5 1 3 



o., 



W 



cos (f ,1 



As cos ^6 =r 0.99, this will hold good for pretty large clouds 

 which, when seen in the 7>enith, are measured by an angular value 

 of 12°. 



At a zenith's distance 



ff = arc cos ( W) 



the apparent cloudiness becomes equal to unity, i.e. the cloudbank 

 begins there, which is always more or less manifest when the clouds 

 are regularly spread over the sky. 



In the foregoing considerations the true cloudiness (TF) is regarded 

 as a proportion of linear quantities, whereas in reality the proportion 

 between white and blue in the plane going through J7„ Af^ M^ and 

 at right angle to the plane of the drawing of fig. (1) ought to be 

 considered, and the question arises in how far it is permissible to 

 substitute a fictitious linear repartition along a line for a real cloud- 

 iness as measured in a plane. 



^^ ^-^ ^-^ In fig. (2) the clouds, assumed to 

 v_y V_y \^ be spherical, are projected upon the 

 plane going through their centra and 

 an observer, looking at this plane from 

 a point below the origin of coordi- 

 r~^ nates, will notice totally different pro- 

 portions between white and blue in 

 /■^ /^ different directions. 

 ^-^ ^-^ If, as in fig. (2), the mutual distance 

 ^-. ^-^ ^-^ A is equal to twice the diameter d, 

 v_/ \^ \y he will notice six different degrees of 

 Fig. 2. cloudiness within an angular distance 



of 45°, as denoted by full lines, and the alignments a and e will 

 be repeated 4 times, the other 6 times over the whole sky. 



The average cloudiness derived from this regular arrangement 

 is then 



1 



20 



1 + 



i/2 2l/5 2V/lO 2l/l3 2i/l7" 



+ 



+ 



+ 



= 0.214. 



2 ' 5 ' 10 ' 13 ' 17 

 From the proportion between the surface of the circles and the 

 total surface of the corresponding plane we find for the true cloud- 

 iness, according to the formula : 



4A^ 16 

 showing a difference of 1.8 "/o- 



