1823.] for Barometrical Measurements, S6\ 



= '868589] the last two factors become log. ^ 



((log. ^ + -868589) ix 

 1 + ~ 7 ~ j which gives exactly M. Ramond's 

 log. g y 



formula, excepting that the constant coefficient remains to be 

 determined. 



This, M. Biot now proceeds to investigate, by taking as at 

 first 8 = density of dry air, that of mercury being 1 , under the 

 pressure A, at temp, tj latitude 4', intensity of gravity g. Then 

 we have* 



> ^ A(l- -0028371 .008.2-4.) gh 



I + t. 0-00375 • ^ 



The most simple means of finding A is to weigh with great 

 exactness known volumes of air and mercury under a given, 

 pressure and temperature, in a place whose latitude and eleva- 

 tion are known. This experiment M. Biot informs us has been 

 tried at Paris with the greatest care by Arago and himself. 

 They found that at the temperature of melting ice, and under the 



pressure of 0*76 m. 5" = TTri^rrr- ; whence A = 



4' being the latitude of Paris* 



10463-0 



1 



10463 .§■ (I - -0028371 . cos. 2 4-) 0-76 in.' 



Consequently representing by M the modulus of the logarithmic 

 tables, or 2-30258509, the coefficient of the barometric formula, 



or -; — , will become 

 A gi' 



iL = 10463(1--0028371 .COS. 2^1.) 0-76 m.M .^. 



As'i gi 



If we reduce this value into numbers taking ^|/ = 48° 50' 14"^ 

 which is the latitude of the Observatory, we find - — =: 



18316-82 m. |, and consequently ^^^ ^i ".0009628) = ■ , 



18334*46 m. - . Let r be the elevation of the inferior station 



gi 



"above the level of the sea, a + r will be its distance from the 

 centre of the earth. The elevation of the place where they 

 tried their experiments on the weight of air and mercury may be 

 assumed at 60 metres above the level of the sea : its distance 

 froni the centre of the earth in metres will, therefore, be « + 60. 



Thus the ratio of the weights ^ =r -^^^-i^, an expression which 

 reduces itself to (l - ^) (l + ^), developing the two 



• Mesures Barometriciues, p. 23. 



