516 



might be obtained, but only by using- a more complicated augment- 

 ing factor. 



When the sun's height decreases or o increases, the influence of ^■ 

 is much stronger; values as k = 0.5 or ^• = 0.12 appeared to be 

 of no use in calculating the duration of sunshine in winter and, after 

 some trials, only the value k = 0.25 proved to give satisfactory results. 



As for the summermonths the factor 2 — cos fp appeared to be the 

 best, although the nriaximum value happens to be somewhat too small ; 

 on the other hand the position of the maximum is almost accurate, 

 corresponding with an apparent cloudiness of 2. 



For the wintermonths, therefore, an almost complete agreement 

 between calculation and observation might be obtained by increasing 

 the augmenting factor and assuming e.g. 2.5 — 1.5 ca? r/-, which would 

 agree with the experiment, the augmentation near the horizon being 

 certainly more than twice. 



The integration-constants 1 -|- -^^ ^^^^^ + ^ i" the formula for I^ 

 (table VIII) had to be added in order to ensure the condition : 



/j = for a; = 



In calculating the elliptical integrals in the expressions for ƒ3, 

 the "Funktionentafeln mit Formeln und Kurven von Jahnke und 

 Emde". Teubner 1909, have been made use of. 



4. The results of this inquiry can be summed up as follows; it 

 is possible to explain the relation between cloudiness and duration 

 of sunshine as found by experiment by means of theoretical reasoning 

 and simple assumptions. In this way a numerical measure of the 

 specific influence of the cloudiness upon radiation, received and 

 emitted, can be obtained according to the nature of the clouds in different 

 seasons. 



In the considerations made use of in treating this problem, it is 

 assumed that in calculating the estimated cloudiness Ws and also 

 the apparent cloudiness R, as derived from the duration of sunshine, 

 the same value W of the true cloudiness obtains. 



This supposition is certainly not quite justified; the former observ- 

 ation is made with incident rays, or more accurately diffuse reflection, 

 the latter with transmitted light and probably (at least for Cirri, 

 Pseudo-cirri and Fracto-Cumuli) the loose, flocky clouds and cloud- 

 borders transmit some light, whereas, with reflected light, they make 

 the impression of an entire covering of that cloudy part of the 

 sky; on the other hand the sunshine-recorders readily discontinue 

 registering when the sun's rays are absorbed. The fact also that the 

 sun's image as formed by the glass sphere or the slit of the sun- 



