652 Lieutenant Rennt on the Constants of 



Various Formulce for determining the Height of Mountains, by means of Obser- 

 vations, Barometrical, Hygrometrical, and Thermometrical. 



Let z be the height of one station above the other. 



Let h be height above the level of the sea of lower station, supposed to be 

 knoivn. 



Let h' be height above the level of the sea of upper station, as yet un- 

 known. 



Then z^{h'-h). 



Sletres. 



Let r be radius of the Earth = 6369668-0 metres = 20898240'0 English feet. 



vfi 



Let r be j4, a known quantity. 



r + h ^ ■' 



rh' 



Let T-, be x, as yet unknown, to be determined by formula. 



r-\-h' ■' 



X- A- 

 Now, it is easy to prove that z - {h' - h) = {x - A) -\ , very nearly. 



Let C be the constant for latitude 45°, at the level of the sea, at freezing- 

 point, and = 18404-9 metres = 60384-6 English feet : vide Appendix. 



Let ^ be the mean latitude of stations of observation. 



Let f be half the increase of gravity from the Equator to the Pole of the 

 Earth =0-002695. 



Let k be expansion of air for one degree of Centigrade thermometer 

 = 0-003665. 



Let I be expansion of air for one degree of Fahrenheit = 0-002036111. 



Let m be expansion of quicksilver for one degree Centigrade = 0-00018. 



Let n be expansion of quicksilver for one degree Fahrenheit =0-0001. 



Let j3, /3' be barometric pressures of atmosphere at lower and upper stations 

 of observation. 



Let T, t' be temperatures (Centigrade) of the atmosphere at lower and 

 upper stations of observation, as shown by the detached thermometers. 



Let t, t' be temperatures (Fahrenheit) of the atmosphere at lower and upper 

 stations of observation, as shown by the detached thermometers. 



Let T, T' be the temperatures (Centigrade) of quicksilver of the barome- 

 ters of the lower and upper stations, as shown by the attached thermometers. 



