J. F. Tocher 
137 
be seen later, these two methods were adopted by the Committee and employed 
by the author as convenient and desirable ones for the purpose of analysis. At 
this stage, however, Mr John Gray suggested " the natural subdivision of the 
country into river basins, as it is well known that watersheds, when they form 
mountain ranges even of moderate size act as racial barriers." The view was 
expressed by him that " if the ordinary subdivision into counties were adopted, 
we should have in many cases to include populations with quite different character- 
istics in the same division and valuable ethnic distinctions would be lost in taking 
an average." The suggestion seemed a good one as a means of determining the 
differences between the populations in the various river basins. Also, when the 
population in each river basin is subdivided into districts, we have the means of 
determining whether any one district significantly differs from another in that basin. 
But this method of grouping is neither supei'ior nor inferior to any other method 
of grouping populations in adjacent areas, as all that can be said in each case 
is that, conformably to size of sample, the population differs or does not differ 
from another population or from the general population of the country. Thus 
counties and groups of counties are quite convenient groups for the statistician to 
deal with, and since this method of grouping is well known to the public, it has 
a slight advantage over any other. Again, one must remember that no one method 
of grouping will solve all the problems the anthropometrician desires to solve. 
For instance, one may wish to contrast a city population with its environs; a 
mining population with a rural one ; or a coast population with an adjacent inland 
population. Thus special groupings are frequently necessary. 
In a small country like Scotland the river basins are exceedingly small, 
compared with the great basins on the continents of Europe, Asia, Africa and 
America. Besides, one has in Scotland a population the vast majority of the 
members of which speak one language and which has bred intraracially for gene- 
rations. It therefore did not seem to the writer to be likely that grouping by river 
basins alone would yield all the information obtainable as to the distribution of 
colour, but the general idea of basins was kept in view in constituting the groups 
intermediate between parishes and counties, namely, districts. Thus a satisfactory 
solution of the area problem was found, since all the groupings discussed, namely 
schools, parishes, districts, counties and river basins, were and are available for 
statistical analysis. 
The writer proceeded to carry out the district* system of grouping, com- 
mencing with the county of Lanark. Altogether 110 districts were thus consti- 
tuted, the task of locating schools on the maps being an exceedingly laborious 
one indeed, so that much time was consumed in the construction of the districts. 
The Key maps opposite page 137 (Maps I.f and II.) show in a general way the 
* The special district grouping has been used by the writer to determine urban, suburban and rural 
differences and, as already stated, is the basis of Mr Gray's memoir. Of course the maps constructed 
by him show the districts graded and do not show the actual numerical district averages as given 
in tables supplied to him. 
t For names of the Divisions see Explanatory Note, p. 148, 
Biometrika vi 18 
