buoyancy is, therefore, closely tied to the abundance of sodium and potassium in the BSP due to their incompatibility in melting processes (Figure \[fig:histogram\]). Because Na is roughly 15 times more abundant than K for the Sun [@Lodd03], we focus on Na as a controlling alkali in the buoyancy calculations. Because all alkalis are moderately volatile in the planetary condensation process [@Lodd03], their abundances are not likely to be mirrored in any orbiting terrestrial planets due to their fractionation relative to the refractory elements (e.g. Mg, Si, Fe) in the planetary formation process. For this model, we assume an incomplete accretion of Na due to volatile loss during planet formation in proportions similar to Sun-Earth fractionation for each star in our sample [$\delta_{ \rm{Na-Sun/Earth}} = \left (\rm{Na/Si}\right)_{\rm{Earth}}/\left(\rm{Na/Si}\right)_{Sun}$ = 0.26 by mole; @McD03; @Aspl05]. Chemical buoyancy is then a function of the total Na in the star as well as the degree of Na volitalization during accretion, $\delta_{\rm {Na}}$: $$\label{eq:fit}
F_{c} \approx -1.15+16.6\left(\rm{[Na/Si]}+log10\left(\delta_{\rm{Na}}/\delta_{\rm{Na-Sun/Earth}}\right)\right)  * 10^{12} \rm{N m^{-1}}$$

![Chemical buoyancy force ($F_{c}$) as a function of bulk planetary Mg and Si normalized to Fe (by mole) for values for three values of $\delta_{\rm{Na}}$. Filled circles are those calculations presented here in Figures 