412 BAROMETRICAL MEASUREMENT OF HEIGHTS. 



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

 L is expressed by L = -~ , /A being the modulus of the common logarithms, its 

 numerical value becomes 



L = 18404 m \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 $', the temperatures of the mercury measured with a brass 

 scale ; we have, 



p_ b ( / a \ 2 (1 -f 0.00001879^ 

 - o m -.76 ' W ' \a -if- h) (1 -f- 0.000180180' 

 and 



(_ a y (1+0.00001879 Q 

 ' \a + &y (1 -f- 0. 



.000180180 

 Therefore, 



logP =log + log(gr) log O m< .76 ^?- p t [0.00018018 0.00001879], 



3i 

 9 TT' 



log P' = log b 1 + log (g) log O m .76 ? ,* t' [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 b t . 0.000070095 ; log B' = log V t' . 0.000070095, 



log*- = logB-logB' + ^-*, 

 and with sufficient accu-racy, 



UI> .76 



Substituting these expressions in the formula, it becomes, 



log B log B' = 



() . H' H F_ L (1 + K T) q . 0.001 748 1Q 0.0301975 T 0.000080170 T 2 ~| 



L(l-f-KT)l ~ (g) ." 7329 755 ~" \/ B"B'~ J' 



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



both stations, we find, after some transformations, 

 D 72 



