GEODETIC AL TABLES. Ixvii 



The computations may be made from the equation 



sin a — sin sin 8 



cos t = 1 



cos 4> cos 5 



where / is the sun's hour angle from the meridian, a is the sun's altitude, 

 considered minus below the horizon, 5 is the solar declination, and <t> is the 

 latitude of the place of observation. 



The solar declinations employed are those given in the American 

 Ephemeris and Nautical Almanac, 1899, pp. 377-384, Solar Ephemeris for 

 Washington. 



The atmospheric refraction with the sun on the horizon has been as- 

 sumed to be 34', and 16' has been allowed for the sun's semi-diameter, so 

 that at the instant of sunrise or sunset, as defined above, the true position 

 of the sun's center is about 50' below the horizon. The difference between 

 this value of / and its value with the sun 6° and 18 below the horizon gives, 

 respectively, the duration of civil and astronomical twilight. 



The computations have been simplified by the use of Ball's Altitude 

 Tables, 1 from which the value of / has been determined for true altitudes 

 of the sun of — 50', — 6°, and — 18 . 



Table 89. Duration of astronomical twilight. table 89. 



The duration of astronomical twilight is given to the nearest minute 

 for the 1st, nth, and 21st day of each month for north latitudes, o°, io°, 

 20 , 25 , and at 2 intervals from 30 to 50 , inclusive. The absence of data 

 for latitude 50 from June I to July II, inclusive, indicates that between 

 these dates at this latitude astronomical twilight continues throughout the 

 night. 



Table 90. Duration of civil tioilight. table 90. 



The duration of civil twilight is given to the nearest minute for the 

 1st, nth and 21st day of each month for north latitudes O , 10 , 20 , 25 , 

 and at 2° intervals from 30 to 50 , inclusive. 



RELATIVE INTENSITY OF SOLAR RADIATION AT DIFFERENT 



LATITUDES. • TABLE 91 , 



Table 91. Mean intensity for 24 hours of solar radiation on a horizontal 

 surface at the top of the atmosphere. 



This table is that of Prof. Wm. Ferrel, published in the Annual Report 

 of the Chief Signal Officer, 1885, Part 2, p. 427, and computed from formula? 

 and constants given in Chapter II of the above publication, pages 75 to 82. 

 It gives the mean intensity, J, for 24 hours of solar radiation received by a 

 horizontal surface at the top of the atmosphere, in terms of the mean solar 



1 Ball, Frederick. Altitude Tables for let. 31° to6o°. London, 1907; [same] for lat. o° to 

 30 , London, 1910. 



