A comparison of the several States with each other, and also of the white and colored races, distinguishing the slaves from the free colored persons, shows in a striking manner the imperfection of the data afforded by the decennial enumerations alone, when considered as means for calculating the true law of the growth of population from natural causes. In Massachusetts, for instance, the rate of increase of the whole population, from 1810 to 1820, was 10.8 per cent.; from 1820 to 1830, it was 16.6 per cent.; from 1830 to 1840, it was 20.8 per cent. In Virginia, from 1810 to 1820, the rate for the whole population was 9.3; from 1820 to 1830, it was 13.7; from 1830 to 1840, it was but 2.3. These two are Atlantic States, from which the stream of emigration flows westward, keeping down the apparent rate of increase. But take instances from the Western States, which are constantly receiving emigrants from the older settlements. In Ohio, from 1810 to 1820, the rate was 152 per cent; from 1820 to 1830, it was 61; from 1830 to 1840, it was 62. In Kentucky, during the same periods, the rates were 38.8, 21.9, and 13.3. It is obvious, that rates of increase fluctuating so rapidly and widely as these afford no clue whatever to the law of the natural growth of population by the excess of births over deaths. In the following table we give the rates of increase for the whole population of the United States, at decennial periods, distinguishing the whites both from the free colored and the slaves. The influx of slaves from abroad ceased before 1810, the trade in them being prohibited, and the law in this respect being very rigidly observed. Still, the rates here given for them for the three following decennial periods must be somewhat below the rates of their increase from natural causes, as numbers of them were emancipated or obtained their freedom by flight, thus increasing the number of the free blacks. Accordingly, the rates for these three periods are too low for the slaves, but too high for the free colored, though the latter were probably not at all increased by immigration from abroad. For the whites, the rate of increase is quite constant and very high, showing that the stream of immigration has in truth very rapidly increased, since it has kept quite even pace with the natural growth of the white population, which was but little over three millions in 1790, while it exceeded fourteen millions in 1840. Many slaves were imported between 1790 and 1810, but the enormous rates of increase of the free blacks at this period show that many of them also were emancipated. The rate for the free colored falls off very decidedly after 1810, and during the last decennial period, it amounts to less than 21 per cent., though their number must still have been largely augmented by emancipated and fugitive slaves. It is certain that the increase of this class from natural causes is much slower than that of the whites or the slaves; probably it does not exceed 15 per cent. for ten years. But our chief object is to ascertain how much of the rapid growth of the white population is attributable to immigration, or how many years it would take for the whites to double their number, if their increase depended only on the excess of births over deaths. Now, there is a mode, first suggested, we believe, by Mr. Godwin,- of deducing by calculation, with a very near approach to correctness, from the number of those who, at each decennial census, are found to be less than ten years of age, the true law of increase so far as it depends on natural causes alone; or, in other words, of eliminating the effects of immigration. The principle of this calculation can be very easily explained. It is evident, that all those who, in 1840, are found to be under ten years of age, have been added to the population since the census of 1830; if we knew precisely how many of those included in the enumeration of 1830 had died during the following ten years, by subtracting the number of these deaths from that of the children under ten years old in 1840, the remainder would show the natural increase of the population during these ten years, or its growth from procreation alone. Suppose, for instance, that in 1840 there were four and a half millions of white children under ten years of age, and that one and a half millions of those who were counted in 1830 had died before 1840 : — then, the growth of the white population during these ten years, from procreation alone, was but three millions, while the census shows a growth of 3,662,970. In other words, 662,970 foreigners came into this country during the period in question. This is a supposed case, because our data are incomplete; we do not know exactly how many of those who were alive in 1830 had died before 1840; but we can estimate their number with tolerable correctness. It is known that in civilized countries, of an