BAROMETRICAL MEASUREMENT OF HEIGHTS. 



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

 L is expressed by L = -^r — ? /* 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 t', the temperatures of the mercury measured with a brass 

 scale ; we have, 



p _ 6^ , . /_*- V ^^ "^ 0.00001879 



"" 0»-.76 • ^^^ * \a+~A/ (1 4- 0.00018018 0' 

 and 



F= X 



b' / \ / a y (1 +0.00001879 Q 



^^^ \a + hy (1-f 0. 



0»-.76 ^^^ \a + A7 (1 4-0.00018018 

 Therefore, 



log P = log 5 4- log (g) — log O^-.TG — ?^ — fji t [0.00018018 — 0.00001879], 



logP = logJ'+log(g)— log 0™- .76 — -^-^ — It «' [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 — f . 0.000070095 ; log B' = log b' — t' . 0.000070095, 

 log I, = log B — log B' + ?J ~ ,^, 



o P' o D I 7329755 



and with sufficient accuracy, 



V'BB' 



\/PP' = 



0°'-.76 



Substituting these expressions in the formula, it becomes, 



log B — log B' = 



( g-) . H' _ H r L (1 -f- K T) a . 0.001748 ^^ 0.0301975 T — 0.000080170 TH 



L (1 4- K T) [ (g) 77329 755 J~^h~ ' \ 



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



2 



both stations, we find, after some transformations, 

 D 74 



