386 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



Here according to the definitions above given, we have 



Q = JQdo 



where the integral is to be taken over the whole surface of the sphere 

 whose radius is r, hence 



— C 2n , , f + 7r A_ 



Q = r» dX \ Q cos fidfi (2) 



Jo J-n/ 3 



Since the quantity of heat Q that comes by insolation to a unit sur- 

 face at any given point of the boundary surface of the atmosphere 

 in the course of a year is a function of the geographical latitude only, 

 this equation becomes 



Q = 2 tt r 2 f ' Q cos (3d (S (3) 



J-n/ 2 



Moreover, as Lambert has demonstrated, for this function of the 

 latitude Q = <p (ft), we have 



<p(p) = <p(-p) 



that is to say, points at the same latitude in the northern and 

 southern hemispheres receive from the sun by radiation equal sum- 

 totals of heat in the course of a year. 



Therefore we can write equation (3) in the form 



£}=4 7rr 2 C" <p(P) cos (3d (3 (4) 



The value of the function <p (/?) is known from the investiga- 

 tions of Meech 10 and Wiener" and is only uncertain to the extent 

 of the uncertainty of the solar constant that enters it as a coeffi- 

 cient. 



Moreover, as is well known, we also obtain the value O in the 

 simplest way from the consideration that the sum total of the radia- 

 tion coming to the whole earth within a given interval of time is 

 equal to that which falls in that time on the great circle of the globe 

 perpendicular to the line connecting the sun and the earth. 



10 Meech: On the relative intensity of the heat and light of the sun. Smith- 

 sonian Contributions, IX, Washington, 1S57. 



11 Wiener: Zeit. Oest. Gesell fur Met. 1879, XIV, p. 113. [See Angot 

 Recherches Theoriques. Paris, 1885. — C. A.] 



