124 HEIGHTS DETERMINED BY THE BAROMETER. 



tion at the surface and at a height z, the negative sign being 

 taken because the density is a decreasing function of the 



height z. 



dp _ 7- 8 dz 



J'' ~h (r + *)' 



Integrating, observing that when z = 0, p = p', we 

 ave 



, P i*l 1 1\ 



log -, = j-( 1: 



6 p h \r + z rP 



P' 



P ~ 



r!/ 1 _._L\ ' 



A \r r+*/ 

 C 



which shows that, if r -f z increases in harmonic progres- 

 sion, - - will decrease in arithmetic progression, and 

 therefore p will decrease in geometric progression. Hence, 



// a series of heights be taken in harmonic progres- 

 sion, when the force of gravity is regarded as variable, 

 the densities of the air decrease in geometric progres- 

 sion. (See Eland's Hydrostatics, p. 258.) 



74. Heights Determined by the Barometer. A 



very important use of the barometer is to find the difference 

 of level of two places situated at unequal distances above 

 the surface of the earth. Since the height of the column of 

 mercury in the barometer depends on the pressure of the 

 atmosphere (Art. 43), and as the pressure of the atmosphere 

 at any point depends upon the height of the column of air 

 extending from that point to the top of the atmosphere, it 

 follows that this pressure will decrease as we ascend above 

 the earth's surface, and therefore that the height of the 

 column of mercury will diminish. That is, the mercury in 

 the barometer will fall when the instrument is carried from 



