Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/10

creases in intensity in the proportion 1 : 0.934 ($\log =-0.0296$), the corresponding value for the unit of water-vapour is 1 : 0.775 ($\log =-0.1105$). These figures are of course only valid for the circumstances in which the observations were made, viz., that the ray should have traversed a quantity of carbonic acid ${\text{K}}=1.1$ and a quantity of water-vapour ${\text{W}}=0.3$ before the absorption in the next quantities of carbonic acid and water-vapour was observed. And these second quantities should not exceed ${\text{K}}=1.1$ and ${\text{W}}=1.8$, for the observations are not extended over a greater interval than between ${\text{K}}=1.1$ and ${\text{K}}=2.2$, and ${\text{W}}=0.3$ and ${\text{W}}=2.1$ (the numbers for ${\text{K}}$ and ${\text{W}}$ are a little different for rays of different kind). Below ${\text{A}}$ is written the relative value of the intensity of radiation for a given kind of ray in the moonlight after it has traversed ${\text{K}}=1$ and ${\text{W}}=0.3$. In some cases the calculation gives positive values for $\log x$ or $\log y$. As this is a physical absurdity (it would signify that the ray should be strengthened by its passage through the absorbing gas), I have in these cases, which must depend on errors of observation, assumed the absorption equal to zero for the corresponding gas, and by means of this value calculated the absorption-coefficient of the other gas, and thereafter also ${\text{A}}$.

As will be seen from an inspection of Table I., the values of $i$ obs. agree in most cases pretty well with the calculated values $i$ calc. But in some eases the agreement is not so good as one could wish. These cases are mostly characterized by a small "weight" ${\text{G}}$, that is in other words, the material of observation is in these cases relatively insufficient. These cases occur also chiefly for such rays as are strongly absorbed by water-vapour. This effect is probably owing to the circumstance that the aqueous vapour in the atmosphere, which is assumed to have varied proportionally to the humidity at the earth's surface, has not always had the assumed ideal and uniform distribution with the height. From observations made during balloon voyages, we know also that the distribution of the aqueous vapour may be very irregular, and different from the mean ideal distribution. It is also a marked feature that in some groups, for instance the third, nearly all the observed numbers are less than the calculated ones, while in other groups, for instance the fourth, the contrary is the case. This circumstance shows that the division of the statistic material is carried a little too far; and a combination of these two groups would have shown a close agreement between the calculated and the observed figures. As, however, such a combination is without influence on the correctness of the calculated absorption coefficients, I have omitted