INTERCHANGE OF HEAT — VON BEZOLD 387 



Hence we have 



Q = 7rr 2 TS (5) 



where S indicates the solar constant as determined for the mean 

 distance between the earth and the sun. 



For Q, we may also establish similar but not nearly so simple 

 formulas. We have the formula 



_ r* 2 n n + n/ 2 __ 



Q = r> dX \ Q cos pdfi (6) 



but the quantity Q is not like Q a function of the geographic latitude 

 only, but also of the longitude, in so far as we take into consideration 

 the individual peculiarity as to outward radiation of each element 

 of the boundary surfaces (referring especially to the lower portion 

 of the atmosphere and the adjacent earth's surface). 



The total insolation that an element at the outer boundary of 

 the atmosphere receives in the course of a year depends only on the 

 geographical latitude; the quantity that is returned to space by 

 radiation through this element varies from point to point of the 

 earth. 



Hence Q = <p (/? , X) and the function (f> is never a simple one and is 

 scarcely expressible empirically. 



The formula 



Q=r 2 f * *d> GM) cos 3d 8 . . . .(7) 



r* 2 n r* + n/ 2 



= r 2 il> (P,X) cos fidp 



Jo J-n/ a 



is therefore not susceptible of further simplification or modification ; 

 but on the basis of the above-given considerations and by the help of 

 equations (4) and (5) the final result, viz: 



Q = C = 7rr 2 r5 



may be given directly. 



Hence the quantities expressing the gain and loss or insolation 

 and radiation show a very great difference in that one is expressible 

 by rigorous mathematical formula but the other is not, unless we 

 can express the latter in terms of the former by theorems relative 

 to the equality of the quantities of gain and loss. 



The difference between these two classes of quantities would be 

 still more striking if the so-called solar constant really were properly 

 so-called, i.e., if the intensity of solar radiation actually remained 

 invariable. 



