470 Mr. Lubbock on the Heat of Vapours 



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

 value of u, 



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

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



, 

 1 



R = H. See vol. xvi. p. 44-0. 

 ~ 



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 



the following formula for calculating heights by observations of the 

 barometer : 



- T [4-740*605] i j^t log ( 1 H q) in French metres, 



1 + 7T 



= [5-2564585] ^ "t/ ' log ( 1 Hq} in English feet, 



= [1-5338195]- + * ' log (1 Hq} in English miles, 



the temperature at the lower station being reckoned from the 

 freezing point. 



Log a = 7'3 187588 for Fahrenheit's scale. 



O 



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= [2-9935785] _ ^ 



J/ + -8405 

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



If we suppose y = 1*5, I find 



/3 = -3333 E = - 1-1920 log H = 9'7354232 



r = I 30 ' 69 * 83 ^ - 448. 

 ;/ + 1-1920 



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

 If we suppose y = 1*6, I find 



=-375 =-1-5112 log H = 9-7794573 



