23G 



THE MECHANICS OF THE EARTH S ATMOSPHERE. 



zero point, which of course woukl demand a continuation of the adia- • 

 batic to intiuity. If we do this in the case when the quantity of moisture-' 



isj7„„then will the projection of thfr' 

 adiabatic be represented by the linfr ■ 

 PM J/>, but by the line FN N2 when « 

 the quantity of vapor is x„, because-' 

 in tbe tirst case under the pressure 

 j\I M,, in the second case under the 

 pressure T A^^, the air passes out of 

 the dry staye into the rain stage, 

 and therefore the adiabatic descends- 

 according to another law, and in 

 fact less precipitously. But the dif- 

 ference in the internal energy cor- 

 responding to the (juantity of vapor- 

 belonging to the condition repre- 

 sented in r, and which by a self evident notation is expressible as 

 .1 [ U,,, — C,,], is graphically represented by the surface .1/.. .1/ N N2, in so 

 far as we imagiue il/2 and N-, extended to intinity and tliere united 

 together. 



When expressed analytically we find for this difference the expres- 

 sion — 



Fig. 32. 



A [ r„, — V„] — x,„ t„ — x„ /„ 4- x„, p„ 



-I'n /■>„■, 



wherein p expresses the internal latent heat, and one has to remember 

 that for given values of j; and v the temperature varies with the inter- 

 mixed aqueous vajjor. However, this ditference is so slight that in most 

 cases it may be neglected, and one can therefore be satistied with the- 

 ai»proximation — 



^ 1 r,„ - r„] = (.r,„ - ,r„) {t + ij). 



By this simplification the a])plieation of the above-described combina- 

 tion of jdanimetric measures and computations to the determination of 

 the quantity of heat interchanged is very much lightened. If the tem- 

 peratures are below O"^ then the last formula must be slightly modified, 

 which here need only to be referred to. 



After having thus exi)lained and established in general terms this 

 new method of presenting the fhermo-dynainic j)ro(;esses peculiar to tlie 

 atmosphere their applicability will now be elucidated by a i^\w exam- 

 ples. 



(1) Tliefoehn. 



Moist air expands during its rise up the side of a mountain chain, and 

 is then again compressed in its descent without having any heat added 

 or withdrawn. 



