Four transformations are considered in detail: that from the zero-order $\mathrm{nl}{m}_l{m}_s$ scheme to the $\mathrm{LS}$-coupling scheme, that from the zero-order $\mathrm{nlj}{m}_j$ scheme to the $\mathrm{jj}$-coupling scheme, that connecting these two zero-order schemes, and that connecting the $\mathrm{LS}$- and the $\mathrm{jj}$-coupling schemes. A correlation between the states of the configuration with $\epsilon$ electrons in shell $S$ plus $\eta$ other electrons and those of the configuration with $\epsilon$ electrons missing from shell $S$ plus the same $\eta$ other electrons is found such that all of these transformations are the same for the two configurations. The transformation between zero-order states in two different schemes is considered in general and a general expression (3.10) is found giving this transformation for an almost closed shell in terms of the transformation for the corresponding simple configuration. Finally, a direct method is found for obtaining the transformation from $\mathrm{LS}$-coupling to $\mathrm{jj}$-coupling for any two-electron configuration, and this transformation is given explicitly for all such configurations up to $\mathrm{dd}$. This then furnishes the $LS-jj$-coupling transformation also for $p^4$, $p^{5}s$, $p^{5}p$, $p^{5}d$, $d^8$, $d^{9}s$, $d^{9}p$, and $d^{9}d$, the configurations for which the $\mathrm{jj}$-coupling scheme is most useful.

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