PAPER BY PROF. BEZOLD. 247 



From this theorem, which iu its latter form reminds one of the 

 theorem of Clausius iu respect to the entropy, "The entropy strives 

 towards a maximum," though not identical with it, one can draw con- 

 sequences of the greatest importance. The next two sections will 1t>e 

 devoted to these. 



/II. THE VERTICAL TEMPERATURE GRADIENT. 



All motions in the atmosphere can be considered as analyzed into 

 vertical and horizontal components. The latier, in so far as they do not 

 closely follow the irregularities of the earth's surface, are subject in 

 only a slight degree to thermo-dynamic changes. On the other hand, 

 in consequence of the expansion or compression in ascending and de- 

 scending currents, the thermo-dynamic cooling or warming plays a very 

 important role. The horizontal movements will therefore for the 

 l)resent be left entirely out of consideration, but the processes going on 

 in the vertical currents will be thoroughly investigated. The changes 

 of condition going on within ascending and descending currents must 

 be considered in the free atmosphere as adiabatic so long as we con- 

 tent ourselves with a first approximation, and that we must do at first, 

 since in the free air there is only a small opportunity given for active 

 radiation and absorption. On the other hand the increase and diminu- 

 tion of heat will always make themselves felt decisively either where 

 the absorbtivity and emissivity are remarkably increased or where the 

 air comes into direct contact with bodies which themselves can strongly 

 emit and absorb or otherwise take in or give out heat. This is the 

 case: 



(a) Iu the neighborhood of the earth's surface, where besides the 

 increase in absorbtivity and emissivity of the air due to cloud or fog, 

 the warming and cooling of the ground by radiation, as well as the 

 ovaporation, the formation of dew or frost, the thawing and freezing, 

 have a powerful infiueuce. 



[b) In fog or cloud, which also possess a special power of absorbtion 

 and emission, and where moreover evaporation can occur; and 

 especially is it the upper limiting layer of clouds that one has to take 

 into consideration. 



In so far therefore as one can leave out of consideration the special 

 localities just indicated, as also the mixture witli other masses of air, 

 one can approximately consider the processes in ascending and de- 

 scending air currents as adiabatic. Even taking into consideration the 

 special locations above mentioned, one can consider a scheme drawn 

 up under the assumption of adiabatic change as to a certain extent 

 an average or normal scheme, since such a scheme always occupies 

 an intermediate position between those where the incoming radiation 

 and those where the outgoing radiation prevails. How such a preva- 

 lence of either radiation must show itself has already been indicated 

 in the previous communication [p. 212J, where the interchange of air 



