444 
PROFESSOR K. PEARSON AND MISS A. LEE ON THE DISTRIBUTION 
In square brackets we have inserted the order of mean barometric pressures. It 
will be seen at once that the 10 stations of least variability are the 10 stations of 
highest pressure. Thus, there is a correlation between high pressure and small 
variability.'" Some changes in the two orders may well be due to the doubt v'hich 
attaches to the reduction to sea level, but taken as a whole the list illustrates the 
local character of the climate at the various stations, so far as it depends upon the 
height and variability in height of the barometer. This method of appreciating 
variability seems to us more satisfactory than a mere measurement of maximum to 
minimum ranges, which, with our data, while leaving St. Leonards first for steadiness 
of climate, would place Geldeston quite close to it, and make both that town and 
Scarborough superior to Southampton ! 
Instead of taking the variability about the mean, we might equally well have taken 
it about the mode, the only difference being that we should now have to calculate 
\/p + 2/y instead of \/p -f- 1 /y; see p. 433, Equations (i.) and (ii.). The compara¬ 
tively large values of p, however, do not allow of any widely divergent differences 
in the results. The more interesting problem of the variabilities in excess and defect, 
which, owing to the skewmess of barometric frequency curves, are not the same, will 
be dealt with in the next section. 
9. On the SJeewness of Barometric Frequency. 
The comparative closeness of the mean to the mode enables us to easily find a 
formula for the probability that the barometric height in any locality shall be in 
excess or defect of the modal height. Using the property of the modal third w^e 
have to integrate 
o 
2/ = yo (1 + jb' 
= y^e 
from 0 to 
Hence the area as far as terms of the order Xjqf 
i Va 
3 7 
11 . -i.± . 
27 p ^ 135 + 
y 
Thus the total area on the mean side of the mode 
= 0-5N + I 
3 7 
= N 0'5+-' 
2 1 4 1\ 
27 p + 135 / j’ 
/i _ 1 L I 1_1^ 
27 p 135 pr } 
3 evr {p + 1 ) 
[* It has been shown for this skew cmwe (Pearson and Filon, ‘ Roj. Soc. Proc.,’ vol. 62, p. 175) that 
the mean is negatively correlated with the standard deviation. Thns we have a theoretical indicaiion 
that high jDressui’c is correlated with small variability. The actual correlation for the mean value 
of yi is ‘25, approximately, this being for a random variation from the standard curve.] 
