ADIABATIC CHANGES OF MOIST AIR NEUHOFF 463 



Hann has also determined the altitudes given in his small table 21 

 from this formula, in which the initial level of o meters corresponds 

 to the atmospheric pressure 760 millimeters. If we desire to pro- 

 ceed more exactly, by considering the temperatures in the deter- 

 mination of the altitudes, then T must be expressed as a function 

 of the altitude. But since the law of the diminution of tempera- 

 ture with altitude is not a general one, therefore we ordinarily 

 assume that in each special case there is to be introduced a value 

 for T that is equal to the arithmetical mean of the two temperatures 

 for the upper and lower levels respectively. 



In this method we assume that the temperature is a linear- 

 function of the altitude, an assumption that is more or less proper 

 but occasionally may be entirely false. 



The adiabatic diagram shows that with adiabatic changes of 

 condition this assumption is perfectly justified during the dry 

 stage, since then the line which indicates the diminution of tempera- 

 ture with altitude is perfectly straight. To a limited extent this 

 is also true up to differences of temperature of io° in the case of 

 the adiabats of the condensation stage; at least the curvature of 

 the line is in this case so feeble that the departure from the linear 

 average temperature can have scarcely any influence on the com- 

 putation of the differences of altitude. We come nearer to the 

 truth in proportion as the changes of condition are closer together 

 or in proportion as the interval of temperature for the two conditions 

 is smaller. We have thus acquired a simple means for computing 

 the total difference of altitude step by step in the condensation stage 

 from corresponding values of temperature and pressure by the sum- 

 mation of small differences of altitude as in mechanical quadrature. 



In the determination of the altitudes the quantity of moisture 

 that is present in moist air is of less influence. The barometric 

 formula of Koeppen takes account of the average moisture con- 

 ditions, viz: 



h = (1S432 + qz) log h = K, log ^° 



P P 



in which r is the average temperature of the upper and lower levels, 

 q is a factor that has the value 72 when r is above o° C, but in other 

 cases has the value 69. 



21 Hann: Die Gesetze der Temperatur-Aenderung in aufsteigenden Luft- 

 stromungen und einge der wichtigsten Folgerungen aus denselben. Met. Zeit., 

 1874, pp. 321-329, 337-347- 



