We report here the results of operation of a torsion balance with a period of $sim 1.27 times 10^4$ s. The analysis of data collected over a period of $sim$115 days shows that the difference in the accelerations towards the Galactic Center of test bodies made of aluminum and quartz was $(0.61 pm 1.27) times 10^{-15} , mathrm{ m , s}^{-2}$. This sets a bound on the violation of the equivalence principle by forces exerted by Galactic dark matter which is expressed by the Eotvos parameter $eta_{DM} = (1.32 pm 2.68) times 10^{-5}$, a significant improvement upon earlier bounds.
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