BAROMETRICAL MEASUREMENT OF HEIGHTS. 413 



, T. , T., (g) (H' — H) (397.25 — KT) 

 log B - log B' ^ ^^25-ir(H-"K T)— ^ X 



r (a + a') . 0.34807 ^^ 0.0301975 T — 0.000080170 TH 



[^ ~~ (397.25 — KT) y/ B B' ' J' 



Making further, 



0.34807 ,^ 0.0301975T — 0.000080170 T^ 



W r^ — . 10 



397.25 — KT 



we shall have for the logarithm of the approximate difference of level between the 

 two stations H' — H, 



log (H' — H) = log [log B — log B'] 



+ log V + log ' + log ^f . 



Table I. gives the values of log V and log W, both of which only depend on the 

 temperature ; the argument is the sum of the temperature of the air, t and t', ob- 

 served at both stations, supposing r -f- t' = 2 T. 



Table II. gives the factor depending on the humidity of the air ; with the argu- 

 ment 



W . loo- ^+_"Q, 

 » y/ B B' ' 



we obtain 



log — 7 — , — ;- = log v. 



V B B' 



Table III. gives the factor depending on the latitude for every degree, viz. 



log G' = lojT 



The logarithm of the approximate difference is thus given by the sum of four 

 logarithms. To obtain the exact elevation, the small correction found in Table IV. 

 must be added to the number corresponding to that logarithm. For we have, with the 

 necessary accuracy, 



h' _ 7t = H' — H -h — - . 

 a a 



Table IV. gives, for every 200 metres, the quantity — ; the number in the table 

 corresponding to — must be added to the approximate elevation ; and the number 



TT 2 



corresponding to — must be subtracted from the same. 



D 73 : 



