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Chartrand et al. (2004) have given an upper bound for the nearly antipodal chromatic number $a{c}^{\text{'}}\left(P_n\right)$ as $\left(\genfrac{}{}{0pt}{}{n-2}{2}\right)+2$ for $n\ge 9$ and have found the exact value of $a{c}^{\text{'}}\left(P_n\right)$ for $n=5,6,7,8$. Here we determine the exact values of $a{c}^{\text{'}}\left(P_n\right)$ for $n\ge 8$. They are $2p^2-6p+8$ for $n=2p$ and $2p^2-4p+6$ for $n=2p+1$. The exact value of the radio antipodal number $ac\left(P_n\right)$ for the path $P_n$ of order $n$ has been determined by Khennoufa and Togni in 2005 as $2p^2-2p+3$ for $n=2p+1$ and $2p^2-4p+5$ for $n=2p$. Although the value of $ac\left(P_n\right)$ determined there is correct, we found a mistake in the proof of the lower bound when $n=2p$ (Theorem $6$). However,...