in the Air upon the Temperature of the Ground. 257 



considered does not alter its albedo as a consequence of the 

 altered temperature. In that case entirely different circum- 

 stances 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 fi but also v. In this case we must remember that 

 a is very small compared to /9. For a we will choose the 

 value 0*40 in accordance with Langley's* estimate. Cer- 

 tainly 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 a, 

 as we have defined it above. On the other hand, the sun 

 may in general stand a little lower than in Langley's measure- 

 ments, which were executed with a relatively high sun, and 

 in consequence of this a may be a little greater, so that these 

 circumstances may compensate each other. For ft we will 

 choose the value 0*70, which corresponds when K = l and 

 W = 03 (a little below the freezing-point) with the factor 1*66 

 (see p. 253). In this case we find the relation between T 

 (uncovered) and T ± (snow-covered surface) to be 



T4 . T 4= A(l + l-0-40) + M A(l + O50-0-20)+M 



• i r (l+l-0-70) : 7(1 + 0-50-0-35) 



1-60 + 1-30+0 

 = 1-30 : 1-15 ' 



if M=0A. We have to bear in mind that the mean M for 

 the whole earth is zero, for the equatorial regions negative 

 and for the polar regions positive. For a mean latitude 

 M = 0, and in this case Tj becomes 267*3 if T = 273, that is 

 the temperature decreases in consequence of the snow-cover- 

 ing by 5°'7 C.f The decrease of temperature from this cause 

 will be valid until 0=1, i.e. till the heat delivered by con- 

 vection 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 /8 upon 

 the temperature T of the earth's surface. If we start from a 

 value T = 273 and /3 = 0*70, we find the alteration (t) in the 



* Langley, u Temperature of the Moon," p. 189. On p. 197 he estimates 

 a to he only 0*33. 



t According to the correction introduced in the sequel for the different 

 heights of the absorhing and radiating layers of the atmosphere, the 

 number 5°*7 is reduced to 4 o, 0. But as about half the sty is cloud- 

 covered, the effect will he only half as great as for cloudless sky, i. e, the 

 mean effect will be a lowering of about 2° C, 



