CHAPTER VI. 



PRACTICAL SOLUTION OF THE HYDROSTATIC PROBLEM FOR 



THE ATMOSPHERE. 



49. Four Forms of the Problem. In the preceding simple cases we have 

 used two different methods of registering numerically the equilibrium relation 

 between pressure and dynamic height. We have registered either the height of 

 given -pressures or the pressure at given heights. In cases of practical occur- 

 rence, when any analytical form to the equilibrium relation can not be given, we 

 shall always try to find the result in one of the same two forms, as a table contain- 

 ing the heights of given pressures or as a table containing the pressures in given 

 heights. 



On the other hand, the observed data from which the equilibrium relation may 

 be deduced will generally be given in one of two forms. The observed quantities 

 may be the correlated values of pressure, temperature, and humidity, or of height, 

 temperature, and humidity. From the first set we can calculate the virtual tem- 

 perature for given values of pressure ; from the second the virtual temperature at 

 given heights. The practical problem, theretore, will present itself in one of the 

 following four forms : 



(1) To calculate the heights corresponding to given pressures, the virtual tem- 

 peratures for these values of the pressures being known. 



(2) To calculate the heights corresponding to given pressures, the virtual tem- 

 peratures at given heights being known. 



(3) To calculate the pressures at given heights, the virtual temperatures tor 

 given values of the pressure being known. 



(4) To calculate the pressures at given heights, the virtual temperatures at 

 given heights being known. 



Of these four problems the first is by far the simplest, and at the same time 

 practically the most important. We shall therefore first direct our attention to the 

 practical solution of this problem. The others will afterwards easily be solved. 



50. Fundamental Formula. As already remarked, the hydrostatic equation 

 in its first integral form, (a), section 40, gives the difference of potential correspond- 

 ing to a given difference of pressure. Passing from the potential <f> expressed in 

 dynamic decimeters to the dynamic height H expressed in dynamic meters, and 

 passing simultaneously from centibar to decibar as unit-pressure, the equation takes 

 the form 



(a) H.-H^-Tadp 



6l 



