GEODETICAL TABLES. Ixxix 



constant Aq, for each tenth parallel of latitude of the northern hemisphere, 

 and for the first and sixteenth day of each month; also the values of the 

 solar constant A in terms of A^, and the longitude of the sun for the given 

 dates. 



Table 99. Relative amounts of solar radiation received on a horizontal surface 

 during the year at different latitudes. 



The second column of this table is obtained from the last line of 

 Table 98 by multiplying by 1440, the number of minutes in 24 hours. It 

 therefore gives the average daily amount of radiation that would be re- 

 ceived from the sun on a horizontal surface at the surface of the earth if 

 none were absorbed or scattered by the atmosphere, expressed in terms of 

 the mean solar constant. The following columns give similar data, except 

 that the atmospheric transmission coefficient is assumed to be 0.9, 0.8, 0.7 

 and 0.6, respectively, and have been computed by utilizing Angot's work 

 {Recherches theorctiques sur la distribution de la chaleur a la surface du globe, 

 par M. Alfred Angot, Annales du Bureau Central Meteorologique de France, 

 Annee 1883. v. i. B 121-B 169), which leads to practically the same values 

 as Ferrel's when expressed in the same units. 



The vertical argument of the table is for lo*^ intervals of latitude from 

 the equator to the north pole, inclusive. 



Table 100. Air mass, m, corresponding to different 'zenith distances of the sun. 



For homogenous rays, the intensity of solar energy after passing through 

 an air mass, m, is expressed by the equation I = Iq a*", where I^ is the in- 

 tensity before absorption, a is the atmospheric transmission coefficient, or 

 the proportion of the energy transmitted by unit air mass, and m is the air 

 mass passed through. If we take for unit air mass the atmospheric mass 

 passed through by the rays when the sun is in the zenith, then for zenith 

 distances of the sun less than 80° the air mass is nearly proportional to the 

 secant of the sun's zenith distance. In general, the secant gives air masses 

 that are too high by an increasing amount as the zenith distance of the sun 

 increases. 



The equation by which air masses are sometimes computed is 



atmospheric refraction 



m 



K sin Z 



where Z is the sun's zenith distance and i^ is a constant. The uncertain 

 factor in this equation is the atmospheric refraction. Table 100 gives values 

 of m computed by Bemporad {Rend. Ace. Lincei., Roma, Ser. 5, V. 16, 2 

 Sem. 1907, pp. 66-71) from the above formula, using ior K the value 58'.'36. 

 The argument is for each degree of Z from 20° to 89°, with values of m 

 added for Z = 0°, 10°, and 15°. The values of m are given to two decimal 

 places. 



