354 Prof. J. Sebelien on the Distribution of Actinic Sunlight 



found that the effect upon a horizontal element of the 

 surface of the earth in one minute may be expressed [in 

 chemical light-units by the zenith-distance of the sun <£ 

 according to the formula 



w x == 2-776 + 80-849 cos (j> - 45*996 cos 2 <£. 



For a larger interval of time, in which the hour angle 

 of the sun is assumed to grow from t 1 to t 2 (expressed in 

 minutes of arc), the total photochemical effect in light-units 

 will be 



Wi= \ M'l 



dt. 



This integration may be executed with the same substitu- 

 tions as above, and will then give the formula 



W 1 = ^A [ 2 . 776 + 80 . 849a _ 45 .99 6 ^2 + ^ fi 



+ (80879/3- 1 x 45-996^) sin u . . (2) 



Even this expression will be simplified for the equinoxes, 

 as Bunsen and lioscoe themselves pointed out. Putting 



8 = 0, cc — 0, j3=*cosp } t= -r , the formula (2) is transformed 



W^ 1998-8 + 37058 cos^- 16559 cos 2 /). 



By means of these formulae Bunsen and Roscoe have cal- 

 culated for a series of localities the total quantity of actinic 

 light expressed in light-units which in the course of the day of 

 equinox falls upon a horizontal element of surface in the form 

 of direct solar radiation as well as in the form of reflected 

 daylight. These numbers are reproduced in the following- 

 Table L, where I have calculated the numbers marked with 

 an asterisk, which are not given in the original table of 

 Bunsen and Roscoe. 



This shows the extent to which the diffused daylight tends 

 to equalize the numbers for the total quantity of light at 

 the different latitudes. While the daily quantity of light due 

 to direct radiation is forty times as great at the equator as 

 it is at the pole, the quantity of diffused daylight is hardly 

 twice as great at the equator as at the pole on the same day. 



Further, the numbers in Table I. show that while at the 

 equator the effect of the direct insolation on the said day has 

 double the value of the daily effect of the diffused daylight, 

 these numbers will become equal in the neighbourhood of 



