XX INTRODUCTION. 



REDUCTION OF THE BAROMETER TO SEA I.EVEI.. 



The fundamental formula for reducing the barometer to sea level and 

 for determining heights by the barometer is the original formula of I^aplace, 

 amplified into the following form — 



in which /i = Height of the upper station. 

 /z„ = Height of the lower station. 

 Z=/i-K. 



p = Atmospheric pressure at the upper station. 

 p^ = Atmospheric pressure at the lower station. 

 R = Mean radius of the earth. 



Q = Mean temperature of the air column between the altitudes 

 h and /^„. 



e = Mean pressure of aqueous vapor in the air column. 



b = Mean barometric pressure of the air column. 



<fi = L/atitude of the stations. 

 J^= Barometric constant. 



a = Coefficient of the expansion of air. 



k = Constant depending on the figure of the earth. 



The pressures /„ and p are computed from the height of the column of 



n 



mercury at the two stations ; the ratio -^ of the barometric heights may be 



substituted for the ratio -f, if B^ and B are reduced to the values that would 



P 

 be measured at the same temperature and under the same relative value of 



gravity. 



The correction of the observed barometric heights for instrumental tem- 

 perature is always separately made, but the correction for the variation of 

 gravity with altitude is generally introduced into the formula itself 



If B^, B represent the barometric heights corrected for temperature only, 

 we have the equation 



/x being a constant depending on the variation of gravity with altitude. 



log^ = log§ + log(i+^|). 



Since -^- is a very small fraction, we may write 



Nap. log ( I f ''/) = "/, and log ( i + "/) ==>^ M, 

 M being the modulus of common logarithms. 



