BAROBIETRICAL MEASUREMENT OF HEIGHTS. 373 



hand, we have no rif^ht to expect such results from single observations, taken, per- 

 haps, in unsettled weather, without paying any regard to the time of the day at 

 which they were made, to the distance or the non-simultaneity of the corresponding 

 observations, or to other unfavorable circumstances. It is too well known that in 

 such cases large errors may and do actually occur ; but for these the formula ought 

 not to be held responsible. 



Arrangement of the Tables. 

 If we call 



h = the observed height of the barometer \ 



r n= the temperature of the barometer > at the lower station ; 



t = the temperature of the air ) 



h' = the observed height of the barometer i 



r' = the temperature of the barometer > at the upper station. 



t' = the temperature of the air ; 



If we make, further, 



Z = the difference of level between the two barometers ; 



L = the mean latitude between the two stations ; 



Jf = the height of the barometer at the upper station reduced to the tem- 

 perature of the barometer at the lower station ; or, 



H= h' ^ -f 0.00008967 {t — t')1; 



The expansion of the mercurial column, measured by a brass scale, for 

 r Fahrenheit = 0.00008967 ; 



The increase of gravity from the equator to the poles = 0.00520048, or 

 0.00260 to the 45th degree of latitude ; 



The earth's mean radius = 20,886,860 English feet ; 

 Then, Laplace's formula, reduced to English, measures, reads as follows : 



t -\-J' — 64\ 

 900 " /• 



|0 + -"-9oo— -;• 



log J. X 60158.6 English feet ^ (1 + 0.00260 cos 2 L). 



0+ 



z + 52252 h ) 



20886860^ ~^ 10443430/^ 



Table I. gives, in English feet, the value of log H or h X 60158.6 for every 

 hundredth of an inch, from 12 to 31 inches in the barometer, together with the value 

 of the additional thousandths, in a separate column. These values have been dimin- 

 ished by a constant, which does not alter the difference required. 



Table II. gives the correction 2.343 feet X (r— t') for the difference of the tem- 

 peratures of the barometers at the two stations, or r — r'. As the temperature at 

 the upper station is generally lower, t — r' is usually positive, and the correction 

 negatwe. It becomes positive when the temperature of the upper barometer is higher, 

 and r — t' negative. When the heights of the barometers have been reduced to the 

 same temperature, or to the freezing point, this table will not be used. 



~ -4- 5''25'^ 

 Table IV. shows the correction D' ^^Z,^"^^^ to be applied to the approxmnate 



altitude for the decrease of gravity on a vertical acting on the density of the 

 mercurial column. It is always additive. 

 D 33 



