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 small-pox, 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 square mile, another column showing in how many of the years during the period 1859-1882 there were any small-pox deaths in the districts. The result shown is very remarkable. In the most thinly populated district no small-pox death occurred in _any one_ of the twenty-four years; in the most densely peopled districts small-pox deaths occurred in _every one_ of the twenty-four years. And the frequency of the occurrence of small-pox in all the intervening groups of districts followed exactly the density of the population. Taking two groups with nearly the same population, the fourth group of 107 districts, with a total population of 1,840,581, had small-pox deaths in only five or six out of the twenty-four years in any of them; while the thirteenth group of thirteen districts, with a population of 1,908,888, had small-pox deaths in twenty-three out of the twenty-four years. But the first group had a density of 160 to the square mile, and the last had 8,350 to the square mile. The Commissioners