98 CAUSES 



14. LET us now fuppofe that z is the whole height to be 

 meafured, and that A is the denfity at that height, the tempera- 

 ture there being alfo found /&, by obfervation. If then x be- 

 come = 2, and y =. A, we will alfo have AZ =: H b, and T+AZ zr 



Hh 



32 H+H h = 32 h =: r b, making r 32. Alfo A =. - . 



z 



Therefore, by fubflituting thefe values of y, x, A, and T+AZ, in 

 the preceding equation, we have, 



Hence, by tranfpofition, ttfc. 



Sp (#) (log. Dlog. &(Hb) g) - z (( i i) ( I-HB) } J 



and x - gp (H ~ b ^ (log ' D ~ log - A ~ C^~ ^)cf ). 



Li r h r 



(I OT) (I OT) 



THUS the height of any column of air is exprefled in ter.ms of 

 the denfity, and of the temperature at the top and bottom of it \ 

 the equation for the height, though an exponential one in its 

 general form, admitting of an eafy refolution, from the circum- 

 ftance of AZ being given by the obfervations of the thermome- 

 ter. 



15. THAT this formula may be applied to the meafurement 

 of heights, it is neceflary to introduce into it the lengths of the 

 columns of mercury in the barometer, inflead of the denfities of 

 the air, at the lower and upper flations. Let b be the height at 

 which the mercury ftands in the lower barometer, and (3 that at 

 which it ftands in the higher barometer j then, fince b is the 

 compreffing force at the furface of the earth, we have 



