This line of argument has been so thoroughly and convincingly expounded by a number of writers that it need not be dwelt upon further here. Its great weakness is that which has been anticipated—it lacks mathematical positiveness. An opponent might readily claim that the appalling decline in the native birth rate (the existence of which no one would care to deny) was due to some one or other of a variety of different causes, or to several operating together. The sections where the birth rate is the lowest are not only those where immigration has been the heaviest. They are also to a large extent those which are characterized most distinctively by manufacturing industry, or where the population is the densest. Why not assign the falling birth rate to one of these causes?[183] The best answer to this counterargument is to strengthen the original position by another and wholly different course of reasoning. This may be done very effectively by applying the fundamental and accepted laws of population to the question in hand, and seeing how they would work out in such a case. If the conclusion thus reached coincides with that resulting from the other method of proof, it will furnish a demonstration amounting almost to a certainty. For this purpose we must go back to the set of doctrines first consistently expounded by Malthus, and known by his name. Though they are now more than a century old, they still stand as one of the profoundest contributions to human knowledge. These doctrines are so familiar to all students of social subjects that the merest summary will serve the present purpose. This may be given in the following words.