236 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



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

 batic to infinity. If we do this in the case when the quantity of moisture 



is # 1U , then will the projection of the 

 ~ adiabatic be represented by the line 



PM Jf„ but by the line PN N 2 when 

 the quantity of vapor is a?„, because 

 in the first case under the pressure 

 M M n in the second case under the 

 pressure N N„ the air passes out of 

 the dry stage into the rain stage, 

 and therefore theadiabaticdesceuds 

 g according to another law, and in 



1jS» fact less precipitously. But the dif- 

 ference in the internal energy cor- 

 responding to the quantity of vapor 

 s-32- belonging to the condition repre- 



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

 A [ U m — U n ], is graphically represented by the surface M 2 M N N 2 , in so 

 far as we imagine M 2 and N 2 extended to infinity and there united 

 together. 



When expressed analytically we find for this difference the expres- 

 sion — 



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

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

 mixed aqueous vapor. However, this difference is so slight that in most 

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

 approximation — 



A[U m - U n ] = (x m - x n ) (t + p). 



By this simplification the application of the above-described combina- 

 tion of planimetiic measures and computations to the determination ot 

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

 peratures are below 0° then the last formula must be slightly modified, 

 which here need only to be referred to. 



After having thus explained and established in general terms this 

 new method of presenting the thermo-dynamic processes peculiar to the 

 atmosphere their applicability will now be elucidated by a few exam- 

 ples. 



(1) ThefoeJm. 



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

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

 or withdrawn. 



