# Estimating the effective grammage of the galaxy

I was reading a text which gives (without derivation/reference) the effective grammage along the line of sight through the disk of the galaxy as about 10^-3 g/cm^2. Is this the proper order of magnitude for the accepted value?

By my calculation, I claim the galaxy has 1 proton/cm^3 ~ 2 x 10^-24 g/cm^3 , and a radius of 15 kpc ~ 5 x 10^22 cm. I get a grammage (=density x galactic radius) of only 10^-1 g/cm^2--100 times greater than the estimate of the text. Of course, I'm assuming the line of sight only passes through ISM.

I suppose my crude estimate just isn't good enough. Technically, grammage will be the path integral of galactic density along the line of sight, but what is the proper model of galactic density? Could someone provide insight on the cause of this inconsistency? I would have though my estimate should be closer than it is.

Thanks!