By studying the alpha-particles emitted in the disintegration of ${\mathrm{B}}^{10}$ by protons it has been shown that there exists an excited state in ${\mathrm{Be}}^7$ at 434.4±4 kev which corresponds to the well-known first excited state in the mirror nucleus, ${\mathrm{Li}}^7$. Measurements on the inelastic scattering of protons in ${\mathrm{Li}}^7$ yield a value 479.0±1.0 kev for the energy of the ${\mathrm{Li}}^{7*}$. The existence of these mirror states adds support to the equality of the $p-p$ and $n-n$ interactions exclusive of electrostatic and magnetic forces. The small difference, 45±4 kev, in the excitation energies is larger than second-order electric effects and is believed to be consistent with the order of magnitude of magnetic interactions in nuclei. The splitting of the ground and excited states must arise in some specific property of the nuclear interactions. In connection with the energy determinations, a detailed discussion is given of the precise measurements of the $Q$-values of nuclear reactions employing high resolution analyzers, electrostatic and magnetic, in the determination of particle energies. Experimental determinations of the cross sections for ${\mathrm{B}}^{10}(p,\alpha ){\mathrm{Be}}^7$, ${\mathrm{B}}^{10}(p,{\alpha }^{\prime }){\mathrm{Be}}^{7*}\left(\gamma \right){\mathrm{Be}}^7$, ${\mathrm{B}}^{10}\mathrm{}(p,p)\mathrm{}{\mathrm{B}}^{10}$, ${\mathrm{Li}}^7\mathrm{}(p,p)\mathrm{}{\mathrm{Li}}^7$, and ${\mathrm{Li}}^7(p,p^{\prime }){\mathrm{Li}}^{7*}\left(\gamma \right){\mathrm{Li}}^7$ are given.

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