1881.] Notes on Physical Geology. 475 



The heat received from the sun by the layer of atmosphere next the 

 ground is dissipated in the following w r ays : — 



1. By convection, or ascent of the warmer surface air into the higher 

 layers of the atmosphere, until it is cooled down to a temperature* a, 

 such that its direct radiation into space is equal to the heat received 

 from the sun and lower layers of the atmosphere at that height in the 

 atmosphere. 



2. By conduction, or transfer of heat from layer to layer, as in 

 solids. 



3. By direct radiation from the surface layer across the atmosphere 

 into star-space. 



The third of these sources of loss of heat may be neglected, because 

 the atmosphere, which absorbs about one-fourth of the luminous sun- 

 heat passing through it vertically, will absorb nearly all non-luminous 

 heat and allow only an infinitesimal fraction to escape into star-space. 



The first source of loss of heat (convection) is much more influential 

 than the second (conduction), but for my present purpose it is not 

 necessary to make any distinction between them, for the loss of heat 

 from both causes will follow the same law and is proportional to the 

 difference of temperature between the surface layer of the atmosphere 

 and the upper, or equilibrium control layer ; that is, the loss of heat is 

 proportional to (6 + a). 



The radiation is therefore represented by 



Eadiation = B(0 + a)dt. 



This expression cannot be summed without assuming some relation 

 between and t, which I do as follows : — It is well known that the 

 diurnal temperature does not reach its maximum and minimum at 

 midday and midnight, but some hours after the sun's passage of the 

 upper and lower meridian ; and it is also well known that the hottest 

 and coldest days of the year do not occur at midsummer and mid- 

 winter, but some days after. 



This law of diurnal and annual change of temperature presents so 

 close an analogy to the law of the diurnal and annual tides, as to 

 justify us in assuming for its mathematical expression formulas similar 

 to those of the well-known equations of the diurnal and annual tides. 



I therefore assume — 



+ ^' 

 where # =mean diurnal temperature, 



/i— sun's hour angle. 



* As a is probably below zero for all latitudes, I shall reckon it positive below 

 zero, and 6 positive above zero. 



