We have thus shown, by a mathematical demonstration, that the words which the _New Englander_ found convenient to put in our mouths, though we really said nothing of the kind, that "if the returns of the provinces were brought into the account, they would more than redress the balance of the cities," are sufficiently made good. We are glad he "proceeded to put our proposition to experiment," and we caution him when he makes any more experiments of this kind to reflect that, whatever may be the judgment of an uncritical public prepared to take his statements without examination, his artifices, misstatements, and false conclusions are sure to be detected by any well-informed reader who will take the trouble of examining them. The result of the comparison of the Protestant and Roman Catholic provinces of Austria and Prussia sums up in this fashion: _False Average of the New Englander._ Protestant 11.7 Catholic 18.6 _True Average._ Protestant 10.2 Catholic 10.3 We have thus finished this part of our task, strictly confining ourselves to the provinces in question; but as it seems more complete to add the other German provinces on both sides, of which returns are given, we do so with the following result: _Provinces already given._ POPULATION PR. CT. IN MILLIONS. Protestant 10.2 9.11 Würtemberg 16.4 1.75 Smaller German States[16] 14.8 6.40 ---- ----- 12.5 17.26 POPULATION PR. CT. IN MILLIONS. Catholic 10.3 41.14 Bavaria 22.5 4.81 Baden 16.2 1.43 ---- ----- 11.7 47.38 We dismiss the _New Englander_ from the examination of provinces with the conviction that he ought now to become a wiser if not a better man. 2dly. The _New Englander_ gives us another division of his work, entitled thus, "3. _Comparison of mixed populations_," the object of which seems to be two-fold: 1st, To show the wonderful effect of a little Protestant salt in a mass of Catholic corruption; and 2dly, to push up the rate of Catholic Austria to a high figure by excluding the best half of it, and thus to come out with flying colors in the grand tabular statement of all the European countries. He commences with the following round but very novel statement: "The empire of Austria includes a population of 31,655,746; of these, 21,082,801 or two thirds, are non-Romanists, belonging to the Protestant church or Greek Church." The population of the empire of Austria is really divided as follows: Catholics 26,728,020 All others 7,703,976