20G TllK MECHANICS OF THE EARTh's ATMOSPHERE. 



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



the end of the first stage. These lines g^ive the greatest qnantity of 



water, expressed in grains and com[)uted according to the formula 



B e 

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



coutaiu 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 Irom 

 gram to gram. If a mixture contains n grains 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 /t, but then we must pass either to the second 

 or fourth stage. 



The limit of the second stage, with resi)ect to the third, is given by 

 the intersection of the corresponding adial)atic beta with the isotherm 

 of C^ C. By the pressure ^>u, that corresponds to this intersection, and by 

 the quantity /< of water, is determined the pressure ^>i, 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 o{ jh- This auxiliary diagram con- 

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

 as ordinate the total (quantity /< of the water in all conditions ex- 

 l)ressed in grams per kilogram of the mixture. The obli(j[ue lines of 

 tljis small table are the curves that corresi)ond to the equation (3) of 

 the third stage, when in this equation we consider />„ ^is constant, but 

 j>i and j.i as the variable coordinates. These lines are not perfectly 

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

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

 case jJi — 2h' The corresponding j.i is not zero, but is equal to the least 

 value, r, that /< must have in order that the mixture may be saturated 

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

 the j>i belonging to a definite value of p^ and /<, then we seek that 

 oblique line whose highest point lies on the abscissa j?,,, and tiien we 

 l)ass along this line downwards to the ordiimte //. The pressure at 

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

 sure we have the i)oint of transition from the third to the fourth stage. 



Uaving 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 (juantity of water that has already 

 been condensed. 



^2.) The density 6 of the mixture can under the adopted approxima- 

 tions be computed for all conditions by the formula 



■>) 

 6 = •^,; or log 6 = log y; — log T— log R. 



