in the Air upon the Temperature of the Ground. 263 



IV. Calculation of the Variation of Temperature that would 

 ensue in consequence of a given Variation of the Carbonic 

 Acid in the Air. 



We now possess all the necessary data for an estimation of 

 the effect on the earth's temperature which would be the 

 result of a given variation of the aerial carbonic acid. We 

 only need to determine the absorption-coefficient for a certain 

 place with the help of Table III. if we know the quantity of 

 carbonic acid (K=l now) and water-vapour (W) of this 

 place. By the aid of Table IV. we at first determine the factor 

 p that gives the mean path of the radiation from the earth 

 through the air and multiply the given K- and W-values by 

 this factor. Then we determine the value of ft which corre- 

 sponds to pK. and pW . Suppose now that the carbonic acid 

 had another concentration K : (<?.#. K x =1'5). Then we at first 

 suppose W unaltered and seek the new value of p, say p l9 that 

 is valid on this supposition. Next we have to seek ft, which 

 corresponds to p±K 1 (l'5p{) and piW. From formula (3) we 

 can then easily calculate the alteration (t) (here increase) in 

 the temperature at the given place which will accompany the 

 variation of ft from ft to ft 1 . In consequence of the variation 

 (t) in the temperature, W must also undergo a variation. As 

 the relative humidity does not vary much, unless the distri- 

 bution of land and water changes (see table 8 of my original 

 memoir), I have supposed that this quantity remains constant, 

 and thereby determined the new value Wj of W. A fresh 

 approximation gives inmost cases values of W-, and ft 1 which 

 may be regarded as definitive. In this way, therefore, we 

 get the variation of temperature as soon as we know the 

 actual temperature and humidity at the given place. 



In order to obtain values for the temperature for the whole 

 earth, I have calculated from Dr. Buchan's charts of the mean 

 temperature at different places in every month * the mean 

 temperature in every district that is contained between two 

 parallels differing by 10 and two meridians differing by 20 

 degrees, [e. g., between 0° and 10° N. and 160° and 180° W.). 

 The humidity has not as yet been sufficiently examined for 

 the whole earth ; and I have therefore collected a great many 

 measurements of the relative humidity at different places 

 (about 780) on the earth and marked them down in maps of 

 the world, and thereafter estimated the mean values for every 

 district. These quantities I have tabulated for the four seasons, 

 Dec.-Feb., March-May, June-Aug., and Sept.-Nov. The 

 detailed table and the observations used are to be found in 

 my original memoir : here I reproduce only the mean values 

 for every tenth parallel (Table VI.). 



* Buchan : Report on the Scientific Results of the Voyage of H.M.S. 

 ' Challenger,' Physics and Chemistry, vol. ii., 1889. 



