438 
PROFESSOR K. PEARSON AND MISS A. LEE ON THE DISTRIBUTION 
is little variation possible in y ; it also has a large correlated error, and these errors 
tend very closely to balance each other, to retain the same shape for the 
frequency curve,^ 
Indeed it can be shown, both theoretically and empirically, that very considerable 
changes may be made in the constant ^9, and the frequency curve will not sensibly 
change its shape provided the correlated error be made in y. 
But these results show us at once that while the frequency curves as determined 
from p and y may fit as indeed they do—the observations very accurately, still p 
and y are not good constants on which to base (when treated separately) any 
discussion of the relative distribution of barouietric frequency with geographical 
position. The best constants are, as we might hope they would be, the physical con¬ 
stants, namely the mean or modal height, the mean or modal frequency, the standard 
deviation or variability, and the skewness. It is accordingly to these constants, as 
the fundamental constants, that we have specially directed our attention. All the 
other quantities involved can be expressed in terms of them. If q be written for the 
skewness Sk. y:q have : 
- 1, M,-M,= aq, 
7 = K H,, - M, = cTjq. 
In Table V. the whole system of probable errors and of correlation between errors 
IS given for the 23 stations, and an inspection of them will show at a glance the 
degree of accuracy which may be expected from any number of years of barometric 
observation. Curves will be found drawn on Plate 9, giving the probable percentage 
errors of the modal frequency, and the standard-deviation together with the probable 
errors of the mean and the skewness for any number of years up to 20, for a station 
having the mean values of cr and p. They will, we believe, be found of service by 
the practical meteorologist for estimating how closely any series of observations w ill 
suffice to determine the theoretical frequency of the station. It is true that these 
eriois aie not merely functions of the number of years of observation ; they depend 
also upon the local values of p and cr, as an inspection of Table V. will illustrate. 
Gompaie, foi example, Southampton with Babbacombe, or Armagh with Glasgow. 
The deviations of the probable errors from the graphical values owing to the 
variation in p and cr may, however, be looked upon as a second order deviation, and 
a reasonable, if rough, appreciation of the magnitude of the errors made may be 
obtained from Plate 9. 
It will be seen from the Table V. as well as from Plate 9, that the value of the 
physical frequency constants are, for the years under consideration, given by the 
calculated values with a very close degree of accuracy. 
* It should be noticed that the term involving^ in the frequency, i.e., ^1 + ^ becomes more and 
more independent of as p increases, ^ 
