The column water vapor abundance, aka precipitable water vapor, could be expressed as mw*Po*H/rho*k*To, this usually called Butler's equation and mw is the mass of water molecule = 18amu; rho is the density ofliquid water = 1000kg/m3; H is the scale height of water vapor = 1.5km; k is the Boltzmann constant = 1.38x10-23J/K; P is the surface atmospheric pressure (in microbar) and T is the surface ambient temperature (in Kelvin).

It usually stated the Butler's equation could be reduced, approximately, to Po/3To, if all the constants are inserted and this is where my problem lies, I do not seem to understand how all those constants could reduce to 1/3, especially with the value of the Boltzmann constant! Could someone please bail me out of this problem? Thanks in advance.