8 CARL STORMER. M.-N. KI. 
Thus the first three derivatives of the function U along the normal M N 
may be formed, and /’” (U) may then be found by substitution in the 
above formula. 
We see that the error & diminishes very rapidly with increasing m. 
2. The above method was worked out for the purpose of simpli- 
fying the study of the integral curves of the system 
dR Er 20 
ds? 2 eR 
d*z  ,40 
Je ae ie (III) 
where Q is the function 
ah ZB San à 
Q = I E == (R2 3 3 | 
and y is constant. 
One is led to this system, when it is a question of calculating the 
trajectories of electric corpuscles in space under the influence of terrestrial 
magnetism I. 
One of my assistants, Mr. E. Steenstrup, engineer, has constructed 
under my guidance, after the above method, more than 50 paths of system 
(III), answering to various values of the constant y. The practical utility 
of the method has thereby been sufficiently tested. The results of these 
constructions will be fully described in Professor Birkeland’s report of 
the Norwegian auroral expedition of 1902—3, in the section that treats of 
the mathematical theory of auroras and magnetic perturbations. 
3. We will here briefly relate our experience with regard to the 
employment of our graphic method of finding the paths defined by 
system (I). 
First a number of equipotential curves, 
neon ge Eee FS 
n N N 
1 See my paper: „Sur les trajectoires des corpuscules électrisés dans l'espace sous l’action 
du magnétisme terrestre, avec application aux aurores boréales“. Archives des Sciences 
Physiques et Naturelles; July —October, 1907. Geneva. 
