his position, has access to the whole body of European official statistics, and his discussion goes to the very root of the whole question. The treatise is divided into nine chapters, and occupies thirty-four closely printed pages of the Blue Book; but, being an elaborate argument founded mainly on a scientific treatment of statistics, there was probably no member of the Commission capable of adequately dealing with it. Yet it is of more value than fully nine-tenths of the remainder of the voluminous reports, with their 31,398 questions and answers. Professor Vogt's treatise covers almost the whole ground, medical and statistical, and enforces many of the facts and arguments I have myself adduced. But there are two points which must be especially mentioned. His first chapter is headed—"A Previous Attack of Small-pox does not Confer Immunity." I have long been of opinion that this was the case, and have by me a brief statement, written six years since, to show that the rarity of second attacks may in all probability be fully explained by the doctrine of chances. But I had not statistics sufficient to prove this. Professor Vogt, however, having the statistical tables of all Europe at his command, is able to show not only that the calculus of probabilities itself explains the rarity of a second attack of small-pox, but that second attacks occur more frequently than they should do on the doctrine of chances alone, indicating that, instead of there being any immunity, there is really a somewhat increased susceptibility to a second attack! [1] This being
- ↑ Brief statement of the argument:
The chances of a person having small-pox a second time may be roughly estimated thus: Suppose the average annual death-rate by small-pox to be 500 per million, and the average duration of life forty years. Then the proportion of the population that die of small-pox will be 500 x 40 = 20,000 per million. If the proportion of deaths to cases is one to five, there will be 100,000 cases of small-pox per million during the life of that million, so that one-tenth of the whole population will have small-pox once during their lives.
Now, according to the law of probabilities alone, the chances
