The Editor: Extinction op Family Namks 



213 



sent the number of adult males in a 

 population, each with a different sur- 

 name. After complicated computa- 

 tions, which represented five genera- 

 tions, and are far too abstruse to be 

 understood by anyone but a mathema- 

 tician, he successfully solves the prob- 

 lem algebraically, concluding: 



"As, therefore, time proceeds indefi- 

 nitely, the number of surnames extin- 

 guished becomes a number of the same 

 order of magnitude as the total number 

 at first starting in N, while the nimiber 

 of surnames represented by one, two, 

 three, etc., representatives is some 

 infinitely smaller but finite number. 

 When the finite numbers are multiplied 

 by the corresponding number of repre- 

 sentatives, sometimes infinite in number, 

 and the products added together, the 

 sum will generally exceed the original 

 number N. In point of fact, just as in 

 the cases calculated above to five 

 generations, we had a continual, and 

 indeed at first, a rapid extinction of 

 surnames, combined in one case with a 

 stationary, and in the other case an 

 increasing population, so it is when the 

 number of generations is increased 

 indefinitely. We have a continual 

 extinction of surnames going on, com- 

 bined with constancy, or increase of 

 population, as the case may be, until at 

 length the number of surnames remain- 

 ing is absolutely insensible, as compared 

 with the niimber at starting, but the 

 total number of representatives of those 

 remaining surnames is infinitely greater 

 than the original number." 



Mathematics, then, indicates that if 

 the world would only last an infinite 

 length of time, all its inhabitants would 

 have the same surname. It is interest- 

 ing to see how rapidly the process 

 proceeds in actual experience, even 

 among a people where the birth-rate is 

 high. 



A SOLUTION FROM LIFE. 



The investigation has been followed 

 out by Dr. Fr. von den Velden^ from a 



^"Aussterbende Familien," von Dr. Fr. von den Velden (Frankfort a M.),in Archiv. f. Rassen 

 u. Ges. Biologic, VI, 3, 3-iO. 



^Riffel's well-known gcnealogical-nosological tables were published in Mitt, liber die Erblichkeit 

 und Infektiositat der Schwindsucht (Braunsch. 1892) and Schwindsucht und Krebs (Karlsr. 

 1905). 



statistical point of view, on the basis of 

 figures compiled by RifEcP concerning 

 1400 marriages of peasant families in 

 Baden. Considering the nature of the 

 material, it will be admitted that the 

 number of family lines which ran out is 

 much smaller than would have been the 

 case had the data been secured in a 

 large city, or among people of a higher 

 social class. The writer's figures may 

 fairly be considered to represent the 

 extent of family-extinction under the 

 most favorable circumstances for con- 

 tinuation. 



He begins by pointing out that we are 

 accustomed to speak of a family as 

 becoming extinct when the male line, 

 and with it the family name, disappears. 

 This is misleading physiologically, be- 

 cause the female line is of equal impor- 

 tance with the male line, to the biologist. 

 He therefore investigates his data in 

 regard to both lines. 



Considering the variotis causes which 

 may contribute to the extinction of a 

 family. Dr. von den Velden says, "The 

 simplest case is when a family remains 

 absolutely childless. The causes of 

 this rather rare occurrence (in the 

 material here used 3% of the marriages 

 are unfruitful) are to be sought in a 

 minority of cases in the fact that one of 

 the partners is of advanced age; more 

 often — probably in two-thirds of the 

 cases — the reason is that one of the 

 partners is weighted by heredity. It is 

 not to be understood that he or she 

 inherits sterility; but sterility ensues as 

 a result of some disease, a tendency to 

 which has been inherited. 



MARRIAGES WITH ONE CHILD. 



"Equally rare with unfruitfulness is 

 the case when, although children are 

 bom, none of them reaches marriage. 

 In the material at hand we find ?)d> such 

 marriages, or 2.3% of the whole. The 

 average number of births in these 

 marriages is 3.8. Marriages which 

 result in only one child predominate, 

 but on the other hand we find one with 



