54 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



therefore counteract each other in their effect upon the fall of temperature, making 

 its variation with the height very gradual. But still it will always increase upward, 

 converging toward the limit 1.0048, which would be reached when all moisture 

 had fallen out. To illustrate this increasing fall of temperature, the values corre- 

 sponding to the case of a mass of air moved upwards from sea-level with the initial 

 temperature of 15 C. are indicated by heavy-faced figures in the table. 



Table D. Adiabatic Fall of Temperature per 100 Dynamic Meters for Saturated Air. 



The case of adiabatic equilibrium for saturated air can not, therefore, be com- 

 prised in the case of equilibrium with constant-temperature gradients treated here. 

 But as the increase of the gradient upward is gradual, we may with some approxi- 

 mation reckon with constant average values for sheets of moderate thickness. 

 Thus the temperature gradient y 0.0005, corresponding to a fall of temperature 

 of 0.5 C. lor every 100 dynamic meters of height, is a value often used by 

 practical meteorologists, and may be taken as an average value of the adiabatic 

 temperature gradient for saturated air in the lower strata of the atmosphere. 



46. States of Stable Equilibrium. Passing to temperature gradients smaller 

 than the adiabatic, we arrive at states of stable equilibrium. If in this case a mass 

 of air be moved upward, the adiabatic cooling will bring it to a lower temperature 

 than that of the surrounding masses and it will sink back again on account of its 

 greater density. 



Interesting mathematically is the case Ry = o, that is, the case of a temperature- 

 gradient zero, 

 0) 7 = 



or of isothermic atmosphere. For greater gradients the atmosphere has been stated 

 to be finite. But in this case it becomes infinite. At the same time the second 

 member of the last equation (a), section 42, and of the two last equations (b), sec- 

 tion 42, become indeterminate. But by the theory of indeterminate expressions, 

 or by renewed integration of the equation of equilibrium (c), section 41, after the 

 substitution &= # , we easily arrive at the following set of formula; representing 

 the state of isothermic equilibrium: 



A 



(A"') 

 (B'") 



& = & 



# = <?.. 



a = a 



t 



4> = irW nat. log.^ 



Po e 





t=ttf 



Ro 



