The branching ratios $\frac{{\tau }^{\prime +}}{(K^{+}\to \mathrm{all})}$ and $\frac{{\tau }^{\prime +}}{{\tau }^{+}}$ were obtained from a sample of $12976K^{+}$ decays including 198 ${\tau }^{\prime +}$ and $693{\tau }^{+}$ decays. It was found that $\frac{{\tau }^{\prime +}}{(K^{+}\to \mathrm{all})}=0.0153\mathrm{}\pm 0.0011$, and that $\frac{{\tau }^{\prime +}}{{\tau }^{+}}=0.286\mathrm{}\pm 0.023$. The $\frac{{\tau }^{+}}{(K^{+}\to \mathrm{all})}$ branching ratio and the ${\pi }^{+}$ energy spectrum in ${\tau }^{\prime +}$ decay were also obtained, and were found to be in good agreement with the more precise determinations of the other experiments. The branching-ratio data suggest a small $\Delta I=\frac{3}{2}$ admixture in the $K\to 3\pi$ decay amplitudes. Comparison with various theoretical models shows fair to good agremeent between experiment and theory.

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