The main historical problem which Curtin’s Census 1 is intended to solve relates to the total number of slaves exported from Africa by way of the Atlantic slave trade during its entire period. Other related questions treated in the book include the proportionate contribution of specified African regions to the estimated total numbers exported; the distribution of the total numbers imported among the importing regions in the Atlantic; and the distribution of the total numbers exported and imported over time. The book is not based on primary data. It is the result of Professor Curtin’s ingenious application of quantitative techniques to the figures in various published works. This exercise produced a total number of 9,566,000 slaves imported into all the importing regions in the Atlantic during the entire period of the slave trade. With all due caution it is stated that the ‘book is not intended to be a definitive study, only a point of departure that will be modified in time as new research produces new data …’ 2 But after all the careful calculations Curtin concludes that ‘it is extremely unlikely that the ultimate total will turn out to be less than 8,000,000 or more than 10,500,000’, 3 which gives a margin of error between +9.8 per cent and —16.4 per cent. In this paper it is proposed, first, to examine the quantitative methods and the data employed in producing the results of the Census in order to see whether this level of confidence is warranted, and, second, to examine Anstey’s minor modifications to Curtin’s work. New evidence will be introduced to suggest that both Curtin and Anstey have underestimated the volume of slave exports from Africa to the Americas.