414 



BAROMETRICAL MEASUREMENT OF HEIGHTS. 



Use of the Tables. 



Reduce first the observed height of the barometer at both stations to the freezing 

 point by means of the usual tables, or by the logarithmic formula, 



log B = log b — t . 0.00007, log B' = log h' — t' 0.00007 ; 



h and i' being, in fractions of metre, the observed heights at the temperatures t and t' 

 marked by the attached thermometers ; and B and B' the reduced height at the lower 

 and upper station. 



Take the difference of log B and log B', and find, in the tables of the common 

 logarithms, the loga-rithm of that difference, viz. log (log B — log B') ; find also 

 the logarithm of the product \/ B B', or 



logVBB'^^^^^^i^^. 



Make further the sum r -j- r' of the temperature of the air at both stations, and like- 

 wise the sum of a -}- a' of the fraction of saturation. 



Then, in Table I., with argument r -|- r', take log V and log W ; further, to log W 

 add log (a -|- a'), and subtract log \/BB' ; and with the logarithm thus obtained as 

 argument, take in Table II. log V'. 



Table 111. with the mean latitude of the stations gives log G'. 



H' — H being the approximate difference of level between the two stations, we 

 have 



log (H' — H) = log (log B — log B') + log V + log V + log G'. 



The altitude of the lower station being known, we deduce from H' — H the ap- 

 proximate altitude, H', of the upper station ; h', the exact altitude, or h' — h, the 

 difference of elevation, is given by the formula, 



JJ'2 JJ2 



k' — h^w — n-^-^ — — . 



' a a 



Table IV. gives the values of and — for the values of H' or H for every 



a a 



200 metres. 



Example 1. 



Computing the height of St. Bernard, taking Geneva, 407 metres above the level 

 of the sea, as the lower station. The observation gives, 



B = 726.43 millimetres B' = 563.64 millimetres 



^ ^ _|- 8°.97 Centigrade r' = — 1°.89 Centig. r + / = + 7°.0S 



a = 0.77 a' = 0.80 a-^ a' = 1 57 



log B =9.86119 log \/ (B B') = 9.8061 



log B' = 9^100 Table I. log W =^ 7.0511 



log B — log B' = aTl019 log (a + «') ^ 0.1959 



log ^" t,i? . W = 7.4409 

 D 74 



