NO. n.] THE METEOROLOGICAL PERIODS IN THE ARCTIC SEA. 591 



.. cosQg' + fc a) cos ft 



sinO*' + & a) 



2. 



sin (/?' + & a) 



The apparent zenith-distance is c. I have taken c from the table 

 given below. 



In order to find the azimuth, reckoned from the antisolar vertical of the 

 sun, e 0i of the point where the arch cuts the horizon of 0, we say = 90 -}- s, 

 and get cos (Z e) = cos /3 cos c = cos (?, or Z= /J'+e. Hence 



_ sin (j? + fc) cos (p -\- e) sin a 



COS 60 - : 7^ ; 7 



sin (p + e) cos a 



. COS 



or tan -~- = 



2 . ( . k . e 



sin f p + -g- + -g 



For computation I assume that R = 6398'147 km., log R = 3'80605 

 (99 = 83), ft = 53 km., r = 16', Q = 40' (Mean temperature of the dark season 

 == _ 30) and e = 3W. The value for e I have taken from a table given by 

 Prof. Feamley in "Forhandlinger i Videnskabsselskabet i Christiania, Aar 

 1859", p. 137. This table, of which the argument is the apparent zenith- 

 distance, I have transformed into the following table with the argument true 

 zenith-distance . 



= 45 60 70 75 80 85 86 87 88 89 90 9027''4 

 e (X-0 0'-8 l'-5 2 /> 2 3''0 4'-5 8''3 9 /> 4 ll'-3 14' 17''9 23'-0 37'-4 



The table is applicable to ordinary temperatures. For the low temper- 

 atures prevailing at the Fram's station, I have taken the horizontal refraction 

 e to be 30*. 



We get thus 



, / S / =721'-5, = 721'; k = 16' + 40' + 30 7 = 86'; 



= 43';-; = 15', 



