F. II. Bigelow — Earths Nonadiahatic Atmosphere. 515 



Art. XLV. — The Thermodynamics of the Earth? $ Non- 

 adiahatic Atmosphere; by Frank H. Bigelow. 



Introduction. 



The observations in tbe free air of the earth, by means of 

 balloon ascensions np to 18,000 or 20,000 meters elevation, 

 indicate that the atmosphere does not conform to the adiabatic 

 relations of pressure, temperature, density and gas coefficient, 

 but that except for occasional conditions it is a nonadiabatic 

 atmosphere. It is, therefore, necessary to derive the thermo- 

 dynamic formulas in forms that are applicable to such an 

 atmosphere, wherein the nonadiabatic relations are incessantly 

 varying through considerable ranges. The formulas here 

 employed have been checked in numerous ways, and they have 

 been applied to the solution of several well-known outstanding 

 meteorological problems, (1) the cause of the semi-diurnal 

 waves of barometric pressure, (2) the cause of the isothermal 

 layer in the upper levels, (3) the general circulation on a 

 hemisphere, (4) the local circulation in cyclones and anti- 

 cyclones, (5) the cause of the diurnal variations of the ter- 

 restrial magnetic field. In this paper our applications of the 

 formulas will be limited to the causes of the isothermal layer. 



The adiabatic and the nonadiabatic formulas. 



The temperature gradients in a vertical direction are taken, 



dT 



a n = — -r^ = — 9*8695° C. per 1000 meters for an adiabatic 



atmosphere ; the}* are actually observed, a = — = — -j- 



and are very variable, so that n ranges through large values, 

 and is n=l for an adiabatic stratum. Assume the following 

 notation : T„ temperature, P pressure, p density, R d gas 

 coefficient in the Boyle-Gay Lussac Law, P =p R T , on one 

 level, and P=pHT on another level, as 1000 meters higher. 

 If the acceleration of gravity is <7 =9'806 meters per second, 

 and the system of constants is that of the kilogram-meter- 

 second system (K.M.S.), as given in Table 14, Monthly 

 Weather Review, March, 1906, we can proceed as follows to 

 develop the corresponding formulas. Assume (1), (2), (3), for 

 the adiabatic and the nonadiabatic systems, respectively, and 

 by simple substitutions the others are readily derived. 



Adiabatic. Nonadiabatic. 



(1) Gravity gpdz— — dP. gpdz = — dP. 



(2) Pressure P = P RT. - P = P RT. 



