( 310 ) 



method of (reatmeni suggested in il and to give some applications 

 of it in frequency-numbers concerning air-temperature, deduced from 

 observations made on board the lightship "Schouwenbank". 



2. The method suggested by Bruns deserves (lie more the con- 

 sideration of all who are occupied with the treatment of frequencies 

 as it is based on the classical works of Besses and Fechner and 

 can be regarded as a logical outcome of the principles indicated by 

 these investigators. 



As a basis is taken the well-known function * 



2 C 1 



* dt 



(i) 



for which in various works tables are given ; the first derivative of 

 this function : 



*, (*) = TV- *~* 



(2) 



assumes after substitution of hx for x and multiplication by h the 

 form of the specific probability of a deviation x according to the 

 law of errors of Gauss in its simplest form. The derivatives of 

 higher order can be written thus : 



<I>, (x) = — e-* . 1 / 



*. (*) = 

 «P, (x) = 



2» 



\/n 

 2 4 

 \/jt' 



2/ 



*' . 3 / 



yn 





- — 1 



o / 1 /J 



S 1_1 



/ 2 .' 1 / / 2'J 



X s x "1 



_ 0/3/ + 1 / 1 / 2'J 



(3) 



V0/2<J 



a; 5 as* x 



0/5/ 1 / 3 / 2' ~ 2 / 1 / 2 4 J 



etc. 



Now Bruns' suggestion is as follows : the specific probability (sum 

 of the numbers = 1) of a deviation from a groundvalue assumed 

 arbitrarily be represented by the series: 



y = A[A *,(**)"+ A ••(**) + A*.(**).+ •■••]• • • (*) 



