H 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 



Let O be taken as the point of observation. 



Then the radius of the elementary zone = r cos B, the circumfer- 

 ence of the elementary zone = 27rr cos B, the width of the elementary 

 zonG = r dB, and the area of the elementary zone = 27rr- cos B dB. Call 

 the horizontal intensity at the center O due to elementary zone = dl. 

 Then dl =:27rr' cos B smB dB. 

 /= J27rr' cos B s'mB dB. 

 = 7ir'^ sin^ 6. 

 (i) For the entire hemisphere (a^ and a^ in observations which 

 follow) /^/'=7rr2. 



(2) From horizon to 30° altitude: 1^^^ ^Ittt^. 



(3) From horizon to 60° altitude: I1^^ = %iTr^. 



Hence in a sky in which every point sends radiation of equal in- 

 tensity toward the point of observation the following intensities 

 from the various 30° zones would be obtained in a horizontal sur- 

 face at the point of observation. 



o 



Fig. 2 



For entire hemisphere (% and a^) Ia=i. 



For upper 60° zone (&) /^zri— 1 = |. 



For upper 30° zone (c) 1^=1—^ = ^. 



In the following observations the values gotten with an entire 

 hemisphere are called " a'' those with the upper 60° open to radia- 

 tion "" h^' and those with upper 30° open to radiation " c." 



Call the horizontal intensity from the horizontal zones themselves 

 X, y, and z, as shown in figure 2. 



Then a=x+y+z 



b=y+s 



c=z; 

 or x=a — b 



y = b-c 



In " equal sky " x=ia. 

 y=ia. 



