CHAPTER III. 



STATISTICAL TREATMENT OF MAGNETIC DISTURBANCES OBSERVED AT 



THE NORWEGIAN STATIONS 19021903. 



INTRODUCTORY. 



94. In the previous treatment of the perturbations given in the first part of this work, each 

 disturbance has been examined individually. This investigation led us to divide the perturbations into 

 groups, each of which possessed certain characteristic properties, especially with regard to the distribution 

 of the perturbation in space relative -to the earth. 



In the following we shall proceed to study the variation in the time of the appearance at our four 

 arctic stations of the magnetic storms occurring during the period of our observations. 



In order to solve this problem, it is necessary first to fix the unit by which we are to measure the 

 quantity of perturbation that has occurred during a certain interval of time. One way would be to 

 count the perturbations, e. g. those which exceeded a certain magnitude. Such a mode of procedure 

 is often employed to obtain a quantitative measure of phenomena of this kind; but the method is not 

 very exact, as perturbations count equally, even when their magnitude varies within wide limits. Further 

 we are met with the difficulty, or rather impossibility, of defining what is meant by one disturbance. 



We have therefore decided to follow a more exact method, which can always be applied without 

 ambiguity. In this method the quantity of perturbation is measured by what we shall call storminess, 

 which is defined as follows : 



We assume the perturbing force in any of the magnetic elements H, D or V in the time interval 

 o <] t <[ T to be found as a function of time. The determination of this function from experiments only 

 requires the possibility of finding the perturbing force at any moment, which can be done in the way 

 described in Part I of this work. 



By the absolute storminess in one of the components say the horizontal component we understand 

 the quantity : 



It is equal to the average perturbing force P, L if the latter is always taken to be positive. 

 It will also be of interest to consider separately disturbances in the positive and negative direction, 

 and for this reason we define the positive and negative storminess 



T 



T 



- f 

 ~T I 



o 

 T 



P"dt 

 o 



where / J ,f is any positive value of P,, in the interval, and P" any negative value. It follows: 



