BAROMETRICAL MEASUREMENT OF HEIGHTS. 399 



In Table I., with the argument 2 r, take r' \ 



In Table III., with the arguments h and T, take C ; 



In Table IV., with the arguments h and <, take C' ; 



Make, further, 



=A + C + C'and^ T '; 

 And if b' be given, and b required, 



In Table II., with the argument Z>, take H ; 



then is H = H' + (u ^ r'), 



and the height of the barometer, in Table II., due to H, is b required. 

 If b be given, and b' required for a level higher by h toises, then, 



In Table II., with the argument J, take H ; . 

 Make, further, 



H ' = H -("-lfo'>' 



and b' is the height of the barometer in Table II., corresponding to H'. 



Example 1. 



Suppose the height of the barometer reduced to the freezing point to be b' = 

 295.39 Paris lines ; the temperature of the air t' = 11.8 Reaumur; and the latitude 

 < = 51. 48 ; the increase of heat downwards being 1 Reaumur for 100 toises. 

 What is the height of the barometer reduced to the freezing point, at a station lower 

 by h = 498.2 toises ? 



In this case, t 1 = 11.8 ; * = 11.8 + 4.98 ;* + *'= 28.58 ; 



2 T = *-^ == 14.29 ; T = 7.15 ; 

 and according to Table I. r' = -j- 6.67. 



With h and T, in Table III., we find C = 1.4 

 With h and <#>, in Table IV., we find C 7 = + 0.3 



We add h = 498.2 

 and we have u = 497.1 ; foo= 4 - 971 



T 4- 6.67 



463.95 



With J', in Table II., we find H' = 367.86 



H = 831.81 



Finally, with H, in Table II., we find b = 330.91 Paris lines, which is the required 

 height of the barometer at the lower station. Gauss's tables (IV.) would give b = 

 330.90 lines. 



D 59 



