88 Proceedings of Royal Society of Edinhurgh. [sess. 
cat by the isatmid line for 3° and 4° on the map, gives the mean 
limit of visibility for air of that dryness coming from that direction. 
Ill this case it is 123 miles. If a circle be now drawn through this 
point, with Falkirk as a centre, the circle so described will be the 
isatmid line at the time of observation. Or supposing the wind 
to be S.W. and dry enough to give a wet bulb depression of 7° or 8°, 
then the S.W. line is cut by the 7° and 8° isatmid at a distance of 
21 miles from Falkirk, and a circle of 21 miles radius described 
round Falkirk would be the isatmid line for the hour. 
The shading in the Plate representing the distribution of popula- 
tion of Scotland and the isatmid lines for Falkirk show in a very 
clear way the relation between the density of the population and the 
purity of the atmosphere. The air brought by the winds from all 
the densely inhabited parts being very impure, as will be seen when 
the wind is from these parts, the isatmid lines shrink and draw 
close to Falkirk, and only separate and expand when the air comes 
from thinly populated areas, the shading and the area enclosed by 
the isatmid lines being complementary ; as the shading deepens 
the lines draw close to Falkirk, and vice versa. 
In the Plate the counties, as already stated, are shaded in proportion 
to their population, and the different counties have generally been 
treated as if the population were evenly distributed, the counties being 
shown shaded equally all over. This evidently does not correctly 
represent the true condition, especially in the counties of Edinburgh, 
Lanark, and Eenfrew, in which there are large towns. As, how- 
ever, these counties are some distance from Falkirk, this method of 
representing the population, and consequent impurity of the atmos- 
phere, does well enough ; but when we come to the shading of the 
areas near the place of observation, this method of representation, 
owing to the peculiar distribution of the population existing near 
Falkirk, would give erroneous impressions, and the representation 
of the population has to be more particularly localised. Stirling- 
shire, in which Falkirk is situated, and Dumbartonshire, situated 
immediately to the west of Stirlingshire, have both a very uneven 
distribution of population, which it is necessary to represent on the 
map to enable us to understand the results of the observations. 
If we draw a line due west from Falkirk, we shall find that the 
part of Stirlingshire north of this line is very thinly populated, with 
