Essays on Mankind and Political Arithmetic

by Sir William Petty

THE THIRD ESSAY.

Proofs that the number of people in the 134 parishes of the London bills of mortality, without reference to other cities, is about 696,000, viz.—

I know but three ways of finding the same.

1. By the houses, and families, and heads living in each.

2. By the number of burials in healthful times, and by the proportion of those that live, to those that die.

3. By the number of those who die of the plague in pestilential years, in proportion to those that escape.

The First Way.

To know the number of houses, I used three methods, viz.—

1. The number of houses which were burnt A.D. 1666, which by authentic report was 13,200; next what proportion the people who died out of those houses, bore to the whole; which I find A.D. 1686, to be but one seventh part, but A.D. 1666 to be almost one-fifth, from whence I infer the whole housing of London A.D. 1666 to have been 66,000, then finding the burials A.D. 1666 to be to those of 1686 as 3 to 4,I pitch upon 88,000 to be the number of housing A.D. 1686.

2. Those who have been employed in making the general map of London, set forth in the year 1682, told me that in that year they had found above 84,000 houses to be in London, wherefore A.D. 1686, or in four years more, there might be one-tenth or 8,400 houses more (London doubling in forty years) so as the whole, A.D. 1686 might be 92,400.

3. I found that A.D. 1685, there were 29,325 hearths in Dublin, and 6,400 houses, and in London 388 thousand hearths, whereby there must have been at that rate 87,000 houses in London. Moreover I found that in Bristol there were in the same year 16,752 hearth; and 5,307 houses, and in London 388,000 hearths as aforesaid; at which rate there must have been 123,000 houses in London, and at a medium between Dublin and Bristol proportions 105,000 houses.

Lastly, by certificate from the hearth office, I find the houses within the bills of mortality to be 105,315.

Having thus found the houses, I proceed next to the number of families in them, and first I thought that if there were three or four families or kitchens in every house of Paris, there might be two families in one-tenth of the housing of London; unto which supposition, the common opinion of several friends doth concur with my own conjectures.

As to the number of heads in each family, I stick to Grant’s observation in page — of his fifth edition, that in tradesmen of London’s families there be eight heads one with another, in families of higher ranks, above ten, and in the poorest near live, according to which proportions, I had upon another occasion pitched the medium of heads in all the families of England to be six and one-third, but quitting the fraction in this case, I agree with Monsieur Auzout for six.

To conclude, the houses of London being 105,315 and the addition of double families 10,531 more, in all 115,846; I multiplied the same by six, which produced 695,076 for the number of the people.

The Second Way.

I found that the years 1684 and 1685, being next each other, and both healthful, did wonderfully agree in their burials, viz., 1684 they were 23,202, and A.D. 1685 23,222, the medium whereof is 23,212; moreover that the christenings 1684 were 14,702, and those A.D. 1685 were 14,730, wherefore I multiplied the medium of burials 23,212 by 30, supposing that one dies out of 30 at London, which made the number of people 696,360 souls.

Now to prove that one dies out of 30 at London or thereabouts, I say—

1. That Grant in the — page of his fifth edition, affirmeth from observation, that 3 died of 88 per annum which is near the same proportion.

2. I found that out of healthful places, and out of adult persons, there dies much fewer, as but one out of 50 among our parliament men, and that the kings of England having reigned 24 years one with another, probably lived above 30 years each.

3. Grant, page — hath shown that but about one of 20 die per annum out of young children under 10 years old, and Monsieur Auzout thinks that but 1 of 40 die at Rome, out of the greater proportion of adult persons there, wherefore we still stick as a medium to the number 30.

4. In nine country parishes lying in several parts of England, I find that but one of 37 hath died per annum, or 311 out of 11,507, wherefore till I see another round number, grounded upon many observations, nearer than 30, I hope to have done pretty well in multiplying our burials by 30 to find the number of the people, the product being 696,360, and what we find by the families they are 695,076, as aforesaid.

The Third Way.

It was proved by Grant, that one-fifth of the people died of the plague, but A.D. 1665 there died of the plague near 98,000 persons, the quintuple whereof is 490,000 as the number of people in the year 1665, whereunto adding above one-third, as the increase between 1665 and 1686, the total is 653,000, agreeing well enough with the other two computations above mentioned.

Wherefore let the proportion of 1 to 30 continue till a better be put in its place.

Memorandum. That two or three hundred new houses would make a contiguity of two or three other great parishes, with the 134 already mentioned in the bills of mortality: and that an oval wall of about twenty miles in compass would enclose the same, and all the shipping at Deptford and Blackwall, and would also fence in 20,000 acres of land, and lay the foundation or designation of several vast advantages to the owners, and inhabitants of that ground, as also to the whole nation and government.