1850s: 58.5
1860s: 55.0
1870s: 55.4
1880s: 51.9
1890: 48.1
1900: 44.4
(It's only in 1890 that he starts breaking it out by year rather than aggregated by decade, for blacks.)
So it looks like the average black birthrate betwen 1860 and 1900 is about 52. Let's increase the 1850s rate on the assumption it was higher for the whole period 1820-1860, let's say 62.
So without adjusting for deaths, that would mean the ratio of natural increase between periods was 62/52, or 1.2 higher in 1820-1860 than in 1860-1900.
So we take the 2.0 multiplier of 1860-1900 and adjust it by 1.2 times to get 2.4 as the natural increase to apply to 1820 to 1860.
So we get for 1820-1860 a natural increase multiplier of 2.4, which subtracted from the total multiplier of 2.5, leaves for imports of slaves, 177,000.
That's about 200,000 slaves imported between 1820 and 1860.
Maybe that's not unreasonable.
Except that the birth rate declined throughout the latter half of the 19th century, which implied it also declined in the first half. It is also reasonable to assume the death rate declined throughout this century.
To use the difference in numbers at the end of the period versus that at the beginning of the period to calculate the number “imported,” I think you’d need to know both the birth and death rates throughout the period in question.
And then it would be well beyong my mathematical abilities to calculate.
Personally, I suspect the number is pretty small. American ships were not subject, after the War of 1812, to search by the RN, but after 1820 or so the American Navy kept a squadron off the African coast to catch them. The sailors got prize money for slavers captured, so they had a huge incentive to be enthusiastic about their work.
Officers and even sailors on the slaveships were subject to huge fines and long jail time if captured, though there was no real risk till after 1860 of their being executed. I don’t know what they were paid, but it seems likely the reward wasn’t commensurate with the risk.
The investors ran the very real risk of having their ship confiscated as a naval prize simply for having it outfitted as a slaver, whether there were any slaves aboard when captured or not. That was an immense financial risk, and the trade being illegal it wasn’t possible to ensure the ship against loss. I’m not sure whether they were also subject to potential criminal prosecution.
The biggest factor that leads me to believe there were few slaves imported after 1808 is that the immense illegal trade this would have represented AFAIK was not used by abolitionists at the time or liberals today to denounce the wickedness of the South or of America. Obviously a massive smuggling trade in such a bulky commodity could not have continued without officials looking the other way.