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.