PAPER BY PROF. BEZOLD. 215 



considerable than when the whole change of condition took place with 

 a horizontal position of the cylinder. 



If the piston were without weight and without any loading, and if it 

 were only at the beginning held fast but then suddenly loosed, and first 

 held fast again at some other position at a greater distance from the 

 base, then indeed the cooling would be attributable alone to the work 

 which was necessary to be done in order to raise the center of gravity 

 of the mass of air, since in this case no work of expansion is accom- 

 plished. By the explanations that I have made in such detail, in con- 

 sideration of the fundamental importance of the question, it certainly 

 ought to be perfectly clear that the cooling and warming in ascending 

 and descending currents of air in the atmosphere are to be considered 

 only as consequences of the work of expansion and compression ; not 

 of the work that is consumed in raising the air or that is gained by its 

 descent, unless the ascending and descending masses belong perma- 

 nently to one system. Since however the work of expansion and com- 

 pression ought never to be left unconsidered, therefore in Guldberg 

 and Mohn's method of consideration these, under all conditions, should 

 have been further taken into consideration, and there would then have 

 resulted for the rate of change of temperature with altitude a value 

 exactly double that given by them. This being premised I will now 

 pass to the problems mentioned in the opening paragraphs. 



For our purpose it is first necessary to establish the fundamental 

 quantities that come into consideration in investigations into the change 

 of condition of a mixture of air and water or aqueous vapor. If in this 

 I do not accord wholly with the steps that Hertz has chosen, this is be- 

 cause he has made various simplifying assumptions that are appropri- 

 ate to the attainment of the end that he had in view, but that are not 

 allowable in the general theoretical investigation that I contemplate. 

 For the same reason I must again review the equations for the various 

 conditions through which the mixture of air and water can pass, and 

 which Hertz has developed in such a perspicuous manner, since not only 

 by reason of the somewhat different notation, but also by the consider- 

 ation of certain points intentionally neglected by Hertz, some material 

 differences result. 



Hertz and others in their investigations have made the assumption 

 ordinarily used in the mechanical theory of heat that the unit of mass 

 of the substance under consideration is given, and that it in succession 

 passes through the different conditions. This assumption can not be 

 rigorously adhered to in the case of atmospheric processes. A kilo- 

 gram of moist air retains unchanged its mass only so long as during 

 the expansion no condensation of aqueous vapor occurs, but suffers a 

 diminution as soon as the formation of precipitation begins and rain, 

 snow, or hail falls from it. When therefore a mass of moist air that 

 is rising within a depression, or on the windward side of a mountain 

 during a foehn on the lee side, is followed on its way through the atmos- 



