59° SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 5.1 



By reason of equation (2a) we have 



K - X C 



(0) ~C p x J {T 2 -T)dm 2 



whence 



f lK + (R) = C p \ (J, - T[)dm 1 + j J (T 2 - T)dm, 



In equation (5) in chapter II, §20, for a, the vertical gradient 

 of temperature, substitute the values g/C p for the masses 1 and 1' 

 and Xgl(K.C v ) (see eq. 6 §36) for the masses 2 and 2' and we obtain 



J 



J 

 J 



s 



B 1 



T x dm x = — . — — . (p 01 T Q1 - /> A T hl ) 



Zg 1 + A. 

 5 1 , , 



T x dn h = — . y^T k ■ (P T - Pi T it ) 



B 1 



7 , d m, = — . Y^TJi •• ^ 02 r ° 2 ~~ ^ r ^ 



5 1 



r dm 2 = — . — -^ • (Pi r*2 - /> A r to ) 



§(38) Example. In order to make the fictitious gas similar to 

 moist air we compute the values for the initial condition in a dif- 

 ferent order of succession than that above given. 



Initial stage. For mass 2: assume T 02 = 303 , p 02 = 760, p h = 

 5oo mm mercury and seek first the value of T h2 for saturated moist 

 air, that is to say, the temperature that such air attains when it 

 expands from 303 and 76o mm to 5oo mm mercury. This value lies 

 between 289 and 290 . 



We adopt T h2 = 290 and with it by equation (ia) compute X = 

 0.1047307 and further the vertical gradient of temperature in 



>* g 



mass 2 or a 2 = — — = 0.0035780 degree Centigrade per meter 



K L v 



which is nearly 3. 6° per 1000 meters. 



Finally we compute 



T — T 



h = — = 3633.29 meters 



a 2 



Initial stage. For mass 1 we adopt the same temperature at 



