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Geophysics. — "On the analysis of frequency curves accordiny to 

 a yeneral method" By Dr. J. P. van der Stok. 



§ 1. Ill working oat meteorological data statistically (climatology), 

 frequencies of all descriptions are found. No doubt the majority are 

 between indefinite limits as most other frequencies of different origin, 

 but it also iiappens that the limits are sharply defined as in the case 

 of observations upon the degree of cloudiness, where they lie between 

 and 10. 



An intermediate form is found in the frequencies of rain showers 

 arranged according to duration or quantity ; on the one hand they 

 are rigidly limited by the zero value, on the other hand the heavy 

 showers are without definite limits, so that the curve gradually 

 approaches the axis of abscissae. 



The elaboration of wind-observations requires the treatment of 

 frequencies in two dimensions, and produces curves, which differ in 

 character from other frequency curves according to the nature of 

 their origin. 



The development in series according to the formula of Bruns^) 

 and Charlier, appears to be the method indicated for frequencies 

 with indefinite limits; but the deduction of this formula is based 

 upon a generalisation in the use of definite integrals as already 

 pointed out by Bessel and therefore not quite free from premises, 

 which may be applicable to the theory of probability but have no 

 connection with the problem in question which may be defined as 

 the analysis of an arbitrary function between given limits. Besides, 

 this method of deduction can hardly be applied in the case of definite 

 limitation. 



The formulae of Pearson, as also those of Charlier, are entirely 

 based upon the premises of the theory of probability and, as they 

 are not given in series form, they only contain a definite number 

 of constants which, in some cases, is too limited to allow a complete 

 characterisation of the curve, particularly in the working out of 

 frequencies of the cloudiness, as will be shown in an example in 

 another communication. 



Besides, the constants, which partly appear in exponential form, 



1) H. Bruns. Wahrscheinlichkeitsrechnung und KoUektivmasslehre, Berlin, 1906. 



Idem. Beitriige zur Qaotenrechnung. Kon. Sachs. Gesellsch. d. Wiss. Bnd. 58. 

 Leipzig, 1906. 



G. V. L. Charlier. Researches into the theory of probability. Meddel. Lunds 

 astr. observ. Ser. II. n"^. 4. 1906. 



Idem. Ueber das Fehlergesetz. Ark. for Matem. Astron. och. Fys. Bnd. 2. n". 8, 1905. 



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