XI. On the distribution of frequency (variation and correlation) of the barometric height at divers stations

Let a curve be formed such, that ify be the ordinate falling between the abscissæx andx + δx , the areay δx represents the frequency of the barometer with height lying betweenx andx + δx for any locality. This curve will be spoken of as thebarometer 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 δx has been throughout taken as 1/10 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.The mean barometric 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.