A device with the parent $^{229}$Th source was constructed to search for variations of the daughter $^{213}$Po half-life ($T_{1/2} = 4.2$ $mu$s). A solar-daily variation with amplitude $A_{So}=(5.3 pm 1.1) times 10^{-4}$, a lunar-daily variation with amplitude $A_L = (4.8 pm 2.1) times 10^{-4}$, and a sidereal-daily variation with amplitude $A_S = (4.2 pm 1.7) times 10^{-4}$ were found upon proceeding the data series over a 622-day interval (from July 2015 to March 2017). The $^{213}$Po half-life mean value is found to be $T_{1/2} = 3.705 pm 0.001$ $mu$s. The obtained half-life is in good agreement with some of the literature values obtained with great accuracy.
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