In 1650 Petty was made Professor of Anatomy at Oxford, and it is a characteristic illustration of his great activity of mind that he was at the same time Professor of Music at Gresham College.  Music had then a high place in the Seven Sciences, as that use of regulated numbers which expressed the harmonies of the created world.  The Seven Sciences were divided into three of the Trivium, and four of the Quadrivium.  The three of the Trivium concerned the use of speech; they were Grammar, Rhetoric, and Logic.  The four of the Quadrivium concerned number and measure; they were Arithmetic, Geometry, Music; and Astronomy, which led up straight to God.  Advance to Music might be represented in the student’s mind by his reaching to a sense of the harmonious relation of all his studies, which, so to speak, lived in his mind as a single well-proportioned thought.

In 1652 Dr. Petty was sent to Ireland as physician to the army of the Commonwealth.  While there his active mind observed that the Survey on which the Government had based its distribution of fortified lands to the soldiers had been “most inefficiently and absurdly managed.”  He obtained the commission to make a fresh Survey, which he completed accurately in thirteen months, and by which he obtained in payments from the Government and from other persons interested ten thousand pounds.  By investing this in the purchase of soldiers’ claims, he secured for himself an Irish estate of fifty thousand acres in the county of Kerry, opened upon it mines and quarries, developed trade in timber, and set up a fishery.  John Evelyn said of him “that he had never known such another genius, and that if Evelyn were a prince he would make Petty his second councillor at least.”  Henry Cromwell as Lord Deputy in Ireland made Petty his secretary.

Petty’s Maps were printed in 1685, two years before his death, as “Hiberniae Delineatio quoad hactenus licuit perfectissima;” a collection of thirty-six maps, with a portrait of Sir William Petty, a work answering to its description as the most perfect delineation of Ireland that had up to that time been obtained.  There is a coloured copy of Petty’s maps in the British Museum, and also an uncoloured copy, with the first five maps varying from those in the coloured copy, and giving a General Map of Ireland, followed by Maps of Leinster, Munster, Ulster, and Connaught.  There was afterwards published in duodecimo, without date, “A Geographical Description of ye Kingdom of Ireland, collected from ye actual Survey made by Sir William Petty, corrected and amended, engraven and published by Fra. Lamb.”  This volume gives as its contents, “one general mapp, four provincial mapps, and thirty-two county mapps; to which is added a mapp of Great Brittaine and Ireland, together with an Index of the whole.”