Feb. 28. 1884] 



NA TURK 



411 



Now if the determination of the apparent height of the 

 upper edge for A and c is taken as a basis for calculation, 

 the height of the same cannot lie ascertained therefrom, 

 but from the crossing point of the lines ka and c b, and 

 so forth. A great many other variations may also be 

 met with according to the dimension and position of the 

 arc. Generally, however, when the arc lies on one side 

 of both places of observation, the edges observed in the 

 respective places are identical. 



In the following simple manner I have succeeded in re- 

 ferring the various places of observation to the vertical plane 

 of Bergen, where my own observatory is situated, in order 

 to find the arc s s' in Fig. i. The direction of the arc I 

 have, in accordance with observations, let form an angle 

 with the circles of latitude of 25". I have constructed a 

 globe with the circles on a large scale in Mercator's pro- 

 jection, on w-hich the various stations have been denoted. 

 Through the place " Bergen " a straight line is drawn 

 under an angle of 25° with the circles of latitude, while 

 the perpendicular distance of the various stations from 

 this line has been determined in the construction and by 

 direct measurements. The stations whose observations 

 are so complete that the angle of the arc above the 

 horizon has been determined have been combined with 

 Bergen. I have succeeded in forming nineteen such com- 

 binations. The heights of the arc calculated at these 



stations vary somewhat, but not very much, and if an 

 average is taken we find that the value of the height of 

 this arc above the earth's surface was most probably 

 I46'95 km. 



It further appears that the observations were not exact 

 enough to obtain an estimate of the thickness of the arc, 

 so that we can only accept the figure given above as an 

 average one, i.e. an average of the distance of the upper- 

 most and lowest layers from the surface of the earth. 



If we compare the height arrived at in this case with 

 those obtained through previous researches, we shall find 

 that it agrees to some extent with the value of the arcs 

 measured in recent times. They differ, however, greatly 

 from old ones. Thus Prof. Fearnley finds, through ob- 

 serving sixteen auForal arcs from one spot, in Christiania, 

 by an ingenious theoretical method, that the average 

 height in these cases was 27-15 geographical miles, or 

 201 "5 km. Newton found, by the same method, that the 

 average height was 130 English miles, or 209'3 km., 

 while Nordenskjold, by a similar method, has come to 

 the conclusion that it is 190 km. The French expedition 

 established at Bossekop during 1838-39 obtained no reli- 

 able statistics on this point, owing to the small distance 

 between the two points of observation, viz. 156 km. But 



from the results obtained it seems that the height must 

 be sought between 100 and 200 km. 



In opposition to this Bergman fixes the height at 753 

 km., Boscovich at 1328 km., and Mairan at 780 km. More 

 in correspondence with our result Dalton found the height 

 of the auroral arc to be 241 km., and Backhouse found 

 the three measured by him to lie between 81 and 160 km. 

 On the other hand, Franklin found at Cumberland House 

 (North America) that several aurora: which he measured 

 had a height only of i r3 km. In fact, the savants who 

 have studied the aurora borealis in the Arctic regions 

 appear to agree that it does not attain the height given 

 above as the results of researches further south. 



I have here only mentioned a few of the very divergent 

 values obtained in 'measuring' the aurora borealis, but I 



Fig. 3. 



do not believe it will be of any service to append more, as 

 the values range from o to 2000 km. 



In Fig. 3 I have attempted to illustrate the height of 

 the aurora referred to by me by comparing it with other 

 well-known heights. The scale is I mm. = I km. Below 

 is drawn a profile of Norway from Bergen in a direction 

 E. 25' N. The heights here range to upwards of 5000 

 feet. Above n n indicates the arc of the aurora in its 

 height of i46'95 km. The thickness given is wholly 

 approximate, and probably too small. For comparison 

 is inserted, a, the highest mountain in the world (Mount 

 Everest, S839 m.) ; b, the greatest height reached by man 

 (Glaisher and Coxwell in their balloon on September 5, 

 1S62, 31,800 feet); c, the estimated height of the cirrus 



