320 



NOTE II. 



THE law of density of the several strata of the air, deter 

 mined by Newton, is not, as we have seen, sufficiently 

 accurate to be of any practical utility. 



Nevertheless the expressions for the density in times of 

 the height are not without their use. Thus they enable 

 us to determine the heights of mountains by barometric 

 observations. Let /?, p, r be the pressure, density, and tem 

 perature at an altitude z. Let a be the radius of the 

 earth, g Q the force of gravity at the surface. Then the 

 force of gravity at an altitude z will be very nearly 



where n is some constant. If the upper station be in the 

 air, the law of gravity shows us that 



n = 2; 



but if, as is usually the case, the upper station be on a 

 mountain, the attraction of the elevated ground must not 

 be neglected. In this case the value of n will depend on 

 the form of the mountain. It is found that 



5 

 * = 4 



is sufficiently accurate for our present purpose. Retaining 

 the general form of g, we have, as before, the two equa 

 tions 



