classical mechanics - Derivation of Bohr model equations (1) in his original paper

My question is rather straightforward. In his original paper ("On the Constitution of Atoms and Molecules") Bohr provides equations (1) for the frequency and major axis orbit:

$$\begin{align} \omega &= \frac{\sqrt{2}}{\pi} \frac{W^{3/2}}{eE\sqrt{m}}\\ 2a &= \frac{eE}{W} \end{align}$$ where $W$ is the energy of the electron, $e$ its charge and $E$ the charge of the nucleus.

How exactly did he derive these equations? I have some troubles doing that. Many thanks.

Radek