﻿892 Mr. E. A. Milne on Radiative Equilibrium: 



be due to a sudden diminution of absorbing power. This, 

 again, would indicate the tropopause as the boundary of the 

 water-vapour atmosphere. The contrary has, however, been 

 urged by Gold * on different grounds, and it is difficult to 

 deny the force of his arguments. The matter is obviously 

 one of considerable difficulty. 



14. Applications. — This concludes the discussion of the 

 idealized problem of which it is the main business of the 

 paper to give an account. The theory is capable of a 

 number cf applications to the earth's atmosphere, but the 

 principal of these, at least in the case when the incident 

 radiation may on the average be taken to be diffuse, have 

 already been made by Emden. Perhaps the result most 

 directly useful is the correction to the Schwarzschild boundary 

 temperature due to the absorption of the incident radiation 

 there, given by formulae (33) or (34), or Emden's form (32). 

 (The Schwarzschild temperature is given by putting ?? = 0.) 

 From a discussion of the observational material, Emden finds 

 that n may be taken to be ^. With cos a = f this gives an 

 increase of 1 per cent., making the calculated value of T 

 (see § 1) about 216°. If n is taken equal to j 1 -^, T becomes 

 219°, the observed value. 



Another application made by Emden is to show that an 

 atmosphere entirely in radiative equilibrium would be an 

 impossibility, even in the absence of the warming effect due 

 to the earth's surface (§ 10 above). For, taking into account 

 the water- vapour distribution^ radiative equilibrium implies 

 at a sufficient depth temperature gradients in excess of the 

 critical gradient for stability ; so that convection currents 

 would be set up. Emden finds that this would occur at 

 a height of about 3 km. 



When Emden wrote, the variation of the temperature of 

 the stratosphere and height of the tropopause with latitude 

 was not fully appreciated. And in the light of this variation, 

 the small improvement in agreement, due to the introduction 

 of n, between the Schwarzschild temperature and the ob- 

 served mean temperature for S.E. England becomes largely 

 meaningless. What is astonishing, a priori, is that the two 

 temperatures should agree as well as they do. The agree- 

 ment can only mean that the actual temperature of the 

 stratosphere over S.E. England must be very close to the 

 mean temperature over the earth. The agreement is partly 

 helped by the circumstance that the latitude of England is 



* Geophysical Memoirs, No, 5, p. 129 (1913). 



