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Resume. In result of the comparison of our analytical theory of lunar physical libration, in particular the free librations, and available now, the empirical theory of the Moon's rotation (Rambaux, Williams, 2011), we have identified period, amplitude, and the initial phase of the forth mode of free libration of the Moon, caused by liquid core. http://202.127.29.4/meetings/iaps2013/Program_IAPS2013.pdf