Barometer applied to the Measurement of Heights. 359 



taining the laws of the density and elastic force of the air which 

 belong to a state of equilibrium in the atmosphere. 



472. To make use of equation (n) for the purpose of measur- 

 ing heights by means of the barometer, let us suppose the ba- 

 rometric altitude at the surface of the earth and at the height h 

 to be known by actual observation, and let them be denoted res- 

 pectively by to, zo', the corresponding temperatures of the mer- 

 curial columns being represented by T, x'. The expansion of 

 mercury being g^ or 0,001025, that is, 0,001 nearly, for each 

 degree of Fahrenheit's scale, if D be the density corresponding 

 to the temperature T of the mercury at the first station, 



D (1 + 0,001 ( T 7 ) 



will be the density which answers to the temperature of the 

 mercury at the second station. Accordingly we have 



zr = Dg zr, and p = vg' w' (1 + 0,001 (T T'). 



The correction for the upper barometric column on account of 

 difference of temperature being made agreeably to this formula, 

 we may consider w' as representing the length of this column 

 thus corrected. Whence, dividing the first of the above equa- 

 tions by the second, we have 



= !L x 



p g 1 



substituting for g' its value ^ * ; and consequently, 



log. = log. + 2 log. (1 + , ( m .) 



since 



Let T, T', be the temperatures respectively of the air at the 

 surface of the earth and at the height h ; T, T 7 , will generally 

 differ from ", T X , the temperatures of the mercury in the barome- 

 ter, since the latter is not ordinarily allowed sufficient time to 

 acquire the temperature of the surrounding air. T, T', are to 



