900 



THE MECHANICS OF THE EARTHS ATMOSPHERE. 



initial point No of the isotherm {Tx..) originally considered as being 



unlimited; that is to say, in 

 order to obtain a point in the 

 dew-i^oint curve *S2 correspond- 

 ing to the quantity of moist- 

 ure Xi. 



The dew-point curves S2, S3, 

 of tigure 21) therefore corre- 

 spond respectively to quanti 

 ties of vapor a72 = 2a'i; ar3 = 3,ri 

 when iS^i corresponds to the 

 quantity of vai)or x^. 



The isotherms {T, Xi) and 

 [T^x-i) ruu so near each other 

 that they can oidy ap})ear sep- 

 arated in a figure drawn to a 

 very large scale,* since be- 

 tween the ordinntes^i and ^^ 



of the two isotherms belonging to a given v, the following relations- 'i 



exist ; 



or also 



P\-Pz = {'ri — X2) 



RiT 



V 



Pi 



A'a -j- .^_, l\i 



Butthisquotieutisalways very nearuiiity, since all the values of a." that 

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

 of cases one can consider all the isotherms (T, .r) corresponding to a» 

 given value T as coinciding witli each other and have then oidy to re- 

 member that accor<ling to the value of x they have their initial ])oiMts 

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

 jjoint curve IS\ we obtain another one S-, in that as already done in 

 figure 29 we simply go with a constant ratio of exi)ansiou or compres- 

 sion further along an equilateral hyperbola drawn through *S']. 



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, ou 

 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, with such very small changes 

 in the constants as depend on the mixing ratio [or the quantity .r]. 



* It must Lere be expressly remarked tbat all the diagrams occuriuor in this memoir 

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

 as they result from the computation the dia<;rams 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. 



