We are met at the outset by two divergent opinions as to the permanent results of immigration upon the growth of population. The one is that all immigrants coming to our shores are net additions, hastening by so much the growth in density of population; the other opinion, the displacement theory, is that immigration has the effect of checking the natural increase of the native stock so much that it does not materially change the total population, or actually causes it to be less than it would have been had no immigration occurred. § 10. #The displacement theory; its fundamental assumption.# The latter opinion which still has many upholders[6] was first advanced by a distinguished economist, Francis A. Walker, but his first statement of it referred only to the period between 1830 and 1860. The main argument in support of this opinion was that in the three decades from 1830 to 1860 during which a large immigration occurred, the decennial rates of increase of the population were almost the same as in the three decades from 1800 to 1830.[7] The conclusion drawn from these figures is that the immigrants were the cause of the decline of the average birthrate that occurred in the families of native stock. The validity of this conclusion is absolutely dependent on the assumption that no other forces were at work to produce this result. Must we believe that, but for immigration, the native birthrate would not have declined at all? This is incredible. The birthrate of the native stock had already begun to decline before 1820 as is shown by many family records, and by the fall of the decennial rate of increase from 35 and 36 in the decades ending 1800 and 1810, to 33.1 and 33.5 in the next two decades. This occurred despite the enormous western settlement then under way on the Louisiana Purchase. The decline of the birthrate began at that time to appear as a world-wide phenomenon, accompanying improved transportation (roads, steamboats, steam railways), the rapid growth of cities, and the general industrial revolution. The general birthrate has declined of recent years in Australia and New Zealand, where there has been little immigration, more rapidly than it has in the United States.[8]