370 On j. Itinospfii ric Electricity and the Aurora Borealis. 



force is =0. "While the vertical component of the earth's 

 induction-force diminishes in general as the latitude increases, 

 the electric tension of the upper strata of the atmosphere, on 

 the contrary j is augmented with the increase of latitude until 

 the tension becomes strong enough to occasion the downflow 

 of the electric fluid into the earth. The annular space of the 

 atmosphere where the electric fluid descends to the earth is 

 evidently closed around the magnetic pole ; it is characterized 

 by the circumstance that in it the vertical component of the 

 earth's induction-force has everywhere the same magnitude. 

 Formula (C) gives an idea of its situation. 



As we have seen above, the electric fluid flows from the 

 said space to the earth in the direction of the dipping needle 

 (of the inclination or dip of terrestrial magnetism). These 

 electric currents in the rarefied air produce the aurora borealis. 

 It is evident that this phenomenon ought chiefly to be seen in 

 the vicinity of the annular space in question. According to 

 the researches of Mr. Loomis, most of the auroras boreales 

 appear, in North America, between the latitudes of 50° and 

 62°, their frequency becoming less at still higher latitudes. 

 The central line of the space in question lies consequently at 

 56° latitude — that is, at 34° from the astronomic and at 17° 

 from the magnetic pole. This central line is denoted by the 

 point t in fig. 11. We have now to ascertain under what 

 degree of latitude the annular space must be situated at 180° 

 of longitude from there, or, in other terms, between what de- 

 grees of latitude auroras boreales will be most frequent in 

 Europe and Asia. 



If in formula (C) we make / = 90° - 34° = 5 6°, we shall have 



kM(r sin 34— p sin 17)p sin 17 

 (r 2 + p 2 -2rp cos 17)* 



&M(V sin 34 + p sin 17)p sin 17 _ 



(f + p 2 + 2rp cos 17)1 ; 



This expression designates the intensity of the vertical com- 

 ponent of the induction-force in North America at 56° latitude. 



If in formula (C) we make /=90°, we shall have the ex- 

 pression of the same component at the astronomic pole, viz. 



Mp 2 sin 2 17 &Mp 2 sin 2 17 



(r 2 + p 2 - 2rp cos 1 7)1 (r 2 + p 2 + 2rp cos 17)1' 



By r is meant the distance from the centre of the earth to 

 the electric molecule under consideration, situated in the atmo- 

 sphere ; p, being (as already observed) less than the earth's 

 semiradius, is consequently also less than \r. Regard being 



