410 Count Paul de Saint-Robert on the Measurement 



This is the expression of the height necessary to ascend to 

 have a fall of one degree in the temperature. We see that it in- 

 creases while the elevation increases, as it ought to be in accord- 

 ance with Mr. Glaisher's results. 



We shall now proceed to investigate the formula for the com- 

 putation of heights by means of the barometer. 



II. Barometrical Formula. 



The equation of equilibrium of the atmosphere, taking into 

 account the variation of gravity, is 



d P=-Vo(y) P dr > 

 g being the gravity at the lower station. Putting, as before, 



we get 



If we assume 



we shall have 



dp=—g pdx. 



P = Po( l — ax )> 



dp=-g p Q {l-aoc)dx; 



whence, integrating, 



/_ ax\ 

 Po-P=9oPo x [ 1 -y)' 



Eliminating a between this equation and the last but one, we 

 shall find 



g= g (Po-P\ 



9oWo-rP> 



We could have obtained directly, without help of the infinite- 

 simal calculus, this expression by the simple consideration that 

 the weight of the column of air comprised between the two sta- 

 tions must be equal to the difference of pressure. 



As the density of the air is not given directly by the instru- 

 ments employed in barometrical mensuration, we shall put in 

 place of p its value 



p — mm 



Consequently we shall have for the barometrical formula, 



T _ 2c Po-P 



g p — mvr p — mvr 



t + t 



