IDEAL STATES OF EQUILIBRIUM IN THE ATMOSPHERE. 53 



Proceeding to values of Ry smaller than 1, we come to states of less pronounced 

 instability. The case Ry = -, corresponding to a decrease of temperature of 

 1. 74 C. for every 100 dynamic meters of height, is interesting mathematically, tem- 

 perature being in direct and specific volume in inverse proportion to the square 

 root of the pressure, and the density being a linear function of the dynamic height. 

 Ry= j; also gives simple formula;, representing a state of equilibrium still unstable 

 but greatly approaching the state of indifferent or adiabatic equilibrium. 



45. Indifferent or Adiabatic Equilibrium. The state of equilibrium will be 

 indifferent if the adiabatic cooling of a mass of air, which is displaced upwards, will 

 always bring its temperature to that of the air-masses in the new level. For in 

 this case no force will arise tending to favor or to counteract the displacement. 

 The distribution of temperature giving adiabatic equilibrium will be different 

 according to the humidity of the air. Considering first the case of a perfectly dry 

 atmosphere, let k be the well-known ratio 1.4053 of the two specific heats of an 

 ideal gas. Introducing 



() Ry= ^^ = 0.2884 



we see that the equations (a) and (b) take the forms 



The two first equations (a") are the well-known ones connecting temperature and 

 pressure, and specific volume and pressure, respectively, in the case of an adiabatic 

 change of state of an ideal gas. The state of equilibrium defined by equations (a") 

 or (b") has therefore the following property: Proceeding upwards to decreasing 

 pressure we find everywhere the temperature which a mass of dry air moved 

 upwards would take on account of its adiabatic cooling. The temperature gradient 



in this atmosphere is 



, . k 1 



(') 7 = o- = 0.0010048 



representing a fall of temperature of 1.0048 C. for every 100 dynamic meters of 

 height. 



Moist air will have the same adiabatic temperature gradient (') as dry air, as 

 long as no condensation takes place. But as soon as condensation begins, the heat 

 of condensation will partly compensate for the adiabatic cooling, and the adiabatic 

 gradient will take one of the values given in table D.* While the adiabatic tem- 

 perature gradient for dry air is constant, that for saturated air varies both with 

 pressure and temperature, decreasing with decreasing pressure and increasing with 

 decreasing temperature. The decrease upward both of pressure and temperature 



*The table is taken from Harm's Meteorology (first edition), p. 241, with the difference that the pressure 

 figuring as argument is reduced from millimeters of mercury to m-bars, while the fall of temperature is taken per 

 100 dynamic instead of per 100 common meters. 



