AEROSTATICS. 245 



But W W is just equal to the weight of the first 

 of the three strata, and W' W" to that of the 

 second ; therefore D D' : D' D" : : D : D', and 

 multiplying extremes and means DD" D' 2 . The 

 density of the middle stratum, is therefore a mean 

 proportional between the densities of the other two, 

 and whatever be the number of equidistant stra- 

 ta, their densities are in continual proportion, 

 



34*0. If, therefore, the heights from the surface 

 be taken increasing in arithmetical progression, the 

 densities of the strata of air will decrease in geome- 

 trical progression. Also since the densities are as 

 the compressing forces, that is, as the columns of 

 mercury in the barometer, the heights from the 

 surface being taken in arithmetical progression, 

 the columns of mercury in the barometer at 

 those heights will decrease in geometrical progres- 

 sion. 



As logarithms have, relatively to their numbers, the 

 same property, therefore if b be the column of mer- 

 cury in the barometer at the surface, and /3 at any 

 height h above the surface, taking m for a con- 

 stant co-efficient, to be determined by experiment, 



h = m (log b log /3), or h m log - . 







It is evident, that m may be determined by finding 

 trigonometrical! y the value of h in any case, 

 where b and /3 have been already ascertained. Now, 



when 



