Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/13

$\lambda =1.5~\mu$, after which it increases rapidly to a maximum at $\lambda =2.6~\mu$, and attains a new extraordinarily strong maximum at $\lambda =4.6$ (Langley's ${\text{Y}}$). According to Ångström the absorption of carbonic acid is zero at $\lambda =0.9~\mu$, and very weak at $\lambda =1.69~\mu$, after which it increases continuously to $\lambda =4.6~\mu$ and decreases again to $\lambda =6.0~\mu$. This behaviour is entirely in agreement with the values of $\log x$ in Table II. From the value zero at 40° ($\lambda =1.0~\mu$) it attains a sensible value ($-0.0296$) at 39°.45 ($\lambda =1.4~\mu$), and thereafter greater and greater values ($-0.0559$ at 39°.30, and $-0.1070$ at 39°.15) till it reaches a considerable maximum ($-0.3412$ at 39°, $\lambda =4.3~\mu$). After this point the absorption decreases (at 38°.45 $=5.6~\mu$, $\log x=-0.2035$) . According to Table II. the absorption of carbonic acid at 38°.30 and 38°.15 ($\lambda =7.1~\mu$ and $8.7~\mu$) has very great values ($\log x=-0.2438$ and $-0.3780$), whilst according to Ångström it should be insensible. This behaviour may be connected with the fact that Ångström's spectrum had a very small intensity for the larger wave-lengths. In Paschen's curve there are traces of a continuous absorption by the carbonic acid in this whole region with weak maxima at $\lambda =5.2~\mu$, $\lambda =5.9~\mu$, $\lambda =6.6~\mu$ (possibly due to traces of water-vapour), $\lambda =8.4~\mu$, and $\lambda =8.9~\mu$. In consequence of the strong absorption of water-vapour in this region of the spectrum, the intensity of radiation was very small in Langley's observations, so that the calculated absorption-coefficients are there not very exact (cf. above, pp. 242–243). Possibly the calculated absorption of the carbonic acid may have come out too great, and that of the water-vapour too small in this part (between 38°.30 and 38°.0). This can happen the more easily, as in Table I. ${\text{K}}$ and ${\text{W}}$ in general increase together because they are both proportional to the "air-mass." It may be pointed out that this also occurs in the problems that are treated below, so that the error from this cause is not of so great importance as one might think at the first view.

For angles greater than 38° ($\lambda >9.5~\mu$) we possess no direct observations of the emission or absorption of the two gases. The sun's spectrum, according to Langley, exhibits very great absorption-bands at about 37°.50, 37°.25, 37°, and 36°.40°. According to my calculations the aqueous vapour has its greatest absorbing power in the spectrum from 38° to 35° at angles between 37°.15 and 37°.45 (the figures for 35°.45, 35°.30, and 35°.15 are very uncertain, as they depend upon very few measurements), and the carbonic acid between 36°.30 and 37°.0. This seems to indicate that the first two absorption-bands are due to the action of water-