THE POPULATION OF IRELAND. — The census of Ireland, taken in June last, is not yet completed; but sufficient progress has been made in the arrangement of the returns from a great variety of districts, to afford sufficient grounds for judging of the general results. First, then, it appears to be quite certain that a most decided check has been given, within the past two years, to the progressive increase of the population in Ireland. The general increase in Ireland, since 1831, has been to a very trifling extent. According to the census of 1821, the population was 6,801,827; in 1831 the population had increased to 7,707,401. Thus the increase in ten years, up to 1831, had been very nearly one million, or about 16 percent. Previous to 1821, the increase had been in a much greater ratio, in as much as the population Ireland, owing to the abatement of penal laws against Roman Catholics and other causes, had nearly doubled within the period of half a century. The rate of increase, on the average, throughout the country, between 1831 and 1841, will not be more than 5 percent. The growing mania for large farms, producing the eviction or removal of tenantry to a vast extent, operates no doubt as a very decided check upon the increase of population. The mortality, it appears, has been immense amongst children, from want of nourishment and sustenance.— Perhaps as large a number of children have been born within the last ten years as within any former corresponding period, but the misery and want resulting from the depopulating system, augmented by the frequent failure of the crops, have accomplished the work of death among the offspring of the poor. But still, notwithstanding the operations of these destroying influences, there has been some increase of the population in every part of Ireland but one. The sole exception is the county of Carlow. In that county, the head quarters of the exterminators, the population has actually decreased since 1831. — [Chronicle.