474 



Rev. S. Haughton. 



[Feb. 24, 



time in the same places ; bnt, so far as I know, no one has written 

 down these inequalities in a mathematical form, or calculated nume- 

 rically the effects upon climate they are capable of producing. I shall 

 attempt to do so in the present note. 



The temperature of any place at any time depends upon sun-heat 

 and terrestrial radiation, and involves the solution of the following 

 differential equation : — 



iOA^)_ B 



at r M 



where 0= temperature of place in Fahrenheit degrees, 



A=a solar constant, 

 0(z)=a known function of the sun's zenith distance, 

 r= distance of earth from sun, 



B=a local atmospheric constant depending on latitude and local 

 conditions, 



a = another local atmospheric constant depending on latitude 

 and local conditions. 



When the absorption of sun-heat by the atmosphere is neglected 



0(z)=COS2', 



and the first term of the equation can be integrated for one day in 

 terms of t, and afterwards summed for all latitudes, for one year ; but 

 when we take account of the absorption of sun-heat by the atmosphere, 

 0(z) becomes an exponential function of cos z, that cannot be inte- 

 grated, even by series. 



It has been shown, however, that, whether we take account of the 

 atmospheric absorption or not, the quantity of sun-heat represented by 



^ A0(z) £ a k- en £ or fchg whole summer is the same, at similar latitudes, 



r 2 • 

 in the northern and southern hemispheres ; and, in like manner, the 

 winter sun-heats are the same in the two hemispheres, whatever may 

 be the perihelion longitude and eccentricity of the earth's orbit. 



This being so, the secular inequalities of climate under discussion, 

 must arise from the second term of equation (1), depending on terres- 

 trial radiation, and ultimately on the fact that the summers and 

 winters in the two hemispheres differ in length, that difference depend- 

 ing on the perihelion longitude and eccentricity, as is well known. 



Before discussing the second (or radiation) term of equation (1), I 

 shall explain my reasons for assuming it to have the form 



and show what that form implies. 



