SCIENTIFIC BALLOON ASCENSIONS VON BEZOLD 313 



peratures horizontally as abscissae. But the curves themselves 

 representing the temperature conditions at a given moment of time 

 I called "tauto-chrones." If we assume that the physical peculiari- 

 ties of the soil are uniform throughout the whole stratum under 

 consideration or at least, and more properly, that the calorimetric 

 values for equal volumes or the so-called volume-capacity is uniform, 

 then the quantities of heat received or given out between any two 

 moments of time are proportional to the areas included between the 

 tauto-chrones that belong to these two moments. 



This same theorem would be true for the curves of condition as 

 to temperature and moisture of the atmosphere corresponding to 

 different moments or intervals of time, if the air had everywhere a 

 uniform density. But, as is well known, this is not the case in the 

 atmosphere; however, by appropriate choice of coordinates we can 

 obtain curves of condition for which, as in the tauto-chrone, the 

 area between two neighboring curves is proportional to the quanti- 

 ties of heat that must be received or given out in the passage from 

 one condition to the other assuming that the masses of air remain 

 the same and that the change of temperature is a simple consequence 

 of gain or loss of heat. Similarly, the curves constructed in a corre- 

 sponding manner for the specific humidity give the increase or loss 

 of water or, since we can in this case start from the condition of 

 absolute dryness, they give the total moisture contained in a given 

 section of the vertical column of atmosphere. 



We obtain such curves of condition if we construct a diagram in 

 which the pressures diminish as ordinates from below upward 

 and the temperatures or the specific humidities diminish backward 

 as abscissas. If we imagine a prism cut from the atmosphere erected 

 vertically on a base of one square meter, and that the barometric 

 pressures /? x and /? 2 prevail at the altitudes h x and h 2 then between 

 these two altitudes there is included a mass of 13.6 (/?, — /? 2 ) kilo- 

 grams of air. 



Hence in the prism between h and h + dh the air mass is 13.6c//? 

 if the barometric pressure is /? at the altitude h. If we further 

 assume that at first the air in this prism nas everywhere the uniform 

 temperature o° C. and that it is to be brought to the temperature t 

 corresponding to that of its temporary condition, then the infinitely 

 thin layer between h and h + dh is to receive the quantity of heat 

 d Q = 13.6 c p tdfi where c p is the thermal capacity or specific heat 

 under constant pressure. But the whole mass of air under consid- 

 eration at whose lower and upper boundary surfaces the barometric 



