Mr Sadler is a bad arithmetician. The increase in the last term is not as he states it, 33 per cent., but more than 34 per cent. Now, an increase of 32 per cent. in ten years, is more than sufficient to double the population in twenty-five years. And there is, we think, very strong reason to believe that the white population of the United States does increase by 32 per cent. every ten years. Our reason is this. There is in the United States a class of persons whose numbers are not increased by emigration,--the negro slaves. During the interval which elapsed between the census of 1810 and the census of 1820, the change in their numbers must have been produced by procreation, and by procreation alone. Their situation, though much happier than that of the wretched beings who cultivate the sugar plantations of Trinidad and Demerara, cannot be supposed to be more favourable to health and fecundity than that of free labourers. In 1810, the slave-trade had been but recently abolished; and there were in consequence many more male than female slaves,--a circumstance, of course, very unfavourable to procreation. Slaves are perpetually passing into the class of freemen; but no freeman ever descends into servitude; so that the census will not exhibit the whole effect of the procreation which really takes place. We find, by the census of 1810, that the number of slaves in the Union was then 1,191,000. In 1820, they had increased to 1,538,000. That is to say, in ten years, they had increased 29 per cent.--within three per cent. of that rate of increase which would double their numbers in twenty-five years. We may, we think, fairly calculate that, if the female slaves had been as numerous as the males, and if no manumissions had taken place, the census of the slave population would have exhibited an increase of 32 per cent. in ten years. If we are right in fixing on 32 per cent. as the rate at which the white population of America increases by procreation in ten years, it will follow that, during the last ten years of the eighteenth century, nearly one-sixth of the increase was the effect of emigration; from 1800 to 1810, about one-ninth; and from 1810 to 1820, about one-seventeenth. This is what we should have expected; for it is clear that, unless the number of emigrants be constantly increasing, it must, as compared with the resident population, be relatively decreasing. The number of persons added to the population of the United States by emigration, between 1810 and 1820, would be nearly 120,000. From the data furnished by Mr Sadler himself, we should be inclined to think that this would be a fair estimate.