The consideration of the phases of the fractional-parentage coefficients allows the extension of the matrix methods to configurations with more than two equivalent electrons. Tables are given for the parentages of the terms of $p^n$ and $d^n$. Applications are made to the spin-orbit interaction of the $d^n$ terms and to the electrostatic interaction between the configurations $d^n$, $d^{n-1\mathrm{}}s$, and $d^{n-2\mathrm{}}{s}^2$. Errata in Part II are indicated.

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