and the Aurora Borealis. 369 



and 



&M(reos l + p sin a 



r 2 + p 2 + 2rpsm{l + a)' 



Both these forces act in the plane in question — the one 

 along mp } and the other along mq (fig. 11). The cosines of 

 the angles formed by them with the terrestrial radius will be 



p cos (7 + a) 



\/ r' 2 + p 2 — 2 rp sin (7 + a) 

 and 



pcos (/+a) 



>/ r 2 + p 2 + 2 ?y> sin (/ + *)' 

 Therefore the sum of the vertical forces will be 

 &M(r cos l—p sin a)/? cos (/ + a) 

 [r 2 + p 2 -2rp sin (/ + «)]* 



feM(y cos / + p sin «)p cos (/ + a) ( ^. 



[f + p 2 + 2rp sin (/+«)]* l ' 



On the other hand, the sum of the tangential forces will be 

 &M(?'COS /— p sina)[r— p sin (/+a)] 

 [?' 2 -t-p 2 — 2rpsin (£ + «)}* 



_ /jM(?' cos l + p sin a) [y + p sin (/+«)] ,-p^ 



[r 2 + p 2 +2rpsin(Z + «)]f ( ' 



If £=90° — a (or the latitude of the magnetic pole) be intro- 

 duced into formula (C), the sum of the vertical forces will be 

 = 0. Therefore the electric molecules in the atmosphere ver- 

 tically over the magnetic poles are not raised in the vertical 

 direction by the terrestrial magnet. 



In the vicinity of the magnetic pole the vertical and tan- 

 gential components of the induction-force are very small : and 

 consequently there the electricity of the air must be inconsider- 

 able, just as it was around the astronomic pole ichen we supposed 

 the coincidence of the two axes. If into formula (D) the same 

 value of / be introduced, this formula takes a positive value : 

 or, in other terms, the tangential component tends to bring 

 the electric molecules thither from the axis of rotation of the 

 earth. On the contrary, the same formula, when /= 90° is 

 introduced into it, acquires a negative value — which signifies 

 that the tangential force-component drives toward the mag- 

 netic pole the electric molecules which are in the atmosphere 

 over the astronomic pole. It is therefore between these two 

 points that the point must be situated at which the tangential 



Phil. Mag. S. 5. Vol. 6. No. 38. Nov. 1878. 2 B 



