138 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



altitude. In truth the temperature will never be uniform on the 

 earth and equilibrium has therefore no place in nature. 



When the atmosphere is in equilibrium the law of variation of 

 the temperature with the altitude has no influence on the equi- 

 librium, but the stability of the equilibrium does depend on that 

 law. It is necessary to distinguish between stability with reference 

 to an ascending movement and to a descending movement. In 

 giving to a particle of air an ascending motion the temperature of 

 the particle of air can change more rapidly or more slowly than the 

 variation of the temperature of the surrounding air. If the tem- 

 perature of the ascending particle decreases more rapidly than the 

 temperature of the atmosphere, the particle will acquire a specific 

 weight greater than the surrounding air, and consequently it will 

 descend when the impressed motion is consumed, and we call the 

 equilibrium stable. If the temperature of the particle of air decreases 

 more slowly than that of the atmosphere, the particle will attain a 

 specific weight less than the surrounding air and it will continue its 

 ascending movement; then the equilibrium is unstable. 



By impressing upon a particle of air a descending velocity we see 

 in the same way that the equilibrium is stable if the temperature 

 of the particle is increased more rapidly than that of the surround- 

 ing air and that it is unstable if the temperature of the particle of air 

 increases more slowly than that of the surrounding air. 



The stability of the atmosphere depends consequently on the 

 law of the variation of the temperature of the atmosphere with 

 the height. 



Let us suppose that in a calm atmosphere the virtual temperature 

 decreases proportionally to the altitude according to the formulas 

 of §4; by impressing a slight velocity upon a particle of air we can 

 calculate approximately the variation of its virtual temperature 

 from formula (17) of §5. Let m be the coefficient of the particle 

 of air and m' that of the calm atmosphere, we see 5 that the equi- 

 librium is stable for an ascending movement when m < m'. 



The general cause of the disturbances of the equilibrium of the 

 atmosphere is the heat from the sun. The sun communicates heat 

 to the atmosphere both directly and by the intervention of the 

 surface of the earth indirectly. This quantity of heat represents 



Lei T and T' be the virtual temperatures of the particle of air and of 

 the calm atmosphere respectively we have 



PS sz 



T = T - — T = r u - — 



a m a m . 



