515 



If Z denotes the duration of sunshine as registered at the same 

 time, then the expression holds good : 



\—Z—R= W V\ f k^ tanf q (5) 



where q is the sun's zenith's distance. 



Ws and R being known by obser\'ation, it is, theoretically, possible 

 to calculate the two unknown quantities W and k from (4) and (5) 

 with the help of (2) and (3). 



Practically the only possibility to come to a result is to give k 

 different vakies and to calculate W and R for a series of vahies 

 of the auxiliary quantity /?. 



In the following calculations the zenith's distance of the sun at 

 2 p.m. has been assumed to be in summer (June — July) 37°42'^ in 

 winter (December — January) 78°37'. 



Table VI shows the results of the calculation for the summer- 

 months and spherical clouds {k = 1) ; it appears then that, starting 

 from the assumed supposition an explanation can be given of the 

 -results of observation concerning the magnitude of the sum or 

 cloudiness and duration of sunshine. The lirst augmenting factor, 

 1 -j- sin ff, leads to values which are somewhat too large ; the 

 second, 2—-cos^ff, to an exact maximum; the last, 2- — cos ff, to a 

 value somewhat smaller than 130. 



The position of the maximum is less satisfactory ; it corresponds 

 in table IV to an apparent cloudiness of 4, whereas in Table VI 

 the greatest values correspond to an apparent cloudiness of 6.5 and 

 5.5. The augmenting factor 2 — cos ff gives the best results because 

 then the calculated duration of sunshine for the hea\y cloudiness 

 7 — 8 is smaller than in the foregoing tables and shows a better 

 agreement with the numbers of table IV. 



For this reason the latter augmenting factor is chosen in calculat- 

 ing the cloudiness and duration of sunshine for three values of k 

 viz. 1.305, 1.5 and 2, all greater than unit}^ and therefore cor- 

 responding with clouds pointed upwards. For values smaller than unity 

 the shifting of the maximum would certainly occur in the wrong 

 direction i. e. to the side of the heavy cloudiness. 



In fact these increased values of k lead to an improvement of the 

 results, the maximum now corresponding with an apparent cloud- 

 iness of 5. 



As might have been expected, the influence of a variation of k 

 upon the position of the maximum is not great when the value of 

 Q is small, because in that case R varies little with ui. 



A more complete agreement between calculation and observation 



