BAR03IETRICAL MEASUREMENT OF HEIGHTS. 399 



In Table I., with tlie argument 2 t, take t' ; 



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



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



Make, furtlier, 



« = /» + C + C and ^^^ r' ; 

 And if I' be given, and b required. 



In Table II., with the argument h, take II ; 



then is H = H' 4- (ti r'), 



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



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



In Table 11., with the argument J, take H''. 

 Make, further, 



H' = H _ („ _ j;„ X'), 



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 h' = 

 29.'j.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 1°.8 ; t = 1 T.S + 4°.98 ; t -\- t' = 28°.58 ; 



2 r = ^^ = 14°.29 ; r = 7°. 15 ; 



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



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

 With h and <^, in Table IV,, we find C = + 0.3 



We add h = 498.2 



M 



and we have u = 497.1 ; io6 "" ^'^'^ 



„ T' = + 6.67 



T == —33.15 29 83 



100 2.98 



.31 



^■^.' = +33.15 



463.95 

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



H = 831.81 



Finally, with H, in Table TI., 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 



