THE CISTEEN BAROMETER. 99 



it. The relation between altitude and atmospheric pressure, as .stated by 

 Gilbert, is as follows: 



The difference in height of ;uiy two localities is equal to a certain constant 

 distance multiplied by the difference between the logarithms of the air pressures at 

 the two localities. 



This relation gives the first and principal term in the various tables for 

 the reduction of barometric, work. Different determinations of the constant 

 distance, known as the "pressure constant," have been made, and these 

 different pressure constants cause the principal differences in the various 

 tables in use. 



Of the different sets of tallies yielding good results, the most con- 

 venient for use are those known as Gruyot's. They are published in the 

 Smithsonian Miscellaneous Collections, No. 13, and republished in this 

 volume tables I to V. These tables are derived from the formula of La 

 Place and use his coefficients. The formula, reduced to English measures, 

 is as follows : 



Zzrlog. A x 60158.6 English feet 



t + tf-64) 



K . 900 



(1+ 0.0026 cos 2 L) 



. Z + 52252 h ) 



I 1 + 20886860 + 10443430 ) 



h — the observed height of the barometer \ 



r — the temperature of the barometer > at the lower station; 



t — the temperature of the air ) 



lil zz the observed height of the barometer \ 



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



t' — the temperature of the air ) 



Z — the difference of level between the two barometers ; 



L zz the mean latitude between the two stations; 



H zz the height of the barometer at the upper station reduced to the 



temperature of the barometer at the lower station; or, 

 H zz V [1 + 0.00008967 (t — t')\. 



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 



