The Dirac vector model, as considered by Van Vleck, has been applied to calculate the energy values of configurations of the type $d^{\mathrm{k}}\mathrm{m}s$ and $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$, in cases where the $d^{\mathrm{k}}$ core conforms to Russell-Saunder's coupling. The spin-orbit energy is not assumed small compared to the electrostatic energy coupling $d^{\mathrm{k}}$ to $\mathrm{m}s$ or $d^{\mathrm{k}}$ to $\mathrm{n}s$. Johnson's formulas for the four vector problem have been used to set up a general secular determinant for configurations of the type $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$. The special cases where $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$ may be treated as a three vector problem or as a case of Russell-Saunder's coupling are also considered. The following multiplets have been examined: Y I, $4d\left({}_{}{}^2{}_{}{}^{}D\right)5s6s$; Cu I, $3d^9\left({}_{}{}^2{}_{}{}^{}D\right)4s5s$; Zr I, $4d^2\left({}_{}{}^3{}_{}{}^{}F\right)5s6s$; Ni I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)4s5s$; Co I, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)4s5s$; Fe I, $3d^6\left({}_{}{}^5{}_{}{}^{}D\right)4s5s$; and Ti I, $3d^2\left({}_{}{}^3{}_{}{}^{}F\right)4s6s$. The exchange integrals are considered as parameters and chosen to give the best fit with experimental data. The agreement with experiment for $d^{\mathrm{k}}\mathrm{m}s\mathrm{n}s$ is better, as it ought to be, with the four vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_d$, ${\mathrm{s}}_{\mathrm{m}}$, ${\mathrm{s}}_{\mathrm{n}}$) than with the three vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_{d+\mathrm{m}}$, ${\mathrm{s}}_{\mathrm{n}}$) which in turn agrees better with experiment than does the two vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_{d+\mathrm{m}+\mathrm{n}}$), the case resulting from the assumption of Russell-Saunder's coupling. Configurations $d^{\mathrm{k}}\mathrm{m}s$ (other than Houston's singlet-triplet case) have been examined as a three vector problem (${\mathrm{L}}_d$, ${\mathrm{S}}_d$, ${\mathrm{s}}_{\mathrm{m}}$). Some examples treated are: Ti II, $3d^2\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Ni II, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Co I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)5s$; Co I, $3d^8\left({}_{}{}^3{}_{}{}^{}F\right)4s$; Pd II, $4d^8\left({}_{}{}^3{}_{}{}^{}F\right)6s$; Fe I, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)5s$; Co II, $3d^7\left({}_{}{}^4{}_{}{}^{}F\right)5s$.

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