Historians have long seen Sir William Petty’s ‘political arithmetic’ as an important contribution to the early social sciences, applying mathematics to the analysis of political and especially economic questions. A closer look at Petty’s political arithmetic manuscripts reveals, however, his political preoccupation with ‘transmuting the Irish into English’ by state manipulation of demography. Large-scale, coerced ‘counter-transplantations’ of ‘exchanges of women’ between England and Ireland would facilitate the ‘proportionable mixture’ and ultimately the ‘union’ of the two populations, stabilizing the turbulent politics (...) of late Stuart Ireland and securing English colonial government there. This paper explores Petty’s use of alchemical concepts in his transmutative political arithmetic, and argues that the idiom of alchemy was essential to Petty’s conception of politics and his solution to the problem of governing culturally distinct colonial populations. It makes a preliminary attempt to identify some of Petty’s likely sources among seventeenth-century proponents of corpuscularian, mechanical accounts of chemical change. Finally, it suggests that the influence of alchemy on the shape of early social-scientific thought may have been more significant than was previously realized.Keywords: Political arithmetic; Alchemy; William Petty; Ireland; Political economy. (shrink)