and corrects the result by comparing it with the number obtained by multiplying the total number of houses in London by 8. From these figures he can compute the population of England, for London bears the eleventh part of the assessment of taxation. The data furnished by the poll money, by hearth money, and by the lists communicants, give an approximately like result.
In the third essay on political arithmetic, published in 1686, we have Petty's final statement on this question. He says there are three methods of reaching the number of people in London. (1) By houses and families. (2) By the number of burials. (3) By the number of those who die of the plague. In the first case he finds by observation that in every family there are on the average 6⅓ persons. In the second he uses his ratio of 1: 30, which he has since confirmed by further observation. In the third he proves by the decrease in the christening list that the plague carried off one-fifth of the population, allowance being made for those who left the city.
Petty was entirely conscious of the great weakness in all these computations. They were conjectural, and he recognized it. He disclaims mathematical accuracy. "I hope no man takes what I said about the living and dieing of men for mathematical demonstration," are the words used in a manuscript letter to Aubrey.
At the Conclusion of his "Observations upon the Dublin Bills" he makes the following confession of the purely tentative character of his deductions:
"Without the knowledge of the true number of the people, as a principle, the whole scope and use of keeping bills of births and burials is impaired; wherefore
