126 HEIGHTS DETERMINED BY THE BAROMETER. 



Let h, h' be the observed barometric heights at the two 

 stations, whose altitudes are z and z' ; let a be the density of 

 mercury at a temperature zero, and r, T', the temperatures 

 at the two stations. Then we have, from (2) of Art. 52, 



p = yah (1 0r), 



and p' = yah' (1 0r'), 



which in (4) gives 



A i * (1 T ) (5) 



" 



where may be taken approximately equal to (r -f r') ; 

 from this equation the difference of the heights of the two 

 stations can be calculated. 



(2) When the force of gravity is regarded as va- 

 riable. 



If the heights above the earth's surface be considerable, 

 it is necessary to take account of the variation of gravity at 

 different distances from the earth's centre. 



Calling g the measure of the earth's attraction at the level 

 of the sea, and r the radius of the earth, then we have, for 

 the measure of the attraction at a height z, 



which, being substituted in (1) for#, gives 



Dividing (7) by (2), we have 



I,**!. - l 9'* dz 



p ' ~ 1 + at (r + *Y 



