Royal Society, he was elected a member of the first council; and although he had left off the practice of physic, his name appears in the list of fellows of the College of Physicians in 1663. About this time he invented a double-bottomed ship, which was to sail against both wind and tide, though we are not told by what means; and, in 1665, he communicated to the Royal Society, along with a model of his invention, a Discourse about the Building of Ships, which being supposed to contain matter too important to be divulged, was taken away by the president, Lord Brounker, who kept it in his possession till 1682, and probably till his death, which happened not long afterwards.

In 1666, Sir William Petty drew up his treatise entitled Verbum Sapienti, containing an account of the wealth and expenditure of England, showing the method of raising taxes in the most equal manner, and endeavouring to prove, that England could bear a charge of four millions per annum, when the exigencies of the government required it. The same year he suffered a considerable loss by the fire of London, the greater part of his house and gardens having been destroyed by that terrible conflagration. In 1667, he married Elizabeth, daughter of Sir Hardresse Waller, and widow of Sir Maurice Fenton. This matrimonial connection, however, did not for a moment distract his attention from his favourite pursuit of making money; for immediately afterwards he established iron-works and a pit-chard-fishery, opened lead mines, and commenced a trade in timber at Kerry, all of which turned to good account. To vary his pursuits, he also composed a piece of Latin poetry, which he subsequently published under the title of Colloquium Davidis cum Anima sua. In 1680, he gave to the world his Politician Discovered, intended to expose the sinister practices of the French; and afterwards wrote several essays on Political Arithmetic, in which, from considering the natural resources of England and Ireland, he shows how both may be strengthened, improved, and rendered superior to all their rivals or enemies. He assisted at the formation of the Dublin Philosophical Society, and in November 1684 was chosen president of that association. On this occasion he drew up a Catalogue of Cheap and Simple Experiments, which was soon afterwards followed by his Suppellex Philosophica, containing a description of forty instruments which he deemed necessary to carry forward the design of the institution. But the ultimate term of all his projects and pursuits was now approaching. A gangrene in his foot, occasioned by the swelling of the gout, having resisted every mode of treatment, at length put a period to his life, on the 16th of December 1687, in the sixty-fifth year of his age. He died at his house in Piccadilly, and his remains were interred at Rumsey, near those of his parents. His will is perhaps the most curious and characteristic composition of the kind in our language, illustrating at once the habits of thinking and feeling peculiar to the man, and the mode in which he realized the enormous fortune which he left to his descendants.

A few particulars of the personal history of Sir William Petty may be gleaned from Aubrey, who appears to have lived with him on terms of intimacy. He possessed strong, shrewd, natural good sense, flavoured with a tincture of humour, and had a most convenient way of shaking himself rid of the trammels of party when it suited his interest to do so, changing sides with a facility that is altogether edifying. His qualifications were indeed various and peculiar. He was an excellent droll, as he showed by proposing to Sir Jerome Sankey, who had challenged him, to fight in a dark cellar with carpenters' axes; a proposal in which the knight, though he had been a soldier, did not deem it prudent to acquiesce. He would also preach extempore, which Aubrey says he did "incomparably," and that too in almost any style, "either in the presbyterian way, independent, capucin friar, or Jesuit." He had "an admirable inventive head, and practical parts," which he turned to good account as far as his own interest was concerned; and, like his friend Hobbes, he boasted that he had read but little since he was twenty-five, declaring, that "had he read as much as some men have, he had not known so much as he does, nor should have made such discoveries and improvements." He told Aubrey that he had "hewed out his fortune for himself," and he even managed to obtain a patent of nobility as Earl of Kilmore, which, however, he suppressed to avoid envy. The variety of pursuits in which he was engaged shows that he had talents capable of achieving anything to which he chose to apply them; and it is certainly not a little remarkable, that a man of such an active and enterprising disposition should have found time to write so much as he did in the course of his busy life.

The following is a list of the works which appeared in his lifetime: 1. Advice to Mr Samuel Hartlib, 1648, in 4to; 2. A Brief of Proceedings between Sir Jerome Sankey and the Author, 1659, in folio; 3. Reflections on some Persons and Things in Ireland, 1660, in 8vo; 4. A Treatise of Taxes and Contributions, 1662, in 4to, republished in 1690, with two other pieces; 5. Apparatus to the History of the Common Practice of Dyeing, 1667; 6. A Discourse concerning Duplicate Proportion, 1674, in 12mo; 7. Colloquium Davidis cum Anima sua, 1679, in folio; 8. The Politician Discovered, 1681, in 4to; 9. An Essay on Political Arithmetic, 1682, in 8vo; 10. Observations upon the Dublin Bills of Mortality in 1681, 1683, in 8vo; 11. Some Experiments relating to Land-carryage, Phil. Trans. No. 161; 12. Queries on Mineral Waters, ibid. No. 166; 13. A Catalogue of Experiments, ibid. No. 167; 14. Maps of Ireland, being an actual Survey of the whole Kingdom, 1685, in folio; 15. An Essay concerning the Multiplication of Pettycotta Mankind, 1686, in 8vo; 16. A further Assertion concerning the Magnitude of London, Phil. Trans. No. 185; 17. Pewter. Two Essays in Political Arithmetic, 1687, in 8vo; 18. Five Essays in Political Arithmetic, English and French, 1687, in 8vo; 19. Observations upon London and Rome, 1687, in 8vo.

His posthumous productions are, 1. Political Arithmetic, 1690, in 8vo, and 1755, with a Life prefixed, and a Letter never before printed; 2. The Political Anatomy of Ireland, to which is added, Verbum Sapienti, 1691, 1719; 3. A Treatise of Naval Philosophy, in three parts, printed at the end of an Account of Several New Inventions, 1691, in 12mo; 4. What a Complete Treatise of Navigation should contain, Phil. Trans. No. 198, drawn up in 1685. In Birch's History of the Royal Society are contained, 1. A Discourse of making Cloth and Sheep's Wool, containing the History of the Clothing Trade, and also that of Dyeing; and, 2. Suppelle Philosophica, already mentioned. There are many of Sir William Petty's manuscripts in the British Museum, amongst which is a sort of confession of his faith, corresponding with the concluding passage of his will, in which he says, "I die in the profession of that faith, and in the practice of such worship, as I find established by the law of my country," a very honest and candid declaration on his part.