26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



the air is proportional to / under average conditions. Individual 

 observations deviate, however, greatly from the computed value, 

 which is to be expected in view of the variety of atmospheric con- 

 ditions. 



Briefly it may be said that the observations agree in showing that 

 on an average the integral water vapor above a certain place is pro- 

 portional to the absolute humidity at that place. The factor of pro- 

 portionality is, however, in general a function of the altitude. 



The application of these results to the present question means that 

 we can replace the water content of the whole atmosphere (P) by 

 the absolute humidity at the place of observation multiplied by 

 a constant, the latter being a quantity it is possible to observe. 



For the general case we thus obtain 



or for the simplest possible case 



E a = K-Ce~yf° 



More difficult is the problem of assigning a mean value for the 

 temperature of the radiating atmosphere. It is evident that this 

 temperature is lower than the temperature at the place of observa- 

 tion, and it is evident that it must be a function of the radiating 

 power of the atmosphere. The most logical way to solve the problem 

 would be to write T as a function of the altitude and apply Planck's 

 law to every single wave length. The radiation of the atmosphere 

 would thus be obtained as a function of the humidity and the tem- 

 perature ; but even after many approximations the expression would 

 be very complicated and difficult to test. The practical side of the 

 question is to find out through observations how the radiation 

 depends upon the temperature at the place of observation. Suppose 

 this temperature to be T . We may consider a number of layers 

 parallel with the surface of the earth, whose temperatures are 

 T 1} T 2 , T 3 , etc. Suppose, that these layers radiate as the same function 

 cT n a of the temperature. Let us write: T 1 = mT ; T 2 ~-nT ; 

 Tz = qT . Then the radiation of all the layers will be : 



J = cT a - [am a + pn a + yq a ] 



at another temperature t the radiation will be : 



i=ct a - [am 1 a + pn 1 a + yq 1 « ] 