average degree of healthiness, from one seventh to one sixth of those who are alive at any one period die in the next ten years. Take, for instance, the slave population of the United States, which we know was not increased at all by immigration during the ten years following 1830. The total increase of the slaves during this period, according to the census, was 478,324; the slave children in 1840, under ten years of age, were 844,069; the difference between these two numbers, or 365,745, represents the loss by death and other causes on the slave population of 1830. This is a loss of rather more than 18 per cent., which is too great to be attributed to death alone; the other causes, which have concurred with death to keep down the increase of slaves, are, of course, emancipation and flight. Applying a similar calculation to the preceding decennial period, we find that the loss was but 15 per cent. on the population of 1820; very few could have been emancipated during these ten years. Take, for another instance, the free colored population of this country, which is not affected by immigration, but is increased by the number of emancipated and fugitive slaves. The increase of free blacks during the ten years preceding 1840 was but 66,636; the number of them under ten years of age in 1840 was 111,492; the difference between these two numbers, or 44,856, represents the loss by death on the free colored population of 1830. This is 14 per cent., which is certainly too small, as that for the slaves was too great; because the number of the free blacks was kept up by emancipation as well as by births. Probably the middle rate between the two, or 16 per cent., nearly one sixth, is that which fairly represents the loss by death alone during ten years. A few European examples will show that this is a fair proportion. The increase of the population of Sweden, from 1825 to 1835, was 254,187; the number under ten in 1835 was 730,128; the difference of these is 475,941, which makes the loss on the population of 1825 to be 17 per cent. In the Netherlands, the two censuses taken in 1830 and 1840 show in a similar manner that the population of the former period was diminished by 18.6 per cent., a fraction so large that we must suppose it to have been increased by emigration. In England, from 1831 to 1841, the corresponding fraction was but 14.3 per cent., which is so small that we are led to conclude that the immigration of the Irish and Scotch more than counterbalanced the departure of the English. The returns of the registration of deaths seem to prove that the diminution of a given population by death alone in ten years is from 15 to 16 per cent. On the whole, it is safe to take 16 per cent. as the medium. With this datum, let us look at the white population of the United States. In 1830, it was 10,526,248; in 1840, it was 14,189,218, thus showing an increase of 3,662,970. But the whites under ten years of age in 1840 were 4,485,130, a number which exceeds this increase by only 822,160, which is less than 8 per cent. on the population of 1830, or less than half of the true proportion of deaths. Take the preceding ten years, and we find the proportion still much too small, though somewhat larger than in the last decennial period. The white population in 1820 was 7,866,539; the census of 1830 showed an increase on this of 2,659,709. But the whites under ten in 1830 were 3,427,730, which exceeds the increase by only 768,021, or less than 10 per cent., on the population of 1820. Going back still another decennial period, we find the proportion to be 10.6 per cent.; from 1800 to 1810, it was still 10.6 per cent., and from 1790 to 1800, it was 11 per cent. The differences between these several rates and 16 per cent., which is the true proportion of deaths, show the effect of immigration. The following table shows the result of the calculation more clearly. The number in the second column is obtained by deducting 16 per cent., for deaths in 10 years, from the number in the first column. The fourth column is obtained by adding together the numbers in the second and third columns, and shows what the population in 1800 would have been, if there had been no immigration. The sixth column, obtained by subtracting the fourth from the fifth, shows the number of immigrants from 1790 to 1800. It should be observed, that the last column shows the number, not only of actual immigrants, but of the children who were born to these immigrants after their arrival in this country, before the next decennial census was taken. The following table is a mere continuation of the preceding for each of the decennial periods at which a census has been taken of our people. one, 84 per cent. Date. White Popu-alive 10 years 10 years af years after-shown by the lation. afterwards. terwards. next Census. No. of Immigrants in these 10 Years. Whites under Calculated Actual Popu- wards. 