BAROMETRICAL MEASUREMENT OF HEIGHTS. 411 



of 336.905 Paris lines, at the temperature of the freezing point, or zero 

 Reaumur, and under the 45th degree of latitude. 



(g) the gravity, at the level of the sea, in the mean latitude between the 

 two places of observation. 



Therefore, calling < the latitude, 



( g )= I 0.0026257 cos <, 



L = the constant barometrical coefficient depending on the relative density of 



the mercury and of the air, 

 K = the coefficient of the expansion of the air, 

 T the mean temperature of the layer of air between the lower and upper 



station, 

 a = the fraction of saturation of the same layer. 



The second term in the parenthesis, destined to take into account the aqueous 

 vapor in the air, was obtained by assuming that the elastic force of vapor for a 

 temperature T is represented, in unit of weight, by the expression, 



^ = 0.0067407 X 10 0.0279712 T - 0.0000625826 T*. 



Multiplying the second member by 336.905 we find the expression of the elastic 

 force of vapor that Laplace deduced from Dalton's experiments. Substituting, in 

 the computation, Regnault's results, the numerical value of these coefficients is some- 

 what changed, and we find then 



;, = 0.0060527 X 10 0.0301975 T- 0.0000801 70 T . 



BessePs tables give the difference of elevation in toises. The logarithm of the dif- 

 ference is obtained by the sum of four logarithms. The same form is preserved in 

 the following tables ; but the differences of elevation are given in metres. 



The term due to the expansion of the air is computed in Bessel's tables for two 

 values of the coefficient, viz. that of Gay-Lussac, 0.00375, and that of Rudberg, 

 0.003648 ; in the new tables it is only computed for that of Regnault, 0.003665. 



The relative density of dry air at the freezing point, under a barometrical pressure 

 of O m '.76, and at the 45th degree of latitude, and of mercury in the same circumstan- 

 ces, adopted by Bessel, is that determined by the experiments of Biot and Arago, viz. 



. The value of that constant derived from Regnault's experiments has been 



substituted. Regnault found the weight of a litre of dry air, at zero Centigrade, 

 under a pressure of O m .76, and at the latitude of Pans, to be 1.293187 grammes, 

 which, reduced to the gravity of the 45th degree of latitude, becomes 1.292732 

 grammes. The weight of a litre of mercury, at zero Centigrade, he found to be 

 13596 grammes ; the ratio is thus : 



D- -1- 



7 10517.3' 



D 71 



