The spin contributed Knight shift $^{59}K_{s}$ of $^{59}\mathrm{Co}$ in the triangular lattice superconductor, $\mathrm{Na_{0.35}CoO_{2} \cdot 1.3H_{2}O}$, has been estimated by NMR experiments in an oriented 2-dimensional powder sample. The Knight shift in the paramagnetic state was estimated by $\delta\nu/(\gamma\mathrm{_{N}}H_{i})$ vs. $(\gamma\mathrm{_{N}}H_{i})^{-2}$ plot at various temperatures. A Knight shift vs. magnetic susceptibility diagram revealed that at least 0.3 % for $K_{x}$ and 0.1 % for $K_{y}$ are attributed to the spin contribution. Below $T\mathrm{_{c}}$, $\delta\nu/(\gamma\mathrm{_{N}}H_{i})$ vs. $(\gamma\mathrm{_{N}}H_{i})^{-2}$ plot does not give unique Knight shift because of the diamagnetic effect and/or the other ones. We concluded that the invariant behavior at about 7 T (between $H\mathrm{_{c1}}$ and $H\mathrm{_{c2}}$) below $T\mathrm{_{c}}$ possibly indicates the nature of the spin-triplet superconductivity.