248 NATURAL INHERITANCE. 



at first, a rapid extinction of surnames, combined in the one case 

 with a stationary, and in the other case an increasing population, so 

 is it when the number of generations is increased indefinitely. We 

 have a continual extinction of surnames going on, combined with 

 constancy, or increase of population, as the case may be, until at 

 length the number of surnames remaining is absolutely insensible, as 

 compared with the number at starting ; but the total number of 

 representatives of those remaining surnames is infinitely greater than 

 the original number. 



We are not in a position to assert from actual calculation that a 

 corresponding result is true for every form of f x (x), but the reason- 

 able inference is that such is the case, seeing that it holds whenever 



f x (x) may be compared with y ' y whatever a, b, or q may be. 



G 



ORDERLY ARRANGEMENT OF HEREDITARY DATA. 



There are many methods both of drawing pedigrees and of 

 describing kinship, but for my own purposes I still prefer those that 

 I designed myself. The chief requirements that have to be fulfilled 

 are compactness, an orderly and natural arrangement, and clearly 

 intelligible symbols. 



Nomenclature. — A symbol ought to be suggestive, consequently 

 the initial letter of a word is commonly used for the purpose. But 

 this practice would lead to singular complications in symbolizing 

 the various ranks of kinship, and it must be applied sparingly. The 

 letter F is equally likely to suggest any one of the three very diffe- 

 rent words of Father, Female, and Fraternal. The letter M suggests 

 both Mother and Male ; S would do equally for Son and for Sister. 

 Whether they are English, French, or German words, much the 

 same complexity prevails. The system employed in Hereditary 

 Genius had the merit of brevity, but was apt to cause mistake ; it 

 was awkward in manuscript and difficult to the printer, and I have 

 now abandoned it in favour of the method employed in the Records 



