Recently, much attention has been paid in the literature on economic growth to the phenomenon of"conditional convergence,"the tendencies of economies with lower-level incomes to grow faster, conditional on their rate of factor accumulation. The author documents that, regardless of conditional convergence, perhaps the basic fact of modern economic history is massive absolute divergence in the distribution of incomes across countries. Discussions of long-run convergence or divergence has been hindered by the lack of reliable historical estimates of per capita income for poor countries. The author shows that to draw reasonable inferences about whether incomes have converged or diverged does not require historical estimates of per capita income as a plausible lower limit for historical per capita incomes combined with estimates of current income in poor countries places a binding constraint on their historical growth rates. Finally, the author estimates that between 1870 and 1985 the ratio of incomes in the richest and poorest countries increased sixfold, the standard deviation of (natural log) per capita incomes increased by between 60 and 100 percent, and the average income gap between the richest and the poorest countries grew almost ninefold (from $1,500 to over $12,000).