( 558 ) 



111 rejiistcriiiü; the oliservations the decimals have been omitled, so 

 that llio numlier of oeciuTences correspond i lift' with a lieiuiit of P 

 nun. includes all values between P -(- 0.5 and P — 0.5 mni. 



Owing to this simplification the anionnl of laliour is less than 

 would appear from the great number of data. The ne.\t work to do 

 was to multiply the frequency numbers with a factor such that the 

 total number for each month amounted to 10.000. The frequencies 

 thus obtained correspond with expressions for the probability of 

 occurrence expressed in 10.000'''^ parts of unity. Then the average 

 height was calculated and, by means of simple, linear interpolation 

 the whole curve shifted in such a manner that the new frequencies 

 correspond with deviations from the average value expressed in 

 multiples of whole numbers. This has been done not only with a view 

 of abridging the computations of the moments of the second and 

 third order but principally in order to obtain an evaluation of the 

 skewness of the curves, which may be defined as the inequality of 

 frequency for equal positive and negative deviations from the arith- 

 metical mean. If of such a series of data the frequencies corresponding 

 with equal deviations are taken together, no iiccount lieing taken 

 of their sign, the skewness is eliminated, and the numbers obtained 

 in this way may be considered as belonging to a symmetrical curve 

 (Table I). " 



For this curve we calculate the factor of precision (stal)ili(y) and 

 investigate in how far the actual curve agrees or disagrees with the 

 curve of the normal exponential law (Table II). 



As has been mentioned above, the inequalities of frc(piciicies for 

 equal deviations of opposite sign have been taken as a measure of 

 the skewness. 



Tables I — III show, separately for each month, the sums and ditfer- 

 ences thus formed. Tlie numbers of Table I added to those of Table III 

 will give twice the number of frequencies corresponding to positive 

 deviations, their differences being twice that corresponding to negative 

 deviations. The values given for Winter, Summer and Spring- 

 Autumn are obtained by taking together the corresponding numbers 

 in the same Tables ; consequently they are not quite identical with 

 the numbers which would have been obtained if the frequencies for 

 these seasons had been calculated from the absolute heights, instead 

 of, as has been done here, from the deviations ; in the latter the 

 annual variation has been left out of consideration. The annual varia- 

 tion, however, being very small, this will not influence the results 

 to an appreciable degree. 



