226 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



cau be seen with the vertex toward the right and above. This results 

 from the circumstance that the isotherm for the rain stage contains the 

 initial points, of all isotherms for the dry stage, which points corre- 

 si)ond to values of j'„ that are smaller than the value of jci, from which 

 one starts out. 



In order to obtain the equation of the adiabatic we must know the 

 quantity of heat, dQ. that is to be communicated for a very small change 

 in the condition. This dQ is composed of thequautity of heatr/^)^ that 

 is given to the dry air and of the quantity dQ^ that is commuui- 

 cateil to the intermingled water or aqueous vapor. The following 

 equations hold good for these quantities:* 



ndv 



d(h= C,dT+ AR^ T- 



V 



and 



dQ, = Td Q": J + (^ + X') dT 



[Where r is the quantity of heat required to vaporize a unit mass of 

 water at the teini)erature T and the pressure ^^.J 



In these x' has values that lie between and x^—x where x^ indicates 

 the (juantity ot vapor that was given to the original kilogram in its 

 passage from the dry stage to the rain stage, x' is equal to wlieu all 

 the condensed water immediately falls down and is thus sei):tiated from 

 the mass; it is equal to x^—x when all such water is carried along with 

 the mass. The two liu)iring cases will occur relatively quite seld(jm in 

 nature, but since at present we have no basis for determining to what 

 extent liquid water is suspended in the air or can be carried along with 

 it, therefore one must in the theoretical investigation confine himself 

 to these limiting cases. Expressed in the language of the graphic 

 presentation one must content himself with investigating those cases 

 in which the indicating point either remains in the same plane as in the 

 dry stage or on the other hand goes further on over to the dew point 

 surface itself. Hitherto the first case only has been taken into consid- 

 eration, although in general the second better agrees with the conditions 

 occurring in nature. 



Therefore the above given equation for dQ^ assumes different forms, 

 according as we consider the one or the other limiting case and we have, 

 either 



dQ,= Td Q^^^Y^adT 



for the case where x^ is constant when all the water formed by conden- 

 sation remains suspended, 



or dQi=Tdf^\-\-xdT 



where x=-^^ 



for the case when all this water immediately separates from the mass. 



• See Clausius Collected Memoirs, Brnnswick, 1884, Memoir v, page 174, or Hirst's 

 translation of Clausius, pages 153 and 3r)3. 



