Since the census of 1840, there have been added to the territory of the Republic, by annexation, conquest, and purchase, 824,969 square miles; and our title to a region covering 341,463 square miles, which before properly belonged to us, but was claimed and partially occupied by a foreign power, has been established by negotiation, and has been brought within our acknowledged boundaries. By these means the area of the United States has been extended during the past ten years, from 2,055,163 to 3,221,595 square miles, without including the great lakes which lie upon our northern border, or the bays which indent our Atlantic and Pacific shores; all which territory has come within the scope of the Seventh Census. In endeavoring to ascertain the progress of our population since 1840, it will be proper to deduct from the aggregate number of inhabitants shown by the present census, the population of Texas in 1840, and the number embraced within the limits of California and the new territories, at the time of their acquisition. From the best information which has been obtained at the Census-office, it is believed that Texas contained, in 1840, 75,000 inhabitants; and that when California, New Mexico, and Oregon came into our possession, in 1846, they had a total population of 97,000. It thus appears that we have received by accessions of territory, since 1840, an addition of 172,000 to the number of our people. The increase which has taken place in those extended regions since they came under the authority of our Government, should obviously be reckoned as a part of the development and progress of our population, nor is it necessary to complicate the comparison by taking into account the probable natural increase of this acquired population, because we have not the means of determining its rate of advancement, nor the law which governed its progress, while yet beyond the influence of our political system. The total number of inhabitants in the United States, according to the returns of the census, was on the 1st of June, 1850, 23,258,760. The absolute increase from the 1st of June, 1840, has been 6,189,307, and the actual increase per cent. is slightly over 36 per cent. But it has been shown that the probable amount of population acquired by additions of territory should be deducted in making a comparison between the results of the present and the last census. These reductions diminish the total population of the country, as a basis of comparison, and also the increase. The relative increase, after this allowance, is found to be 35.17 per cent. The aggregate number of whites in 1850 was 19,631,799, exhibiting a gain upon the number of the same class in 1840, of 5,436,004, and a relative increase of 38.20 per cent. But, excluding the 153,000 free population supposed to have been acquired by the addition of territory since 1840, the gain is 5,283,004, and the increase per cent. is 37.14.