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78 it is not quite so much. Even the most ardent vaccinists do not claim a greater protection. But none of them ever doubt the fact of the protection gained by having had the disease, and yet none of them, nor any of the Commissioners, thought that any evidence, much less proof, of the fact itself was needed. They took it for granted. "Everybody knows it." "Very few people have small-pox a second time." No doubt. But very few people suffer from any special accident twice—a shipwreck, or railway or coach accident, or a house on fire; yet one of these accidents does not confer immunity against its happening a second time. The taking it for granted that second attacks of smallpox, or of any other zymotic disease, are of that degree of rarity as to prove some immunity or protection indicates the incapacity of the medical mind for dealing with what is a purely statistical and mathematical question.

Quite in accordance with this influence of small-pox in rendering the patient somewhat more liable to catch the disease during any future epidemic, is the body of evidence adduced by Professor Vogt, showing that vaccination, especially when repeated once or several times, renders the persons so vaccinated more liable to take the disease, and thus actually increases the virulence of epidemics. This has been suspected by some anti-vaccinators; but it is, I believe, now for the first time supported by a considerable body of statistics. The other important feature in Professor Vogt's memoir is the strong support he gives to the view that small-pox mortality is really—other things being approximately equal—a function of density of population. All the evidence I have adduced goes to show this, especially the enormously high small-pox death-rate in crowded cities in approximate proportion to the amount of crowding. Professor Vogt adds some remarkable statistics illustrating this point, especially a table in which the 627 registration districts of England and Wales are grouped according to their density of population, from one district having only sixty-four persons to a square mile to six which have 20,698 per