GEODETICAL TABLES. lxV 



TABLE 8?. 



Table 87. Duration of sunshine at different latitudes for different values of 

 the suns declination. 



Let Z be the zenith, and NH the hori- 

 zon of a place in the northern hemi- 

 sphere. 

 P the pole; 



QEQ' the celestial equator; 

 RR! the parallel described by the sun on 



any given day; 

 5 the position of the sun when its upper 



limb appears on the horizon; 

 PN the latitude of the place, <f>. 

 ST the sun's declination, 5. 

 PS the sun's polar distance, 90 — 8. 

 ZS the sun's zenith distance, z. 

 ZPS the hour angle of the sun from meridian, /. 



r the mean horizontal refraction = 34' approximately. 

 5 the mean solar semi-diameter = 16' " 



2 = 90 + r + s = 90 50' 

 In the spherical traingle ZPS, the hour angle ZPS may be computed 

 from the values of the three known sides by the formula 



sin \ ZPS 



(ZS+ PZ - PS) sin \ {ZS + PS- PZ) 



or 



sin 





sin PZ sin PS 



(2 + 8 - 4) sin \{z - 8 +<t> ) 



cos 4> cos 8 



The hour angle t, converted into mean solar time and multiplied by 2 

 is the duration of sunshine. 



Table 87 has been computed for this volume by Prof. Wra. Libbey, Jr. 

 It is a table of double entry with arguments 8 and <f>. For north latitudes 

 northerly declination is considered positive and southerly declination as 

 negative. The table may be used for south latitudes by considering south- 

 erly declination as positive and northerly declination as negative. 



The top argument is the latitude, given for every 5 from o° to 40 , for 

 every 2° from 40 to 6o°, and for every degree from 6o° to 8o°. 



The side argument is the sun's declination for every 20' from 5 23 27' 

 to N 23 27'. 



The duration of sunshine is given in hours and minutes. 



To find the duration of sunshine for a given day at a place whose lati- 

 tude is known, find the declination of the sun at mean noon for that day 

 in the Nautical Almanac, and enter the table with the latitude and declina- 

 tion as arguments. 



