Convection Currents in the Atmosphere. 115 



its original amount. Sea-water would presumably absorb it 

 still more rapidly. Some of the ultra-violet radiation is 

 more penetrating *, but it is smaller in amount than either 

 of the other two types and will here be omitted. As 

 annual temperature oscillations in the ocean are known to 

 penetrate to a depth of some hundreds of feet this step seems 

 justified. 



At considerable altitudes the actual atmosphere is known 

 to become very much rarefied and the absorbing constituents 

 very much diminished, so that the amount of radiation ab- 

 sorbed per unit thickness must decrease as altitude increases. 

 The part of/ due to direct radiation is therefore assumed to 

 be Ve~ KZ , where k. is a constant and P a function of the 

 time. 



The percentage of reflected radiation absorbed per unit 

 thickness will decrease upwards still more rapidly, as in this 

 case the effects of rarefaction and loss due to absorption act 

 in the same direction. We therefore take the part of/ due 

 to reflexion as Qe~ vZ , where Q differs for land and sea and 

 v is much greater than k. 



A similar argument holds for radiation from the heated 

 earth. This is taken to be \<£>e~ vz , where <E> is the tempera- 

 ture of the surface vertically below the point under con- 

 sideration and \ a constant depending upon the emissivity 

 of the surface. 



The nature of the equations that arise is such that their 

 solution is almost impossible unless we can make them linear 

 with constant coefficients. This cannot be done with either 

 an isothermal or an adiabatic atmosphere. It is necessary, 

 therefore, to replace the actual atmosphere by a homogeneous 

 incompressible fluid layer, of finite height, so that there is a 

 free surface at the top. The height of this in the disturbed 

 condition can, of course, be found from the variable part of 

 the pressure by means of the ordinary dynamical conditions 

 at a free surface. The height is, nevertheless, assumed to be 

 so great that the reflected waves from the free surface can 

 be neglected. 



In such an incompressible fluid there is no difference 

 between an isothermal expansion and an adiabatic one. 

 The two specific heats are, therefore, equal. Expansion 

 due to variation of temperature is included among the possi- 

 bilities, but not expansion due to variation of pressure. The 

 essential feature of the actual atmosphere is retained — namely, 

 the possibility of convection currents. 



* Murray, ' 'The Depths of the Ocean,' pp. 250-253. 

 12 



