xHv INTRODUCTION. 



TABLES FOR DETERMINING HEIGHTS, AND CONVERSIONS 

 INVOLVING GEOPOTENTIAL. 



THE HYPSOMETRIC FORMULA AND ITS CONSTANTS. 



The fundamental formula for reducing the barometer to sea level and 

 for determining heights by the barometer is the original formula of Laplace, 

 amplified into the following form — 



or, where gi, the value of local gravity is unknown, 



(2) Z = K{i+ad)(-—^ \i+kcos2cl>-k'cos^-2 4>^C)fi+^-^^)\og^ 



in which h = Height of the upper station. 



ho = Height of the lower station. 



Z = h — Jiq. 



p = Atmospheric pressure at the upper station. 



po = Atmospheric pressure at the low^er station. 



R = Mean radius of the earth. 



6 = Mean temperature of the air column between the alti- 

 tudes h and Iiq. 



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



b = Mean barometric pressure of the air column. 



(}> = Latitude of the stations. 



K = Barometric constant. 



a = Coefficient of the expansion of air. 



k and k' — Constants depending on the figure of the earth. 



C = Constant = the ratio ^JUZl^ . 



9. 

 Qq = Standard value of gravity = 980.665 dynes. 

 gi = Local value of gravity. 



The pressures p^ and p are computed from the height of the column of 



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



. p . ^ 



substituted for the ratio — , if -Sq 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 

 temperature is always separately made, but the correction for the variation 

 of gravity with altitude is generally introduced into the formula itself. 



If Bq, B represent the barometric heights corrected for temperature 

 only, we have the equation 



p, B,( Z\ 



