PAPER BY PROF. BEZOLD. 225 



becomes that of simple saturation.* This occurs as soon as the curve 

 of change of couditioii attains the dew-point curve x + x' . Having 

 iu mind the geometrical presentation one can express this proposition 

 as follows : 



In the rain or snow stage, changes of condition are only reversible 

 when and so long as they find their representation above the dew-point 

 surface. If they hud this in the dew-point surface itself, then only 

 those changes are possible by whicli the representative point approaches 

 the quasi horizontal coordinate plane, that is to say slides down toward 

 the surface or in the limiting case becomes the dew-point curve itself. 

 An ascent to the dew-point surface is in the free atmosphere only im- 

 aginable in exceptional cases (as for instance in case of the falling of 

 rain through other layers or the mixing of other layers with moist air); 

 a further progress toward the concave side of the dew-point curve or 

 toward the lower side of the dew-point surface indicates a transition 

 over into the dry stage. 



Therefore in making use of the graphic presentation one must always 

 keep in mind that in the rain and snow stages the curves in general 

 can only be travelled over in one direction best rei)resented by arrows 

 and that a backward movement on the same curve is an impossibility. 

 Nevertheless for the forward progress in the one possible direction 

 exactly the same formula* are applicable as for the reversible changes 

 of condition. Therefore the case here occurring may with propriety 

 be designated as " limited reversible." 



We now turn to the consideration of the isotherm and the adiabatic 

 for the rain stage. The equation of the isotherm we obtain at once as 

 soon as we consider the temperature T as constant in the equation of 

 elasticity 



i) =— ^ h e. 



V 



Since in this case e is also constant, therefore this curve as in the dry 

 stage is an equilateral hyperbola, one of whose asymptotes, as in the 

 dry stage, coincides with the axis of 7;, but the other is by the small 

 quantity e shoved from the axis of v toward the side of positive j?. 

 At the same time however, in so far as we exclude super-saturation and 

 starting from a given initial condition, this equation holds good only for 

 •diminishing values of v. 



Moreover a glance at the equations of the isotherms in the dry and 

 the rain stages sufl&ces to show us that the two curves for any given 

 temperature differ from each other only very little and that iu the 

 transition from the dry to the rain stage only a very small indentation 



* In a certain sense the case where liquid water or ice is mixed with the air should 

 certainly also be called that of super saturation, but of course with the reservation 

 that any confusion with the condition of super-saturation properly so called, iu which 

 the excess above the quantity needed for saturation is present in gaseous form, shall 

 Tae excluded. 



80 A 15 



