During this time the population increased from 270,089 to 312,710 (in 1845) or about 35.1 per cent., while the increase in crime was 354.6 per cent. The average number of inmates in the Tombs was, in 1846, 174; in 1848, 216, an increase of 21.2 per cent. in two years, or over three times the growth of the city, which of late was about 6.90 per cent. for two years. This startling disproportion, is more or less true of all large cities. It is a law of our social state, that growing prosperity shall find its drawback in the parallel increase of misery; and that crowded communities, as they offer the most liberal rewards to good conduct and enterprise, so shall contain likewise the most seeds of evil, the strongest temptations to vice, the largest amount of misery. And besides our own neglected and depraved population, the tide of emigration, now setting in stronger and stronger every year, while it enriches our country, leaves much of its refuse in our city. Pauper families, and even felons, are not unfrequently sent over to us, as a cheap way of disposing of them, by the selfishness or mistaken humanity of those whose duty it is to provide for them at home, thus swelling the number of houseless, friendless and lawless youth, drifting loose upon society, to become utterly ship-wrecked, unless the active hand of benevolence is stretched out to save them.” Of those children received in 1848, 209 were boys, (192 white and 17 colored,) and 55 were girls, (45 white and 10 colored.) 140 of the whole number were from the Police and Sessions of the city, and of the white children only THIRTY-NINE were of American parentage. 127 were of Irish birth! Of 141 boys discharged, 53 were indentured to farmers, 14 to shoemakers, and 19 sent to sea; and of 47 girls discharged, 33 were indentured to housewifery. The average age of the inmates received during 1848, was thirteen and two and a half twelfths years. Seventy-seven were over fifteen when received. _New House of Refuge at Rochester._--Our readers are perhaps aware, that an institution similar to the present House of Refuge in New York, is about to be established in Rochester for the accommodation of the Western counties of the State. A friend has kindly furnished us with the following description of the buildings, &c. Mr. Wood, the present superintendent of the New York House of Refuge, is expected to take charge of the new establishment, and the discipline will probably be substantially the same. An appropriation is expected at the present session of the legislature, that will enable inmates to be received this spring. No provision is yet made for females.