[26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



tion. This distribution is a function of the temperature, and con- 

 sequently even the pressure of a dry atmosphere will vary with 

 the temperature in such manner that the pressure will diminish in 

 proportion as the temperature increases. However, the variation 

 of gravity for atmospheric strata at slight elevations is so slight that 

 its action can be neglected in meteorology. 



§3. Temperature of the atmosphere 



Temperature depends on many considerations and there has 

 not yet been found any function that expresses the temperature 

 in terms of the coordinates of position and the time. 



The heat of the sun and of space, the absorption of the earth and 

 of space, the radiation, the conductibility and the movement of the 

 air, all affect the temperature. Hitherto we have sought to deter- 

 mine the temperature at the surface of the earth as a function of the 

 time. We shall see that the variation of the temperature with the 

 height is of the greatest importance in meteorology. The observa- 

 tions of this phenomenon are not numerous and it seems not to 

 follow simple laws. But one can at least recognize that at slight 

 elevations where the action of the sun is most energetic the layers 

 of air experience equal variations of temperature, while it is very 

 probable that in somewhat elevated strata the variation is slight, 

 and that whatever may be the temperature at the surface of the earth, 

 we shall always arrive at the same temperature at a certain height 

 which will however oscillate slightly. 



We shall apply some approximate formulas. The most simple 

 hypothesis is that the temperature decreases proportionally to the 

 height; then we have 



t = t - az\ 



where z is the height; a, a constant and r the temperature at 

 the surface of the earth. In some problems it will be more con- 

 venient to introduce the above described virtual temperature and 

 write 



T = T - a z. 



These two formulae apply only to small heights; if we wish to cal- 

 culate the variation of temperature for the greatest height, we can 

 divide the whole elevation into layers and apply the formula to 

 each stratum with different values of a. 



