104 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, igO2 1903. 



It will be seen from the above that there is also a quantitative correspondence between the actual 

 field and that which is produced by the calculated systems. 



The first answers to a system in which the horizontal portion of the current lies at a height of 

 200 kilometres, its length being a little less than double the distance between Kaafjord and Axeleen, 

 or than the distance from these two stations to Dyrafjord; it is thus a comparatively low, compressed 

 system. It appears that the force here diminishes a little more quickly than it is found to do during 

 our most typical elementary storms. 



In the second system, on the other hand - - in which the horizontal portion of the current is at a 

 height of 300 kilometres, its length being 2500 kilometres - the distribution of force shows a great 

 resemblance to that found during the polar elementary storms. The length of the horizontal portion is 

 here a little less than the distance between Dyrafjord and Matotchkin Schar, which is roughly 3000 

 kilometres. 



For the value if) = 10, we have passed, as the table shows, the point of convergence or diver- 

 gence, and the perturbing force is about y 1 - of what we find at the storm-centre. At greater distances 

 from this, the force varies in a manner corresponding fairly well with that found during the polar elemen- 

 tary storms. 



In the third system the horizontal portion of the current is 5000 kilometres in length, and at the 

 same height above the storm-centre as in the preceding case. The points of convergence and diver- 

 gence are now situated at a rather greater distance from the storm-centre; and for greater values of ip, 

 the forces are now of a comparatively greater strength than before. 



On the whole, the fields produced by the last two current-systems correspond fairly exactly with 

 those found during the polar elementary storms. 



In order, in the next place, to investigate the effect of the horizontal part, if that part became very 

 long, we have calculated the effect for / = oo . We then see distinctly how the directions change at 

 the above-mentioned points of tangency. 



On a closer examination, it will be easily seen that Pm/> at the storm-centre, and its immediate sur- 

 roundings, will always be greater than Piy -\- Puiy- In order to inquire into the manner in which the 

 latter change in relation to one another, we have, in the next place, calculated the effect at the storm- 

 centre of some systems of various forms, where the horizontal portion of the current is made compara- 

 tively short. 



We see, that for the small values of /, i.e. 2 / = 400 and 200 km., with the horizontal part lying 

 at a height of 200 km. above the storm-centre, the proportion between P^, -\- Puiy and Pn,/, is about 

 i : 2. For the third system, 2 /= 1000 and h = 300 km., the proportion is somewhat less. 



Finally, we have calculated some forces along the principal axis, in order to obtain a general idea 

 of the way in which the forces change here. The formulae that will be employed are developed in a 

 manner exactly similar to the previous ones; all that has to be done is to insert in the general formula 

 some other values for distance and limits. 



There is no need for a more careful investigation here, and we have therefore contented ourselves 

 with calculating a few values for the system 2 / = 1600, // = 200. We have chosen this especially, in 

 order that the changes might be more noticeable. 



For this system we have found = 6 56'. 8. 



In the storm-centre, and at the distances 2 30' and 5 from it, we have found the respective values 



-803.35, - 75 6 - J 3 an d -603.06. 



Here too, then, the change is not so great when we keep between the two vertical currents. If 

 we withdraw farther to the other side of one vertical current, however, the force will diminish more 

 rapidly. 



