NO. 17.] THE METEOROLOGICAL PERIODS IN THE ARCTIC SEA. 



589 



where ^ is the zenith-distance of tiie sun's centre. The depression of the 

 sun's centre is r -{- q, r being the sun's semi-diameter, and q the horizontal 

 refraction. I have assumed that r equals 16' and q equals 40', according to 

 the low temperature (in the dark season — 30° C) prevailing during the drift 

 of the Fram. Hence ?• + ?== 56 ' and, for logarithmical calculation, 



sm 



2 = sec 5P sec d sm (^ ^-^ -' ) sm (^ ^ — -J. 



For the corresponding azimuth of the sun's centre a, we have 



sin a = sin t . cos 6 . cosec ^ ^ sin < . cos d . cosec 90° 56'. 



When the sun is below the horizon, and the depression of its centre is 

 less than about 16°, we have more or less of the sky illuminated by the 

 sun. This is the Twilight. The highest point of the line of demarcation 

 between the twilight and the shadow of the earth lies in the vertical of the sun. 



Let Ca = Cb = Gc 

 be the radius of the 

 earth {R) and QCS 

 a ray from the sun's 

 centre through the 

 centre of the earth, 

 a another ray which 

 would be tangent to 

 the earth in a if there 

 were no refraction in 

 the atmosphere. The 

 ray from the sun's 

 upper limb would be 

 tangent in the point 

 b, the angle aCb being equal to the semi-diameter {r) of the sun. The 

 ray from the upper limb of the sun will be deflected by the horizontal 

 astronomical refraction (q) so as to touch the earth in a point c, the angle 

 b Cc being equal to q. From the point c the ray pursues its way through 

 the atmosphere and becomes deflected by the terrestrial refraction from the 

 direction of the tangent cd, so as to meet that highest layer of the atmos- 



