SCIENTIFIC BALLOON ASCENSIONS VON BEZOLD 315 



of the temperature t over into that of the temperature t r is 

 a-<2= i3-6c g (F f -F) - 13.6 c p F* 



where the area 7\ 7\' 7y T 2 is represented by F*. 



In the method of graphic presentation here chosen, where equal 

 lengths of ordinates correspond to equal differences of pressure, the 

 curves of condition are actually therefore tauto-chrones, and the 

 surfaces bounded by two horizontal lines and the portions of two 

 curves of condition intercepted between them, give us a measure 

 of the quantities of heat that have to be given to the corresponding 

 portion of the column of air in order to convert it from one condition 

 to the other under constant pressure. 



These considerations are applicable not only to the temperature 

 but equally well to the humidity. If y is the specific humidity, 

 i. e., the quantity of water contained in a kilogram of moist air, then 

 the quantity of water Y contained in the vertical prism erected on 

 a base of one square meter and at whose limiting end surfaces the 

 pressures B l and B 2 prevail, will be 



A 

 Y = 13.6 j ydp = 13.6 F 

 A 



if the specific humidities are laid off as abscissae. 



If the diagram be drawn in such manner that the zero of abscissas 

 corresponds to the zero of specific humidity then the total quantity 

 of water in the vertical column is proportional to the surface 

 bounded by the two axes and by the curve of condition for specific 

 humidity. 



Hence the last mentioned method of presentation, in which equal 

 differences of atmospheric pressure correspond to equal lengths 

 offers specific advantages. 



If we would represent numerically the dependence of any quan- 

 tity whatever on the atmospheric pressure, we must of course also 

 proceed by equal differences of pressure instead of equal differences 

 of altitude as was done above. 



But in this method of presentation one must never forget that 

 the portions of the vertical column corresponding to equal differ- 

 ences of pressure have very various altitudes corresponding to the 

 absolute values of the pressure and to the temperatures. Thus, for 

 example, the layer above considered between the pressures /? x and 

 /J, has different altitudes for the two conditions represented by the 



