222 



THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



initial point N 2 of the isotherm (T# g ) originally considered as beiug 



unlimited; that is to say, in 

 order to obtain a point in the 

 dew-point curve S 2 correspond- 

 ing to the quantity of moist- 

 ure x 2 . 



The dew-point curves # 2 , S 3 , 

 of figure 29 therefore corre- 

 spond respectively to quanti 

 ties of vapor # 2 = 2#i; x z = '5x x 

 when Si corresponds to the 

 quantity of vapor x x . 



The isotherms (T, x{) and 

 (T,x 2 ) run so near each other 

 that they can only appear sep- 

 arated in a figure drawn to a 

 very large scale,* since be- 

 tween the ordinates_pi and p 2 



of the two isotherms belonging to a given r, the following relations 



exist : 



Fig. 29. 



2>i -i>2 = 0»t — X *) 



R&T 



v 



or also 



Pi __ Exjj-jCj_R^_ 

 p 2 ~ Rk + x 2 Rs 



But this quotient is always very near unity, since all the values of a? that 

 here come into consideration lie between zero and 0.03. In the majority 

 of cases one can consider all the isotherms (T,x) corresponding to a 

 given value T as coinciding with each other and have then only to re- 

 member that according to the value of x they have their initial points 

 at different places on the same hyperbola. Therefore from any one dew- 

 point curve ^we obtain another one S 2 in that as already done in 

 figure 29 we simply go with a constant ratio of expansion or compres- 

 sion further along an equilateral hyperbola drawn through Si. 



If we confine our consideration still to that portion of the plane of a 

 constant quantity of vapor x that lies to the right (that is to say, on 

 that side of the dew-point curve that is distant from the coordinate 

 axes) that is to say to the dry stage, then in this region the same 

 theorems will hold good for the characteristic curves as for the so-called 

 perfect gas, and particularly as for air, Avith such very small changes 

 iu the constants as depend on the mixing ratio [or the quantity x]. 



* It must here be expressly remarked that all the diagrams occuring in this memoir 

 have a purely illustrative character. If we should introduce the separate quantities 

 as they result from the computation the diagrams would lose perspicuity. The method 

 here given therefore will need special modifications (as is hereafter to he shown) 

 before it can be applied to graphical computations. 