1790 3,172,464 2,664,869 1,479,315 1800 4,304,489 3,615,770 2,016,479 1810 5,862,004 4,924,083 2,625,790 1820 7,861,937 6,604,027 3,427,730 10,031,757 10,526,248 1830 10,526,248 8,842,048 4,485,130 13,327,178 14,189,218 Whole number of immigrants in 50 years, from 1790 to 1840, 2,058,655 4,144,184 4,304,489 160,305 5,632,249 5,862,004 229,755 7,549,873 7,861,937 312,064 494,491 862,040 This number may appear incredibly large; but the census of Boston, taken in 1845, shows that foreigners make up one fourth of the population of the city, and if their children be counted with them, they constitute one third of the whole number of citizens. Nearly two fifths of the citizens of New York, according to the enumeration of 1845, are of foreign birth, and if their children be added, they form a majority in the city; more than one eighth of the population of the State of New York are foreigners. If we add the immense German population in Pennsylvania, Ohio, and other States, the conclusion at which we have just arrived, that more than two millions of immigrants came hither in the half-century preceding 1840, will not seem extraordinary. And their number is increasing with marvellous rapidity; it is quite certain that as many as 250,000 arrived in the single year 1847. Of course, it is from the calculated population, or the fourth column in the preceding table, that the true rate of increase of the native population, from procreation alone, is to be deduced. Making the calculation on the principles of compound interest, we find that the yearly rate is about 2.39 per cent., and that the population would double in somewhat more than twenty-nine years. The latest European statisticians have placed the yearly rate as high as 3.27, and estimated that the number of the people would double in little over twenty years. But their data are wholly erroneous. XIV. THE ICE-TRADE OF THE UNITED STATES. By N. J. Wyeth, Esq. THE ice-trade of the United States was commenced by Frederic Tudor, of Boston, in 1805. This gentleman, having previously sent agents to the West Indies to procure information, determined to make his first experiment in that region. Finding no one willing to receive so strange an article on shipboard, he was compelled to purchase a vessel, the brig Favorite, of about 130 tons, which he loaded with ice from a pond in Saugus belonging to his father, and sent to St. Pierre, Martinique. This first enterprise resulted in a loss of about $4,500, but was, nevertheless, followed up until the embargo and war put an end to the foreign trade, at which period it had yielded no profit to its projector. Its operations had been confined to Martinique and Jamaica. After the close of the war, in 1815, Mr. Tudor recommenced his operations by shipments to Havana under a contract with the government of Cuba, which enabled him to pursue his undertaking without loss, and extend it, in 1817, to Charleston, S. C.; in the following year, to Savannah, Ga.; and in 1820, to New Orleans. In the mean time it had been tried again (by other parties) at Martinique and St. Thomas, and failed, and by Mr. Tudor at St. Jago de Cuba, where it also failed, after a trial of three years. On the 18th May, 1833, the first shipment of ice was made to the East Indies, by Mr. Tudor, in the ship Tuscany, for Calcutta, and since that period he has extended his operations to Madras and Bombay. Previously to 1832 the trade had been chiefly confined to the operations of the original projector, although several enterprises had been undertaken by other persons and abandoned. The increase of shipments to this period had been small, the whole amounting, in 1832, to 4,352 tons, which was taken entirely from Fresh Pond, in Cambridge, and shipped by Mr. Tudor, who was then alone in the trade. Up to this time the ice business was of a very complicated nature. Ship-owners objected to receive it on freight, fearing its effect on the durability of their vessels and the safety of voyages; ice-houses abroad and at home were required, and the proper mode of constructing them was to be ascertained. The best modes of preparing ships to receive cargoes were the subject of expensive and almost endless experiments. The machines to cut and prepare ice for shipping and storing, and to perform the operations of hoisting it into storehouses and lowering it into the holds of vessels, were all to be invented, involving much expense and vexation. Many of these difficulties have now been overcome, and since 1832 the trade has increased much, and appears destined to a still more rapid increase for some years. It has also been divided among many parties, and its methods have been further improved, and a knowledge of them more widely diffused. The ice has been chiefly taken from Fresh and Spy Ponds, and since 1841 mainly transported on the Charlestown Branch Railroad, which was |