[9] As an example of the Commissioners’ statistical fallacies in treating the subject of changed age-incidence, see Mr. Alexander Paul’s _A Royal Commission’s Arithmetic_ (King & Son, 1897), and, especially, Mr. A. Milnes’ _Statistics of Small-pox and Vaccination_ in the Journal of the Royal Statistical Society, September, 1897. [10] The highest small-pox mortality in London was in 1772, when 3,992 deaths were recorded in an estimated population of 727,000, or a death-rate of not quite 5,500 per million. (See Second Report, p. 290.) [11] The small-pox deaths under one year in England have varied during the last fifty years from 8·6 to 27 per cent. of the whole. (See _Final Report_, p. 154.) [12] This almost exactly agrees with the ages of the boys who are admitted between nine and eleven, and leave at fourteen. (See Low’s _Handbook of London Charities_.) [13] From 1850 to 1873 the private vaccinations have been estimated according to their proportion of the whole since they have been officially recorded. [14] Although the Commission make no mention of Mr. Biggs’ tables and diagrams showing the rise of infant-mortality with increased vaccination, and its fall as vaccination diminished, they occupied a whole day cross-examining him upon them, endeavouring by the minutest criticism to diminish their importance. Especially it was urged that the increase or decrease of mortality did not agree _in detail_ with the increase or decrease of vaccination, forgetting that there are _numerous_ causes contributing to all variations of death-rate, while vaccination is only alleged to be a _contributory_ cause, clearly visible in general results, but not to be detected in smaller variations (see Fourth Report, Q. 17,513-17,744, or pp. 370 to 381). Mr. Bigg’s cross-examination in all occupies 110 pages of the Report. [15] It was introduced into the Navy in 1801, and in that year the medical officers of the fleet presented Jenner with a special gold medal! [16] These figures (for the Army and Navy) are obtained by averaging the annual death-rates given in the tables referred to, and are therefore not strictly accurate on account of the irregularly varying strength of the forces. But the error is small. In the case of the Navy, from 1864 to 1888 the mortality accurately calculated comes out _more_, by nearly six per cent. than the mean above given, and in the case of the Army for the same years about one per cent. more. For Ireland the calculation has been accurately made by means of the yearly populations given at p. 37 of the _Final Report_, but for the Army and Navy materials for the whole period included in the diagrams materials are not available in any of the Reports.