Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/26

Rh that the radiation of the earth is much less refrangible. But in the absence of a more appropriate determination we may use this for our purpose; it is probable that for a less hot radiator the absorptive power of the carbonic acid would come out a little greater compared with that of water-vapour, for the absorption-bands of CO2, are, on the whole, less refrangible than those of H2O (see pp. ). Using the number 0.09 vol. p. c. for the quantity of carbonic acid in the atmosphere, we find that rays which emanate from the upper part of the air are derived to the extent of 40 p. c. from a layer that constitutes 0.145 part of the atmosphere. This corresponds to a height of about 15,000 metres. Concerning this value we may make the same remark as on the foregoing value. In this case we have neglected the absorption by the small quantities of water-vapour in the higher atmosphere. The temperature-difference of these two layers – the one absorbing, the other radiating – is, according to Glaisher's measurements (with a little extrapolation), about 42° C.

For the clouds we get naturally slightly modified numbers. We ought to take the mean height of the clouds that are illuminated by the sun. As such clouds I have chosen the summits of the cumuli that lie at an average height of 1855 metres, with a maximum height of 3611 metres and a minimum of 900 metres. I have made calculations for mean values of 2000 and 4000 metres (corresponding to differences of temperature of 30° C. and 20° C. instead of 42° C. for the earth's surface).

If we now wish to adjust our formul , we have in  and  to introduce $$\theta$$ as the mean temperature of the radiating layer and $(\theta+42)$, $(\theta+30)$, or $$(\theta+20)$$ respectively for the mean temperature of the absorbing layer. In the first case we should use $$\nu=1$$ and $$\nu=0.925$$ respectively, in the second and the third case $\nu=0.22$.

We then find instead of the formula  another very similar formula