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at first, a rapid extinction of surnames, combined in the one case with a stationary, and in the other ease 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 off, (x), but the reasonable inference is that such is the case, seeing that it holds whenever

fl (x) may be compared with (( a+ b~q whatever a, b, or q may be. G.


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 different 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