Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/22

Rh considered does not alter its albedo as a consequence of the altered temperature. In that case entirely different circumstances enter. If, for instance, an element of the surface which is not now snow-covered, in consequence of falling temperature becomes clothed with snow, we must in the last formula not only alter $$\beta$$ but also $\nu$. In this case we must remember that $$\alpha$$ is very small compared to $\beta$. For $$\alpha$$ we will choose the value $$0.40$$ in accordance with Langley's estimate. Certainly a great part of this value depends upon the diffusely reflected part of the sun's heat, which is absorbed by the earth's atmosphere, and therefore should not be included in $\alpha$, as we have defined it above. On the other hand, the sun may in general stand a little lower than in Langley's measurements, which were executed with a relatively high sun, and in consequence of this $$\alpha$$ may be a little greater, so that these circumstances may compensate each other. For $$\beta$$ we will choose the value $0.70$, which corresponds when $$\text{K}=1$$ and $$\text{W}=0.3$$ (a little below the freezing-point) with the factor $$1.66$$ (see p. ). In this case we find the relation between $$\text{T}$$ (uncovered) and $$\text{T}_1$$ (snow-covered surface) to be if $\text{M}=\phi\text{A}$. We have to bear in mind that the mean $$\text{M}$$ for the whole earth is zero, for the equatorial regions negative and for the polar regions positive. For a mean latitude $$\text{M}=0$$, and in this case $$\text{T}_1$$ becomes $$267.3$$ if $\text{T}=273$, that is the temperature decreases in consequence of the snow-covering by 5°.7 C. The decrease of temperature from this cause will be valid until $$\phi=1$$, i. e. till the heat delivered by convection to the air exceeds the whole radiation of the sun. This can only occur in the winter and in polar regions.

But this is a secondary phenomenon. The chief effect that we examine is the direct influence of an alteration of $$\beta$$ upon the temperature $$\text{T}$$ of the earth's surface. If we start from a value $$\text{T}=273$$ and $$\beta=0.70$$, we find the alteration ($t$) in the