  The observed velocity dispersion of the classical dwarf spheroidal (dSph)
galaxies of the Milky Way (MW) requires the Newtonian stellar mass-to-light
($M_*/L$) ratios in the range of about 10 to more than 100 solar units that are
well outside the acceptable limit predicted by stellar population synthesis
models. Using Jeans analysis, we calculate the line-of-sight velocity
dispersion ($\sigma_{\emph{los}}$) of stars in eight MW dSphs in the context of
the modified gravity (MOG) theory of Moffat, assuming a constant $M_*/L$ ratio
without invoking the exotic cold dark matter. First, we use the weak field
approximation of MOG and assume the two parameters $ \alpha $ and $ \mu $ of
the theory to be constant as has already been inferred from fitting to the
observed rotational data of The HI Nearby Galaxy Survey catalogue of galaxies.
We find that the derived $M_*/L$ ratios for almost all dSphs are too large to
be explained by the stellar population values. In order to fit the
line-of-sight velocity dispersions of the dSph with reasonable $M_*/L$ values,
we must vary $\alpha$ and $\mu$ on a case by case basis. A common pair of
values cannot be found for all dSphs. Comparing with the values found from
rotation curve fitting, it appears that $\mu$ correlates strongly with galaxy
luminosity, shedding doubt on it as a universal constant.
