TRANSACTIONS OF SECTION H. 707 
9, The Distribution and Variation of the Surnames in East Aberdeenshire 
in 1696 and 1896. By J. F. Tocusr, £..C. 
In a recent paper’ some results were given of an analysis of the frequency of 
surnames occurring in Hast Aberdeenshire in 1896. The author has now made a 
complete analysis of the whole of the surnames occurring in the ‘ List of Pollable 
Persons within the Shire of Aberdeen’ in 1696. ‘This paper deals with the distri- 
bution found to exist in East Aberdeenshire at that time, and its relationship to 
that found in 1896. It was found that the two most common surnames of 1696 were 
still the most common two hundred years later, these being Smith and Milne. 
The surnames of four great county families, Gordon, Hay, Forbes, and Fraser, were 
frequent in 1696, but have now, with the exception of the Frasers, very few repre- 
sentatives in East Aberdeenshire. The number of surnames existing in the district 
in 1696 was found to be 841, as against 725” found in 1896. The total number, 
taking both periods, amounted to 1,121, of which 445 were common to both 
periods. Of the 841 in 1696, 396 have died out, while 280 new surnames appear 
in 1896. The form of the distribution of surnames with respect to the magnitude of the 
number of representatives possessed by each has been found to follow that of Type I. 
of the series deduced by Pearson * (general form y= yo( 1+ 2) ( 1- =) oe 
the equation to the curve being y = *6525 a0 (7 —a)?797°, “Tf the surnames 
in the surrounding districts are taken into consideration in both the series, a curve 
of the same variety of Type I. results. It is evident from the results that, besides 
the disappearance of surnames from a district due to migration, the extinction of 
surnames is going on on a large scale. Such extinction is not due to any diminu- 
tion in fertility, but to the laws governing fertility—to its chance nature in 
general. Galton and Watson* have considered this problem from a theoretical 
standpoint, and have shown that with an equal distribution of surnames a certain 
number would become extinct in each generation. The number of surnames having 
1, 20,40 . . . m representatives at the tenth generation have been successively 
calculated (using Galton and Watson’s values of the constants) when a distribus 
tion similar to the observed one was obtained. From this it appears that any 
community adopting a different surname for each male would in the course of a 
few generations inevitably drift into a distribution similar to what has been shown 
to exist in East Aberdeenshire. The degree of association of the two series having 
an interval of 200 years between them has also been considered. It has been ascer- 
tained by Pearson’s contingency method ® that the deviation from independent 
probability is considerable, the value of @* being found to be 1°57. The two series 
are therefore, as would be expected, distinctly correlated. The correlation existing 
between the commonly occurring surnames of both series amounted to ‘5437, 
while that between the two complete series amounted to ‘3924. Among the 
surnames common to both periods, 23 per cent. maintained the frequency of 1696 
in 1896, while 40 per cent. were more frequent in 1896 than in 1696, and in 37 per 
cent. of the cases the surnames were less frequent at the end of two centuries, 
This gives, irrespective of whether it is due to emigration, immigration, or the laws 
governing fertility, an idea of the rate of change in the frequency of surnames, in @ 
veneral way, in Aberdeenshire during the last 200 years. 
Brit. Assoc. Report, 1901, p. 799. 
751 was the actual number given in 1896, but of thuse 26 were variants. 
‘On Skew Variation in Humogeneous Material,’ Roy. Soc., vol. clxxxvi., p. 381. 
4 Natural Inheritance, pp. 241-248. 
5 «On the Theory of Contingency, &c.,’ by Professor K. Pearson, Drapers’ Come 
pany Research Memoirs, Biometric Series I., 1904. 
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