( 321 ) 



In a paper ^) published some years ago, Schols has drawn the at- 

 tention to the fact that ditferences of this deserii)tion are almost always 

 found when sntïieiently extensive series of errors are put to the test 

 of the normal law ; in this paper he shows that these differences 

 cannot be explained by the omission of terms in Bessel's develop- 

 ment of the exponential law and suggests that their origin mast be 

 sought for in the superposition of observations of different degrees 

 of precision. 



In the observations alluded to by Schols, it will in general not be 

 possible to estimate these degrees of precision any more than the 

 relative subfrequencies with which the different groups are represented 

 in the result ; in the case of monthly means such as are being 

 discussed here, the factors of steadiness are approximately known 

 and the subfrequencies of the different groups are all identical. 



If we arrange the 12 groups according to increasing values of h, 

 it appears that we may take its change to be uniform ; consequently 

 it is possible to find an approximate solution of the problem in 

 finite form. 



We have then to consider A as a variable quantity z and to ask 

 what form the expression will assume for a sum of elementary surfaces: 



C I e- ^'^' dx (3) 



if z varies in a continuous manner from h to H. If the subfrequency 

 of these elementarj' groups be also regarded as a function of z 

 (which occurs e.g. in the case of wind-frequencies), (3) must be 

 equated to <p{z)dz, (f {z) being subject to the condition: 



H 



I. 



(f{z)dz — \ (4) 



h 



The constant C is determined by the expression 



^ z(p{z)dz 



y/üt 



(5) 



and if, as in our case, 



{Ii-h)\/:t 



1) Veisl. Wis. Xal. Af.l. K. Akad. Wet. I. 1893 (p. 104—202). 



22 



Proceedings Royal Acad. Amsterdam. Vol. VIII. 



