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The official statement of the United States' census, published at Washington in December last, furnishes us with the means of knowing what our American brethren have been doing in the ten years from 1840 to 1850. In that decennial period, the whole territory had increased from 2,055,163 to 3,221,595 square miles, exclusive of the great lakes in the interior, and deeply-indenting bays on the coast. The gross population in June 1850, numbered 23,246,201; an increase from June 1840 of 6,176,848. Of these, 19,619,366 were whites; 3,198,298 were slaves; and free blacks, 428,637; the increase having been respectively, 5,423,371—711,085—42,392. The whole increase was equivalent to 3½ per cent.; while in Europe, it is not more than 1½ per cent.; and if it continue as at present, the population will, forty years hence, exceed that of England, France, Spain, Portugal, Sweden, and Switzerland put together. The deaths in the last of the ten years were 320,194, being 1 to each 72.6, or 10 to each 726 of the inhabitants; this return is, however, supposed to involve an error, as the mortality is less in proportion than in the most favoured parts of Europe; whereas the reverse is generally considered to be the fact. In the same year, 1467 slaves were manumitted, and 1011 escaped. The number of emigrants from foreign countries during the 10 years was 1,542,850.

Among the individual states, the most populous are New York, which numbers 3,097,394 inhabitants; Pennsylvania, 2,311,786; Ohio, 1,980,408; Virginia, 1,421,661; Massachusetts, 994,499; Indiana, 988,416; Kentucky, 982,405; Georgia, 905,999. Taking the whole 31 states, the proportion of inhabitants is 15.48 to the square mile: the free states comprise 13,605,630, and the slave states, 9,491,759 of population.

To supply this population, there are 2800 newspapers: 424 in the New England states; 876 in the middle states; 716 in the southern states; and 784 in the western states. Three hundred and fifty are dailies, 150 three times a week, 125 twice a week, 2000 weekly, 50 fortnightly, 100 monthly, and 25 quarterly: the aggregate circulation being 422,600,000 yearly. There is 1 periodical for every 7161 free inhabitants.

The capital invested in manufactures, excluding the establishments under 500 dollars of annual value, amounted to 530,000,000 dollars; the value of raw material was 550,000,000; the amount paid for labour (in one year we presume), 240,000,000; value of articles manufactured, 1,020,300,000; persons employed, 1,050,000. There were 1094 cotton 'establishments' in operation, which produced 763,678,407 yards of sheeting; 1559 woollen establishments, which produced 82,206,652 yards of cloth; 2190 iron establishments, which produced 1,165,544 tons of iron of various kinds.

Of improved lands, there were 112,042,000 acres; of wheat, 104,799,230 bushels were grown in the last year; 591,586,053 bushels of Indian corn; 199,532,494 pounds of tobacco; 13,605,384 tons of hay; 32,759,263 pounds of maple-sugar were made; 314,644 hogsheads of cane-sugar of 1000 pounds each; 312,202,286 pounds of butter; and 103,184,585 pounds of cheese.