The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9.

For determined shortest wavelength, $n_{2}=\infty$

Lyman series $\bar{v}_{L}=\frac{1}{\lambda_{L}}=R\left[\frac{1}{(1)^{2}}-\frac{1}{\infty^{2}}\right]$

Paschen series $\bar{v}_{P}=\frac{1}{\lambda_{P}}=R\left[\frac{1}{(3)^{2}}-\frac{1}{\infty^{2}}\right]$

$\frac{\bar{v}_{L}}{\bar{v}_{P}}=\frac{\lambda_{P}}{\lambda_{L}}=9$