Using the transverse field muon spin relaxation technique we measure the temperature dependence of the magnetic field penetration depth $lambda$, in the Na$_{x}$CoO$_{2}cdot y$H$_{2}$O system. We find that $lambda,$ which is determined by superfluid density $n_{s}$ and the effective mass $m^{ast}$, is very small and on the edge of the TF-$mu$SR sensitivity. Nevertheless, the results indicate that the order parameter in this system has nodes and that it obeys the Uemura relation. By comparing $lambda$ with the normal state electron density we conclude that $m^{ast}$ of the superconductivity carrier is 70 times larger than the mass of bare electrons.
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