1907.J AND MOUNTAIN FORMATION. 401 



revolves. That the incandescent nucleus could effect the magnetism 

 of the earth seems highly improbable. 



2. The annual and diurnal variations of the magnetic needle are 

 most easily explained by the seasonal and diurnal effects of the sun, 

 exerted indirectly through the paramagnetic medium of the atmos- 

 phere, the electric forces of which are modified by the sun's varying 

 radiation of charged particles. 



Fig. 4. Showing the lines of force about a spherical magnet, or a mag- 

 netized spherical shell, such as the crust of the Earth. 



3. The aurora is one of these effects and has been treated by 

 Arrhenius v^^ith characteristic penetration. 



§ 20. Gauss' Analysis of the Earth's Magnetism and the Con- 

 clusions Which May he Drawn From it. — If we denote by J/x the 

 quantity of magnetism present in an element of space, and by p its 

 distance from any point in space, whose rectangular coordinates 

 referred to any system may be x, y, z ; then we have for the potential 

 function of the earth's magnetism 



V: 



/?■ 



where the integration is to be extended over the entire volume of 

 the earth. The forces resolved parallel to the coordinate axes are 



