BAROMETRICAL MEASUREMENT OF HEIGHTS. 



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

 In Table III., with the arguments A and r, take C ; 

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

 Make, further, 



M =. A + C + C and ^ r' ; 

 And if h' be given, and h required, 



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



then is H = H'H-(t^-j^r'), 



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



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



In Table II., with the argument 5, take H'. 

 Make, further, 



H' = H - (« - j2-„ /), 

 and h' 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 J' = 

 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' = 11°.8 ; t = 11°.8 -f- 4°.98 ■ t -\- t' = 28°.58 ; 



2 T = ^^ = 14° .29 ; r = 7°.15 ; 

 and according to Table I. t' = "h 6.67. 



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

 With h and <^, in Table IV., we find C = -{- 0.3 



We add h = 498.2 



and we have u = 497.1 ; 



— Za r = — 33.15 

 100 



463.95 

 With b', 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 61 



