[The following article, from the pen of Hon. R. J. Walker, forms the APPENDIX to the volume just published in England, and now exciting great attention there, containing the various pamphlets issued by him during the last six months. The subjects discussed embrace Jefferson Davis and Repudiation, Recognition, Slavery, Finances and Resources of the United States. It would be difficult to overestimate the effect of these Letters abroad. As our readers already possess them in the pages of THE CONTINENTAL, we enable them to complete the series by furnishing the ensuing Appendix. It closes with an extract from an 'Introductory Address' delivered by Mr. Walker before the National Institute, at Washington, D. C., giving a short account of the various improvements and discoveries made by our countrymen in the Inductive Sciences. As showing to England what a high rank we had even then taken in the world of science, and pointing out to her the number and fame of our savants, it will be read with just pride and interest. As the Address was delivered in 1844, it of course contains no details of our marvellous progress since that date in science and discovery.--ED. CONTINENTAL.] We have seen by the Census Tables, if the product _per capita_ of the Slave States in 1859 had been equal to that of the Free States for that year, that the ADDITIONAL value produced in 1859 in the Slave States would have been $1,531,631,000. Now as our population augmented during that decade 35.59 per cent., this _increased_ value, at that ratio, in 1869 would have been $2,052,332,272. If multiplying the amount _each year_ by three only, instead of 3-559/1000 the result, during that decade, would have been as follows: Product of 1860, $1,559,039,962 " 1861, 1,605,811,060 " 1862, 1,654,085,391 " 1863, 1,703,707,952 " 1864, 1,754,819,198 " 1865, 1,807,464,773 " 1866, 1,861,688,716 " 1867, 1,917,539,377 " 1868, 1,975,065,558 " 1869, 2,034,317,524 ------------- Total augmented product of the $17,873,539,511 decade That is, the total _increased_ product of the Slave States, during the decade from 1859 to 1869, would have been $17,873,539,511, if the production in the Slave States had been equal, _per capita_, to that of the Free States. This, it will be remembered, is gross product. This, it will be perceived, is far below the actual result, as we can see by comparing the real product of 1869, $2,052,332,272, as before given, with the $2,034,317,524, as the result of a multiplication by three each year.