476 Rev. S. Haughton. [Feb. 24, 



Integrating (2) for one day, we have — 



Diurnal radiation =27rB(0 o + «) (3)- 



Again, assuming 



*=<vh££! w. 



where 6 = niean annual temperature, 



I — sun's longitude, 

 Summing for the whole year, we find — 



Annual radiation=2^(G + a) tyt . . . . (5), 



but, by the theory of the earth's motion, we have — 



2tt (l + ecos0) 2 v y ' 



where T = earth's periodic time of revolution, 



e= eccentricity of earth's orbit, 

 #=true anomaly, 

 w = earth's perihelion longitude. 



Substituting in (5) and summing, we find, for the year, 



Annual radiation =2?rBT(l-e3)f x j (e (l + + a) ± ^ e j 



.... (7), 



or, neglecting quantities of the order of the square of the eccentricity, 



Annual radiation=27rBT x ((0 o + a) ±(jf ^ ^jej . (8). 



From this equation, we find — 



Secular range of temperature = 2 eVx^ + fi^ (9), 



= e X Annual range of temperature. 



From this we may calculate the secular range of temperature in the 

 northern and southern hemispheres, with the following results : — 



