4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82 



From the tabular data, it is clear that values of total precipitable 

 water are frequently observed at Montezuma closely approaching the 

 value assumed by Simpson for the stratosphere. These values are 

 found in winter, with a surface air temperature of +9° C, on the 

 edge of the tropics at 2,710 m. altitude. 



In view of these observations at Montezuma, and considering the 

 rapid decrease of humidity with temperature (the vapor pressure at 

 — 50° and 0° C. being respectively 0.03 and 4.58 mm.) and also the 

 fact that three-fourths of the superincumbent atmosphere lies between 

 Montezuma station and the bottom of the stratosphere, one is forced 

 to conclude that the value of the precipitable water contained by the 

 stratosphere is vanishingly small, rather than 0.3 mm. as assumed by 

 Simpson. This materially affects his argument, especially that part 

 which relates to cloudy skies. 



As an independent approach, instead of Simpson's two other basic 

 assumptions, which we have designated as (b) and (c), we have em- 

 ployed Fowle's two summaries of the results obtained in his long-tube 

 experiments.' To make these results of Fowle's applicable to the 

 problem of atmospheric radiation and absorption, as set by Simpson, 

 we have prepared a large scale plot, reproduced in reduced size in 

 figure I. From this plot we take table 2. In choosing the quantities 

 of precipitable water to be used, we have doubled the values given by 

 Simpson for successive layers in the table he designates as " Fig. I," 

 page ^2, of his paper " Some Studies in Terrestrial Radiation." This 

 doubling we do because of the following consideration. 



We are proposing to ascertain the radiation which certain layers of 

 the free atmosphere, containing natural loads of water vapor and car- 

 bon dioxide, will send upwards in all directions within a solid angle 

 filling a complete hemisphere. We assume, as does Simpson, that for 

 monochromatic rays the emission of such a layer bears the same pro- 

 portion to the emission of the perfect radiator that the absorption of 

 the layer in question bears to unity. While some rays are emitted ver- 

 tically, most rays are emitted obliquely, so that the average emission 

 and absorption of a layer exceeds that which corresponds to the pre- 

 cipitable water vapor and carbon dioxide found in a vertical path. It 

 is readily proved by performing the integration over a complete 

 hemisphere that the average upward path is double the vertical one. 

 Hence we have doubled Simpson's figures for the precipitable water 

 contained in the layers he has chosen. These data appear in table 2. 



* See Annals, Vol. 4, Table 102, p. 286; also Smithsonian Physical Tables, 

 7th Rev. Ed., 4th reprint, p. 308. 



