440 Lieutenant Rennt on a new Barometric 



But according to our definitions, the modulus of elasticity of dry air at the 

 freezing point is a, and, making allowance for increase of elasticity in conse- 

 quence of increase of temperature, we have a. \l + l(T — 32) j for the expres- 

 sion of the modulus of elasticity of the dry air of the mixture having a tempe- 

 rature T. Therefore, equating these two expressions, we have 



A- — ^^ = a.\l-\-l(T-32)\ or A = a.\l + I (T- 32)\ .■ 



Substituting this value of J. in equation (1) we have 



in which equation p indicates the density or specific gravity of mixture or union 

 of dry air and vapour of water, having a temperature T, and under a pressure tt ; 

 i, the expansion of gas for each degree of Fahrenheit ; and a, the modulus of 

 elasticity of dry air at the freezing point ; and F, the tension or elastic force of 

 the vapour of water of said mixture, having the temperature T. 



3. Let us now suppose a cylindrical column of a mixture or union of dry 

 air and vapour of water to exist between the stations of barometric observa- 

 tions, and let us suppose L to express the area or surface of an extremely thin 

 stratum of said mixture at a distance above the level of the sea - z, then dz 

 is the thickness of such stratum, -1- Ldz is the solid content of such stratum, 

 SMd. — Ldzpg' is the weight of said stratum. Moreover, Lit and L{T:-\-dTt) 

 express the pressures on the upper and lower surfaces of the stratum, the dif- 

 ference of which pressures is obviously equal to the weight of the stratum : we 

 have, therefore, Z (t + d-rr) - Lt: = - Ldzpg\ or d-n = - dzpg'. Substituting 

 in this last equation the value of p given by equation (2), we have 



— q'dz , - r,. 



^- ail.f4^-32)r ^^-^^^- 



But g' = a. TT ; therefore we have, after substitution and modification, 



dTT — gr'^ dz ^ „ \ 



■t-^F ^ ajl-t-;(r-32)| ■ (r + z)' ' ^ ' 



