516 F. II. Bigelow — Thermodynamics of the 



Adiabatic. Nonadiabatic. 



(3) Temperature . T = T - a z. T = T - az = T - — ° z. 



dT= - adz. dT = - adz = - — ° dz. 



11 



„, _ . . . dT RadP dT R a<l dP 



(4) Logarithmic. -7^ = — -tT • -rrr = '-=-• 



v/& T g P T # » . P 



From formula (26) of the paper referred to above. 



....... R *— 1 R «„ A-i 



(5) Auxiliaries — «„ = — 5 — . " = — 7—. 



v ' g k g n nk 



It is seen that one passes from the adiabatic system to the 



nonadiabatic system by the factor n = — the ratio of the two 



a , , 



gradients. Take the general law in two strata for the ratio, 

 _pR _P T, 



P 



and substitute the value of p respectively from 6, 







1 n , 1\ 



pR_ /T\fc=i + pR_/T\k=i + ( n - 1) ' 



Hence we make the following important inference : 



1 n n — 1 



This means that the gas coefficient R is a constant in the 

 adiabatic system, but it is a variable in the nonadiabatic 

 system. The further significance of interest is that the specific 

 heat is a variable in the nonadiabatic air. 



k k 

 (9) Cp a = R„ = (constant) . Cp = R j (variable) . 



K 1 rC 1 



* k = ratio of specific heat at constant pressure, divided by specific heat 

 at constant volume. 



