470 Mr. Lubbock on the Heat of Vapours 



At the summit of the atmosphere q = 1, if w" be the corresponding 

 value of u, 



u" = - Nap. log ( 1 — H) c~ u " = 1 - H, 

 c being the number of which the hyperbolic logarithm is unity. 



. ^i a = — //. See vol. xvi. p. 440. 



l — Ep' 1 * 



p being the pressure at the lower station ; the pressure for -76568 m 

 or 30-14 inches of mercury in the barometer being unity. 

 I get, when 



r = l-5 ^ = ~"J £ = -1-192, 



the following formula for calculating heights by observations of the 

 barometer : 



— — r = [4-7404605] ^-jr^ log (1 - Hq)m French metres, 



= [5*2564585] ^ ^/ log (1 - Hq) in English feet, 



= [1-5338195] ^ "t/ ) log (I — JETy) in'English miles, 



the temperature at the lower station being reckoned from the 

 freezing point. 



Log a = 7*3187588 for Fahrenheit's scale. 

 If we assume the 21st observation of Gay Lussac, and suppose 

 y = 1-4, I find 



£ = - -2857 E = - -8405 log H = 9*6596173. 

 In Fahrenheit's scale 



T = P*M5785] - 448°. 

 y 3 + -8405 

 Height in miles = [1-9885722] log (1 — H q). 



If we suppose y — 1*5, I find 



/3=--3333 E=- 1-1920 log iJ= 9*7354232 



t = [SO'694832] _ ^ 

 / + 1-1920 

 Height in miles = [1-8457978] log (I - H q). 

 If we suppose y — 1*6, I find 



/3=--375 JS = — 1-5112 log #= 9-7794573 



