A T M 



AlwofpJiere, density of. 



7. The density of the air is in proportion to the force which compres- 

 ses it, or to its elasticity, or inversely as the spaces within which the 

 same quantity of it is contained. 



8. If altitudes be taken from the earth's surface in arithmetical pro- 

 gression, the density of the air decreases in geometrical progression. 



9. Given the altitude above the earth's surface, to find the density of 

 the air ; and conversely. 



Let y density at the distance .T from the earth's surface, & the den- 

 sity at the surface, and // the height of the homogeneous atmosphere, 

 then 



y d x e * , or by Art. 6, y I X * * D 

 Or conversely, having given the density to find the altitude, we have 



x It, x hyp. log. ; or in common logs, nearly x 1000 x log. 7T. 



In the above formulae I and y denote the atmospherical pressures at 

 the surface and altitude #, for which we may substitute M and m, the al- 

 titudes of the mercury in the barometer at those distances ; we shall then 

 have 



x = 1000 x log. . 

 tn 



This gives only the approximate height; for the correct formula- 

 see Barometer. 



10. If, instead of supposing gravity constant, we assume it to vary in- 

 versely as the 71 power of the distance, we shall have, putting the 

 earth's radius r, 



y a *. 



which is a general Equation, expressing the relation between the alti- 

 tude and density. 



Cor. If F varies as -Y^J V %. j j 



^T- \~r "" r+Tr/ 



hence if r -f x increase in harmonical progression, is in arithm?- 



4. x 



tic, and ,*, the densities themselves \vi]l decrease in geometric. 



