592 



H. MOHN. METEOROLOGY. 



[NORW. POL. EXP. 



sin (& 4' - I) sin (o 44' - j 



... s i n (847'-a) 



apparent h = ft,, + c. 

 positive from the zenith towards the sun. 



o 



tan -jf 



cos 



ffiy + |) sin(|-028') 



-- cos (J + 28') 



e a reckoned from the antisolar part of the sun's vertical. 

 The top or apex of the twilight rises or sets on the horizon, when 



r o =90 or fe = or when a = p' + p + k, and when a = /f 

 The last equation corresponds with the rising or setting of the sun, the first 

 with the rising or setting of the apex of the arch in the vertical of the sun. 

 The apparent zenith-distance of the apex is 90 when ==/?' -]-/? + & + or 

 = 16 38'. The hour-angle of this moment, t, is given by the formula 



sin 



J . /10638' + (o> <5)\ . 



jr = sec <p . sec d . sin I -- ^-^ - '-]. si 



sin 









and the corresponding azimuth a 



sin a = sin t . cos d . cosec 106 38'. 



When the sun is below the horizon, it is shining in the vertical of a 

 place above a certain altitude, which in the polar regions is of dimensions 

 rather terrestrial than cosmical. The radiation of heat from the surface of 

 the earth and from the sky may be partly dependent on the distance of the 

 sun's rays from the surface. The shortest distance (H) to the limit of the 



earth's shadow, Z, I have com- 

 puted in the following manner: 



The angle h = a (r -\-Q-\-E) 



the terrestrial horizontal refraction 

 being nearly equal to the astro- 

 nomical. We then have 



H=R . tan - sin h. 



