Recently, two new chemical concepts have been introduced, namely, the atomic compressibility beta' = r(A)/Z(eff) and the corresponding group (molecular) compressibility G beta' = Sigma(i=1)(N)n(i)beta'(i). Here, r is the radius of the atom, Z(eff) is the effective nuclear charge, n is the number of atoms of a given element i, and N is the total number of different elements in the molecule. The physical meaning of these two compressibility parameters is examined briefly in this work. A fundamental difficulty with the derivation of the primary relationship beta' = r(A)/Z(eff) is pointed out. We have investigated the origins of an observed linear variation of G beta' with molecular polarizability alpha'(mol) for a series of predominantly organic molecules. We show that a linear correlation is to be expected for a plot of G beta' vs alpha'(mol) if certain conditions are satisfied for all members of a given set of molecules. In particular, if the average value of r/Z(eff) for the constituent atoms is similar for each molecule in the series, then a linear variation is to be expected for G beta' vs alpha'(mol).