VI. 



LAPLACE'S FORMULA FOR COMPUTING DIFFERENCES OF ELEVATION FROM 

 BAROMETRICAL OBSERVATIONS, MODIFIED BY BABINET. 



IN the Comptes Rendus de P Academic des Sciences for March, 1851, M. Babinet 

 proposes the following modification of Laplace's formula, the object of which is to 

 dispense both with the use of logarithms and with tables of any kind. 



Laplace's formula is, 



% = 18393 metres (log H - log h) [l + - ( ^+- ) -] , 



z being the difference of level between the two stations, 



H, the height of barometer at the lower station, 



A, the height of barometer at the upper station, 



T, temperature of air at the lower station, 



Z, temperature of air at the upper station. 



The two barometers are supposed to be reduced to the same temperature. The 

 small correction for the latitude is omitted. 



For elevations less than 1000 metres, and even for much greater elevations, if 

 approximate results only are needed, the formula may be transformed into the fol- 

 lowing : 



Example 1. 

 Suppose, 



at lower station, barometer at zero Cent. = 755 mm> ; temperature of air 15 Cent. 

 at upper station, barometer at zero Cent. = 745 mm - ; temperature of air 10 Cent. 



H h = 10 mm - T + t = 25 Cent. 



H + h = 1500""- 2 (T + t) = T $fo = .05. 



Then z = 16000 T |^ X (1.05) = 112 metres. 



Laplace's formula, by Delcros's tables, would give 111.6 metres. 



Example 2. 

 Suppose, 



at lower station, barometer at zero Cent. = 730 mm ; temperature of air 20 Cent. 

 at upper station, barometer at zero Cent. = 635 mm ; temperature of air 15 Cent. 



H h = ~95 mm ' T + t =~35 Cent. 



H + h = 1365 mm - 2 (T + = T&&IF = - 07 - 



Then z = 16000 T || x (1.07) = 1191.5 metres. 



Laplace's formula, by Delcros's tables, would give 1191.1 metres. 

 For greater elevations an intermediate station may be supposed. 

 Babinet's formula reduced to English measures becomes, 



= 52494 English feet * ~ J [l + 



but as, in this form, it loses the simplicity of its coefficient, it will be found, on trial, 

 that its use requires rather more computing than the author's tables (II.), p. 38, which 

 give more accurate results. 

 D 6t> 



