Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/28

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 aërial 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 (${\text{K}}=1$ now) and water-vapour (${\text{W}}$) of this place. By the aid of Table IV. we at first determine the factor $\rho$ that gives the mean path of the radiation from the earth through the air and multiply the given ${\text{K}}$- and ${\text{W}}$-values by this factor. Then we determine the value of $\beta$ which corresponds to $\rho {\text{K}}$ and $\rho {\text{W}}$. Suppose now that the carbonic acid had another concentration ${\text{K}}_{1}$ (e. g. ${\text{K}}_{1}=1.5$). Then we at first suppose ${\text{W}}$ unaltered and seek the new value of $\rho$, say $\rho _{1}$, that is valid on this supposition. Next we have to seek $\beta$, which corresponds to $\rho _{1}{\text{K}}_{1}$ ($1.5\rho _{1}$) and $\rho _{1}{\text{W}}$. 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 $\beta$ from $\beta$ to $\beta _{1}$. In consequence of the variation ($t$) in the temperature, ${\text{W}}$ must also undergo a variation. As the relative humidity does not vary much, unless the distribution 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 ${\text{W}}_{1}$ of ${\text{W}}$. A fresh approximation gives in most cases values of ${\text{W}}_{1}$ and $\beta _{1}$ 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^[1] 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.).

1. Buchan: Report on the Scientific Results of the Voyage of H.M.S. 'Challenger,' Physics and Chemistry, vol. ii., 1889.