Chapter 4 connects the emergence of transformative demographic governance to changes in natural philosophy, in particular to Francis Bacon’s works and their influence among projectors associated with the Hartlib Circle in the mid-seventeenth century. The problem of managing the qualities of populations in an empire raised the question of natural constraints on the power of policy to “improve” populations; the chapter examines Hartlibian projects concerned with this question on a large scale, including some in which putatively immutable racial boundaries and the enslavement of Africans indicate both limits to and paradoxes of demographic governance. It then turns to Cromwellian Ireland, showing that opposed arguments for either Irish transplantation or English –Irish mixture proceeded from a similar centering of demographic governance. Mid-century projects fed into William Petty’s “political arithmetic” in the Restoration. This fused Baconianism, alchemical ideas and quantification, treating the control of the numbers and of the economic, political, religious and cultural qualities of populations in England, Ireland and the empire as essentially similar problems for the state.