+Average number of children in each generation; the families being grouped according to the number of generations they attained.+ The families of 1807 (original families) and their descendants were classed into five groups, according to the number of generations they attained in Mannheim. For each group is calculated the average number of children within one generation--for each separate family as well as for the entire family (_i.e._, the total of all the separate families which have sprung from the same "original family"). For instance: "Original families" which have lasted into the third generation, 464; the separate families show in the first generation, 464 families, 2,377 children; in the second generation, 718 families, with 3,645 children; in the third generation, 754 families, with 2,454 children. Accordingly, the total families show average numbers 5.1, 7.9, 5.3; the separate families, 5.1, 5.1, 3.3. All these averages are minimum figures, because it was impossible to eliminate the moderate number of couples who emigrated before the number of their offspring was completed. In the generations up to the third inclusive, reproduction may be considered as terminated, but in the fourth, and especially the fifth and sixth, it still is in progress. [Sidenote: C 39] +Age intervals separating the various generations.+ Taking into account all the families investigated, the average length of time between the birth of the originator of the family and his first born son was 33-1/4 years, his first born grandchild 63-2/3 years, and his first born great grandchild 95-1/3 years. The curves become gradually flatter, because the possible difference between minimum and maximum age distance from one generation to another increases in arithmetical progression. [Sidenote: C 40] +Prolificness of first marriages in the 19th century.+ Taking the entire period from 1811 to 1890 together the percentage of large families (six children or more) and of small families (one-two children) produced by all first marriages, excluding childless ones, is indicated by the horizontal centreline. The positive or negative deviations from the average during each decade are entered respectively above and below this line. The note in Figure C 38 referring to the families which may have emigrated while still productive applies here also. The temporary increase in prolific marriages after 1870 may be in connection with the material decrease in the age of those contracting marriage for the first time, as compared with the preceding decade. (Men 28.65 in the earlier period as against 27.41 in the later, and women 25.92 against 24.68 years.) The extinction of the families is undoubtedly due partly to other causes than the voluntary limitation of families--to a process of degeneration. A very remarkable proof of the degenerative character of the dying out of families is given by Pontus Fahlbeck in his book, "The Aristocracy of Sweden" (Fischer, Jena, 1903).