This appendix is included to provide a comparison between the findings published in the Population history of England, which were obtained using the technique of back projection, and those resulting from the use of generalised inverse projection applied to national totals of births and deaths which have been revised in the light of the evidence afforded by reconstitution. The results also reflect a mean age at maternity which changes over time and, similarly, provision for a changing relationship over time between the level of infant and child mortality on the one hand and adult mortality on the other hand. Fuller details may be found in chapter 8. The form of the table which is appended is designed to parallel table A3.1 in the earlier work. Note, however, that the fertility and mortality measures in table A9.1 relate in every case to the five-year periods between successive ‘censuses’ for which population totals are given, whereas in the parallel table in the earlier work, the comparable data always refer to five-year periods centring on the ‘census’ dates. In table A9.1, therefore, the rates on the line for 1541 refer to the period 1541–6. For the purpose of calculating the rates given here, it was assumed that populations and their component elements changed exponentially between any two successive ‘censuses’. The censuses relate to the midpoint of the year, and the rates therefore run, for example, from July 1541 to June 1546, and so on.