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XL On the Distribution of Frequency {Variation and Correlation) of the Barometric 
Height at Divers Stations. 
By Karl Pearson, F.B.S., and Alice Lee, B.A., B.Sc. 
Received June 15.—Read June 17, 1897. 
[Plates 9-17.] 
X.—On the Frequency at Divers Stations of the several 
Barometric Heights. 
1. Introduction. 
Let a curve be formed such, that if y be the ordinate falling between the abscissae 
X and cc + Fx, the area y^x represents the frequency of the barometer with height 
lying between x and x -f Sx for any locality. This curve will be spoken of as the 
barometer frequency curve for the given locality. The curve in any series of actual 
observations will be represented by a, polygonal line ; in the present case the element 
Sx has been throughout taken as n)- inch of barometric height. 
Such frequency curves occur in innumerable physical, anthropological and economic 
investigations, and can in many cases be fairly accurately represented by the normal 
curve of frequency, i.e., Laplace’s curve of errors. The barometric frequency curve 
is, however, a marked exception to this rule. Lhe mean baroinetiic height is 
very far from coinciding with the ‘ mode ’ or height of maximum frequency. While 
barometric frequency curves are remarkably smooth when a very large number of 
observations are dealt with, the distribution of frequency does not obey the normal 
law,’'' but some other law which up to the present has not been fully discussed. 
In a memoir published in the ‘ Phil. Trans.,’ A, vol. 186, pp. 343-414, a series of 
generalised frequency curves are introduced, and it is shown, pp. 351 and 382, that 
the asymmetry of the barometric frequency curve can probably be dealt with by one 
or other of these generalised curves. 
The importance of this conclusion lies in the fact that the distribution of 
barometric frequency in any locality can then be lully described by the statement 
of the values of three or four well defined constants. 
* This seems first to have been pointed out by Dr. Venn, in a letter to ‘ Nature, September 1, 1887. 
7.3.98. 
