BAROMETRICAL MEASUREMENT OF HEIGHTS. 



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

 L is expressed by L = -^ 

 numerical value becomes 



L is expressed by L = -^ , /t being the modulus of the common logarithms, its 



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 I' 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_\ 8 (1+ .0.000018790 



- O m.. 76 (S) ^ a _j_Ay (i -j-0. 00018018 0' 

 and 



p,_ V , v /a y (1 -f- 0.00001879 Q 



- O m. >76 (S) ^a-j-Ay (i _j_ o.OOOl 801 8 1)' 



Therefore, 



log P = log I + log (g) log O m -.76 !5i ,, t [0.00018018 0.00001879], 



I 

 log P = log If + log (g) log O m -.76 ?^ __ p 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 I t . 0.000070095 ; log B' = log V t' . 0.000070095, 



and with sufficient accuracy, 



0"'-.76 

 Substituting these expressions in the formula, it becomes, 



log B log B' = 



(g) H/ H T L (1 -f K T) a . 0.001 748 0.0301 9 75 T 0.000080170 T 2 "| 

 L (1 + K T) L 1 - ( g ) . 73 29755 " ^~^~ ' 1( 



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

 both stations, we find, after some transformations, 



D 



74 



i 



