Page:On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground.pdf/23

temperature which is caused by the variation of $\beta$ to the following values to be $\beta =$ 0.60 $t=$ +- 5° C.
$\beta =$ 0.80 $t=$ + 5° C..6
$\beta =$ 0.90 $t=$ +11° C..7
$\beta =$ 1.00 $t=$ +18° C..6.

These values are calculated for $\nu =1$, i. e. for the solid crust of the earth's surface, except the snowfields. For surfaces with another value of $\nu$, as for instance the ocean or the snowfields, we have to multiply this value $t$ by a fraction given above.

We have now shortly to consider the influence of the clouds. A great part of the earth's surface receives no heat directly from the sun, because the sun's rays are stopped by clouds. How great a part of the earth's surface is covered by clouds we may find from Teisserenc de Bort's work^[1] on Nebulosity. From tab. 17 of this publication I have determined the mean nebulosity for different latitudes, and found: –

Latitude. .	60.		45.		30.		15.		0.		-15.		-30.		-45.		-60.
Nebulosity.		0.603		0.48		0.402		0.511		0.581		0.463		0.53		0.701

For the part of the earth between 60° S. and 60° N. we find the mean value 0.525, i. e. 52.5 per cent. of the sky is clouded, The heat-effect of these clouds may be estimated in the following manner. Suppose a cloud lies over a part of the earth's surface and that no connexion exists between this shadowed part and the neighbouring parts, then a thermal equilibrium will exist between the temperature of the cloud and of the underlying ground. They will radiate to each other and the cloud also to the upper air and to space, and the radiation between cloud and earth may, on account of the slight difference of temperature, be taken as proportional to this difference. Other exchanges of heat by means of air-currents are also, as a first approximation, proportional to this difference. If we therefore suppose the temperature of the cloud to alter (other circumstances, as its height and composition, remaining unchanged), the temperature of the ground under it must also alter in the same manner if the same supply of heat to both subsists – if there were no supply to the ground from neighbouring parts, the cloud and the ground would finally assume the same mean temperature. If, therefore, the temperature of the clouds varies in a determined manner

1. Teisserenc de Bort, "Distribution moyenne de la nébulosité," Ann. du bureau central metéorologique de France, Année 1884, t. iv. 2^de partie, p.  27.