The mechanism proposed by Oppenheimer and Phillips for the disintegration of nuclei by deuterons with proton emission ($d\ensuremath{-}p$ reaction) is examined. A formula is derived which expresses the probability of this process in terms of the sticking probability of the neutron (\textsection{}2) and the penetrability of the potential barrier. The importance of the finite (rather than zero) nuclear radius for the penetrability is pointed out and the penetrability is calculated for various values of the radius (\textsection{}3). The energy distribution of the emitted protons is found to be given directly by the sticking probability of the neutron (\textsection{}5). Therefore it may differ considerably from the distribution in "ordinary" nuclear reactions by containing relatively more high energy protons. A measurement of the energy distribution would allow direct conclusions about the width of low nuclear levels which is of importance for the theory of the $\ensuremath{\alpha}$-decay and therefore of the nuclear radius (\textsection{}5). The probability of the O-P reaction is compared with that of ordinary nuclear reactions. The O-P mechanism is found to prevail in the $d\ensuremath{-}p$ reactions for nuclear charges of about 25 and higher; if the reaction leads to a nucleus which emits fast $\ensuremath{\beta}$-rays, the O-P mechanism will be valid at still lower charges. The relative probability of $d\ensuremath{-}p$ as compared to $d\ensuremath{-}n$ reactions is found to be (on the average) unity for very light nuclei, to decrease with increasing atomic number until the O-P process becomes prevalent, and to increase from there on. The excitation function of reactions with nuclei up to $Z\ensuremath{\sim}30$ is found to be an inadequate test for the O-P mechanism (\textsection{}6). The question of secondary (cascade) disintegration following the $d\ensuremath{-}p$ reaction is discussed and it is found that such disintegrations (e.g. $d\ensuremath{-}pn$ or $d\ensuremath{-}p\ensuremath{\alpha}$) should be rare with deuteron energies below the top of the potential barrier (\textsection{}7).