in the Air upon the Temperature of the Ground. 259 



(without alteration of their other properties, as height, com- 

 pactness, &c), the ground will undergo the same variations of 

 temperature. Now it will he shown in the sequel that a 

 variation of the carbonic acid of the atmosphere in the same 

 proportion produces nearly the same thermal effect indepen- 

 dently of its absolute magnitude (see p. 265) . Therefore we 

 may calculate the temperature-variation in this case as if the 

 clouds covered the ground with a thin film of the albedo 0*78 

 (v=0'22, see p. 256). As now on the average K = l and 

 W= 1 nearly, and in this case ft is about 0'79, the effect on the 

 clouded part will be only 0*25 of the effect on parts that have 

 v=l. If a like correction is introduced for the ocean 

 (v= 0*925) on the supposition that the unclouded part of the 

 earth consists of as much water as of solid ground (which is 

 approximately true, for the clouds are by preference stored 

 up over the ocean), we find a mean effect of, in round num- 

 bers, 60 p. c. of that which would exist if the whole earth's 

 surface had v=l. The snow-covered parts are not considered, 

 for, on the one hand, these parts are mostly clouded to 

 about 65 p. c. ; further, they constitute only a very small 

 part of the earth (for the whole year on the average only 

 about 4 p. c), so that the correction for this case would not 

 exceed - 5 p. c. in the last number 60. And further, on the 

 border countries between snowfields and free soil secondary 

 effects come into play (see p. 257) which compensate, and 

 perhaps overcome, the moderating effect of the snow. 



In the foregoing we have supposed that the air is to be re- 

 garded as an envelope of perfectly uniform temperature. This 

 is of course not true, and we now proceed to an examination 

 of the probable corrections that must be introduced for elimi- 

 nating the errors caused by this inexactness. It is evident 

 that the parts of the air which radiate to space are chiefly 

 the external ones, and on the other hand the layers of air 

 which absorb the greatest part of the earth's radiation do not 

 lie very high. From this cause both the radiation from air 

 to space (/37# 4 in eq. 1) and also the radiation of the earth 

 to the air (/37v(T 4 — 4 ) in eq. 2), are greatly reduced, and 

 the air has a much greater effect as protecting against the 

 loss of heat to space than is assumed in these equations, and 

 consequently also in eq. (3). If we knew the difference of 

 temperature between the two layers of the air that radiate to 

 space and absorb the earth's radiation, it would be easy to 

 introduce the necessary correction in formulae (1), (2), and 

 3). For this purpose I have adduced the following con- 

 sideration . 



As at the mean composition of the atmosphere (K = l, 



