412 • ' BAROMETRICAL MEASUREMENT OF HEIGHTS. 



or about ^-^g smaller than the value adopted by Bessel. If the constant coefficient 

 L is expressed by L = w^ , /x being the modulus of the common logarithms, its 

 numerical value becomes 



L = 18404'"-.8. 



In order to reduce the formula into tables, Bessel caused it to undergo several 

 modifications, which we have followed, introducing the values of the constants above 

 mentioned. 



Let b and b' be the heights of the barometer, expressed in the metrical scale, at 

 the two stations; t and i', the temperatures of the mercury measured with a brass 

 scale ; we have, 



p_ ^ (fr\ { ^ Y-* (1 + 0.00001879 

 ~ 0'"-.76 * '^^ * \a + h) (1 -j- 0.00018018 0' 

 and 



.00001879/') 



on,.. 76 VS/ \^a + /<7 (1 + 0.( 



.00018018 r) 

 Therefore, 



log P = log 5 + log (g) — log 0"^- .76 — ^~^- — fi t [0.00018018 — 0.00001879], 

 log P ==: logZ''4- log(^) — log0'"-.76 — "^ '^ — ^f [0.00018018 — 0.00001879]. 



If we call B, B' the heights of the barometer reduced to the freezing point, which 

 we obtain by making 



log B = log J — K 0.000070095 ; log B' = log V — i> . 0.000070095, 



log l = log B _ log B' + ^ - ^, 

 and with sufficient accuracy, 



0"'".<b 



Substituting these expressions in the formula, it becomes, 



log B — log B' = 



(flr).n' — HI" L(1+KT) a. 0.001748 0.0301975 T — 0.000080170 TH 



L (T4nv~T) [ (a) . 7329755 y^B B' ' J' 



If we set instead of a the half sum - of the fraction of saturation observed at 



2 



both stations, we find, after some transformations, 

 D 72 



