How to determine atomic number density of an element in a star based on equivalent width measurements Given an equivalent width measurement $W$ of a spectral line of element $X$ and the effective temperature $T_{eff}$ of a star, how can you determine the atomic number density of $X$ in that star?

According to Warner 1965, for the 6707.8 Lithium line we can apply the approximation

$$\log{\frac{N^*(X)}{N^{\odot}(X)}} = \log{\frac{W^*(X)}{W^{\odot}(X)}} - 4.93 (\gamma -1)$$

where $\gamma = \frac{T^{\odot}}{T^*}$ and $\log{W^{\odot}(X)}$ must be measured. The same paper says that $\log{W^{\odot}}(Li)=-6.15$ (my goal is to solve for the abundance of Lithium given a measured W of the 6707.8 $\overset{\circ}A$ line.

Under what regime is this approximation valid? Also, I am unable to solve this equation because I don't know what $N^{\odot}(Li)$ is. How can I determine a reputable value for $N^{\odot}(Li)$?
The measurement of a chemical abundance is not a question of using a simple equation.

The simplest it gets is using a "curve of growth", which relates equivalent width to abundance and assumes you already know the temperature of the star and its surface gravity.

For the Li 6708A line, the relevant tables, that can be interpolated, are found in Soderblom et al. (1993). http://adsabs.harvard.edu/abs/1993AJ....106.1059SS . These are LTE curves of growth based on Atlas atmospheric models.

As an aside, the equivalent width of this line in the Sun is 3 mA. The formula you quote looks like some sort of linear approximation, but this resonance line rapidly enters the saturated (non-linear) portion of the curve of growth for equivalent widths of 50 mA or more. As the equation is couched in terms of ratios, then the units you use are entirely up to you.