1826.] Measurement of Heights by One Barometei-. 41 



Shuckburgh estimate it, as might be anticipated from their igno- 

 rance of the laws of the dilatation, 8cc. of moist air, considerably 

 in error, stating it to be 60000. 



Being, however, assured by Laplace that his formula agrees 

 with the ensemble of the excellent observations of Ramond, we 

 may venture to adopt it as the basis of the tables. Calling X 

 the difference of level, H the height of the barometer, T that of 

 the centigrade thermometer at the lower station, and k, t, the 

 analogous quantities at the upper one, the pressures being cor- 

 rected for difference of temperature of the mercury, the formula 

 s;ives 



X = 60345 ft. {I + -002837 cos. 2 lat.} \^+ ^ZoV^ l ^^^-f' 



Adapted to the more convenient zero of Fahrenheit's scale, 

 the formula becomes 



X = 56054 {1 + -002837 cos. 2 lat.} \l+ |^'j log. ?.* 



If we conceive a number of barometers so stationed one above 

 another that they shall indicate, in an atmosphere uniformly of 

 the temperature of0° F. equal differences of pressure of the 

 value of '01 inch, we may find the perpendicular height of the 

 upper one h', standing at 21 inches, above the level of those 

 beneath it, by the formula 



66054 feet, log. „ " ■ . (See Table II.) 



' => 21'00 inches ^ "^ 



The resulting heights with the corresponding pressures from 

 21-00 to 31-00 inches, being arranged in a table, the difference 

 of level of any two of the inferior barometers, of which the pres- 

 sures are given, is obtained by mere subtraction. 



The pressures being generally expressed in thousandth parts 

 of an inch, the value additive in feet of the last figure (from -001 

 to -009) may be found and tabulated by multiplying it by 24-345 

 divided by the required pressure. (See Table III.) 



• Adopting the Daltonian theory of the constitution of the atmosphere, the correction 

 for humidity will be very simple. We have but to subtract from the pressures (reduced 

 to 3'i" F ) the force of the vapour corresponding to the observed dew point ; and make 

 the calculation after the following fo-.mula for an atmosphere of perfectly dry air, viz. 



■r = log. (-~r\ . 562S0 . (I +002837 . cos. 2 lat.) (l ^') \ 1 + ?-!^? , 



wherein R is the elevation of the lower station, and r that of the upper one above the 

 level of the sea ; n, the earth's radius in feet ; F the tension of the vapour at the base ; 

 and / its force at the summit. 



When F is to II as /is to //, the pressure of the atmosphere of vapour on the mercury 



does not affect the calculation, and we may use — or indifierently. The ratio of 



/ to A being greater (or less) than tliat of F to H, the altitude computed with — in lieu 



h 



of the pressure! diminished by the tension of the vapour, will err in defect (ox excess). 



