THERMODYNAMICS OF ATMOSPHERE -VON BEZOLD 253 



where /? x and /? 2 represent the barometric pressure respectively 

 before and after the cessation of supersaturation. 



But the objection may be raised that the curve of saturation 

 quantity is drawn under the assumption of a constant initial pres- 

 sure ft v since such a constant pressure is everywhere assumed in the 

 diagrams of the previous memoir. 



But this assumption is, however, even now justifiable in so far 

 as concerns the curve F' F' . For a knowledge of the initial pressure 

 /?! is only necessary in order to be able to determine the volume that 

 a kilogram of air occupies at a given temperature; since this volume 

 experiences no change during the extraordinary short time that we 

 have under consideration while the change in temperature makes 

 itself apparent by the increase in pressure, therefore the assump- 

 tion is perfectly unobjectionable. 



In order to judge as to the probability of the occurrence of such 

 supersaturation as would suffice to explain the observed changes of 

 pressure in thunderstorms it will be best to consider the supersatura- 

 tion as a consequence of adiabatic expansion without the accompany- 

 ing condensation. 



Adiabatic expansion, in the absence of dust or ions that can act 

 as nuclei for condensation, is the only process by which the occur- 

 rence of supersaturation in the atmosphere is conceivable. On the 

 other hand adiabatic expansion does play the most prominent part 

 in the formation of thunderstorms. 



In considering the present problem we can profitably make use of 

 the method of presentation used in the first memoir 5 but whereas 

 in that memoir it is assumed that we imagine one kilogram of dry 

 air to be mixed with x kilograms of aqueous vapor, we shall now 

 assume that one kilogram of the mixture contains y grams of water. 



It is easy to see that within the limits of the ordinary values of x 

 or y the diagram drawn for one method of consideration also serves 

 for the other, since only slight changes will be needed which in fact 

 can only be appreciable when the diagrams are drawn with unusual 

 accuracy. 



Especially is this possible so long as we assume that the precipi- 

 tated water is carried along with the air; if we drop this assumption 

 then minor modifications must enter into the treatment of the prob- 

 lem, but these are not important in the present memoir. 



In general it is easy to see that the following equation will hold 

 good : 



1000 



1 + x = - 



]()()() - y 



5 See No. XV, p. 212 of the 189 1 series of these translations. — Ed. 



