206 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



can be found for the different stages. The dotted lines serve to show 

 the end of the first stage. These lines give the greatest quantity of 

 water, expressed in grams and computed according to the formula 



7? p 



v== ~' J, that a kilogram of the mixture in the different conditions can 



contain as vapor. Thus, for instance, the curve designated by 25 con- 

 nects all those conditions in which one kilogram of the mixture when 

 saturated contains 25 grams of vapor. These curves are drawn from 

 gram to gram. If a mixture contains n grams of vapor in every kilo- 

 gram of mixture, then evidently we have to follow the curve of the first 

 stage up to the dotted line n, but then we must pass either to the second 

 or fourth stage. 



The limit of the second stage, with respect to the third, is given by 

 the intersection of the corresponding adiabatic beta with the isotherm 

 of 0° 0. By the pressure^ that corresponds to this intersection, and by 

 the quantity jx of water, is determined the pressure p h at which the 

 transition takes place from the third to the fourth stage. The small 

 auxiliary diagram that is given beneath the main table of Fig. 28 

 serves for the graphic determination of p x . This auxiliary diagram con- 

 tains as abscissa the pressure arranged as in the larger diagram, and 

 as ordinate the total quantity j.i of the water in all conditions ex- 

 pressed in grams per kilogram of the mixture. The oblique lines of 

 this small table are the curves that correspond to the equation (3) of 

 the third stage, when in this equation we consider p as constant, but 

 Pi and }.i as the variable coordinates. These lines are not perfectly 

 straight, but are not to be distinguished from such in a diagram ou 

 this scale. The highest point of each of these lines corresponds to the 

 case p x = jOo- The corresponding jj. is not zero, but is equal to the least 

 value, v, that ).i must have in order that the mixture may be saturated 

 at 0°C, and the auxiliary table come iuto use. If one wishes to find 

 the px belonging to a definite value of p and /*, then we seek that 

 oblique line whose highest point lies on the abscissa jp , and then we 

 pass along this line downwards to the ordinate //. The pressure at 

 which we attain this ordinate is the desired pressure^. In this pres- 

 sure we have the point of transition from the third to the fourth stage. 



Having in this way determined the totality of the stages through 

 which the mixture runs, we find the remaining desired quantities for 

 each stage in the following manner: 



(1.) The dotted line which one selects, (corresponding to the condi- 

 tion given,) indicates directly the number of grams of water still remain- 

 ing in the form of vapor. If we subtract this quantity from the original 

 total quantity /<, we obtain the quantity of water that has already 

 been condensed. 



(2.) The deusity d of the mixture can under the adopted approxima- 

 tions be computed for all conditions by the formula 



gyp-, or log 6 = log p — log T— log E. 



