A home-tourist, halting in the quiet churchyard of Mortlake, in Surrey, about half a century since, fell into the following reflective train of calculation of generations:
“I reflected that, as it is now more than four hundred years since this ground became the depository of the dead, some of its earliest occupants might, without an hyperbole, have been ancestors of the whole contemporary English nation. If we suppose that a man was buried in this churchyard 420 years ago, who left six children, each of whom had three children, who again had, on an average, the same number in every generation of thirty years; then, in 420 years, or fourteen generations, his descendants might be multiplied as under:
| 1st | generation | 6 |
| 2d | ” | 18 |
| 3d | ” | 54 |
| 4th | ” | 162 |
| 5th | ” | 486 |
| 6th | ” | 1458 |
| 7th | ” | 4374 |
| 8th | ” | 13,122 |
| 9th | ” | 39,366 |
| 10th | ” | 118,098 |
| 11th | ” | 354,274 |
| 12th | ” | 1,062,812 |
| 13th | ” | 3,188,436 |
| 14th | ” | 9,565,308 |
That is to say, nine millions and a half of persons; or, as nearly as possible, the exact population might at this day be descended in a direct line from any individual buried in this or any other churchyard in the year 1395, who left six children, each of whose descendants have had on the average three children! And, by the same law, every individual who has six children may be the root of as many descendants within 420 years, provided they increase on the low average of only three in every branch. His descendants would represent an inverted triangle, of which he would constitute the lower angle.
“To place the same position in another point of view, I calculated also that every individual now living must have had for his ancestor every parent in Britain living in the year 1125, the age of Henry I., taking the population of that period at 8,000,000. Thus, as every individual must have had a father and mother, or two progenitors, each of whom had a father and mother, or four progenitors, each generation would double its progenitors every thirty years. Every person living may, therefore, be considered as the apex of a triangle, of which the base would represent the whole population of a remote age.
| 1815. | Living individual | 1 |
| 1785. | His father and mother | 2 |
| 1755. | Their fathers and mothers | 4 |
| 1725. | ” ” | 8 |
| 1695. | ” ” | 16 |
| 1665. | ” ” | 32 |
| 1635. | ” ” | 64 |
| 1605. | ” ” | 128 |
| 1575. | ” ” | 256 |
| 1545. | ” ” | 512 |
| 1515. | ” ” | 1,024 |
| 1485. | ” ” | 2,048 |
| 1455. | ” ” | 4,096 |
| 1425. | ” ” | 8,192 |
| 1395. | ” ” | 16,384 |
| 1365. | ” ” | 32,768 |
| 1335. | ” ” | 65,536 |
| 1305. | ” ” | 131,072 |
| 1275. | ” ” | 262,144 |
| 1245. | ” ” | 524,288 |
| 1215. | ” ” | 1,048,576 |
| 1185. | ” ” | 2,097,152 |
| 1155. | ” ” | 4,194,304 |
| 1125. | ” ” | 8,388,608 |
That is to say, if there have been a regular co-mixture of marriages, every individual of the living race must of necessity be descended from parents who lived in Britain in 1125. Some districts or clans may require a longer period for the co-mixture, and different circumstances may cut off some families, and expand others; but, in general, the lines of families would cross each other, and become interwoven, like the lines of lattice-work. A single intermixture, however remote, would unite all the subsequent branches in common ancestry, rendering the contemporaries of every nation members of one expanded family, after the lapse of an ascertainable number of generations.”[[33]]
[31]. Dr. Johnson.
[32]. The Doctor.