the Barometric Formulce, ^c. 669 



or, 



^~ ^~Z5 iT7~zrv 1 1 / z) 



^^ |o-76 ~ ra 2 io-76j "" n» 3 i^O-TeJ " '^°- 



But Z) is a fixed quantity, very small, and w is a number indefinitely great; we may, there- 

 fore, omit in the denominator of the right-hand side of the last equation, every term after 

 the first. Doing so, we have — 



^ 0-76 



My. D 



metiea.—Q.E.D. 



Now M= 0'43429, and from calculations made by experiments by Regnault at Paris, 



we have at freezing-point, for the value of D at the level of the sea of latitude 45°, the 



1 0'7fi 

 expression D = „ ; these values being substituted in the equation C = -jr j^ 



metres, we have C = 18404-9 metres, consequently C (the constant for an atmosphere of 

 dry air, at the freezing-point, at the level of the sea of latitude 45°) = 184049 metres. 



Let us now calculate a constant C for an atmosphere consisting of an union or mixture 

 of dry air and vapour of water, having an elastic force (or tension) represented by F 

 metres, peculiar to the freezing-point, such as maybe found in an approved table of elastic 

 forces of vapour of water, or obtained in any other manner correctly, such union or mix- 

 ture being under a pressure of 0'76 metres of quicksilver. 



Let D' be the ratio of the specific gravity of such an union or mixture of dry air and 

 vapour of water (£> being the corresponding ratio of dry air alone) to that of quicksilver, 

 under a pressure of 0'76 metres of quicksilver at freezing-point. 



Now it is well known that D' = D jl - rr™::!. for proof of which, vide former paper by 



Mr. Renny, Article 2, p. 439, supra. 



But |i^= 000190 metres, and D = ,„,,_ „ , therefore we have — 



10ol7o 



r,, 1 (, 0-001901 1 



^ " 105rr3 r " 0^76000) " i054F7 '"'''"'''• 



T, ^, 0-76 0-76 ,„,^, ^ 



But C = -Tr — n, metres = ■ metres = lo451-5 metres. 



^•^2*^^''l054r7 



Reproducing our constants, we have — 



Being the constant of a barometric formula for a suppositious 

 C = 18404*9 metres | atmosphere of dry air, at the level of the sea, freezing-point, of 

 latitude 45°. 



