BAROMETRICAL MEASUREMENT OF HEIGHTS. 370 



hand, we have no right 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 } 



T = the temperature of the barometer > at the lower station ; 



t = the temperature of the air ) 



h' = the observed height of the barometer } 



T ' = 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 ; 



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

 perature of the barometer at the lower station ; or, 



H= h' \l + 0.00008967 (r r')\ ; 



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

 1 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 : 



Z = log - X 60158.6 English feet < 



1 



/ 

 . \ 



900 



(1 + 0.00260 cos 2 L). 

 +52252 



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 (T T') for the difference of the tem- 

 peratures of the barometers at the two stations, or r r 1 . As the temperature at 

 the upper station is generally lower, r r 1 is usually positive, and the correction 

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

 and T 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. 



z I 52252 

 Table IV. shows the correction D' - - to be applied to the approximate 



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

 mercurial column. It is always additive. 

 D 33 



