If magnetic monopoles exist, they are evidently too massive to have been produced in man-made radiation, too rare to have been observed directly in cosmic radiation, and too energetic to have accumulated in ferromagnetic surface minerals. Primordial monopoles which escaped immediate recombination would be destined to undergo progressive acceleration by the solenoidal magnetic fields they would encounter in the universe. They would by now have acquired energies of the order of ${10}^{20}$ eV and should therefore arrive isotropically, unaffected by the earth's atmosphere or magnetic field. Secondary monopoles produced in the upper atmosphere are also likely to have more residual energy than they can lose to the atmosphere. Ocean water of more than the penetration depth would thermalize monopoles without immobilizing them, and thus allow monopoles to accumulate in the magnetic component of deep-sea sediment. The slow deposition rate of sediment thus makes it the most promising terrestrial source of monopoles. We have constructed apparatus capable of extracting magnetic monopoles from massive quantities of sediment, accelerating them to 50 GeV and detecting them by an array of scintillation counters. Assuming that monopoles are bound only to ferromagnetic and paramagnetic materials, we have established an upper-limit arrival rate of 1 per ${\mathrm{cm}}^2$ in 8×${10}^{16}$ sec for an energy ≤4×${10}^{15}$ eV, and 1 per ${\mathrm{cm}}^2$ in 6×${10}^{17}$ sec for an energy ≤2×${10}^{14}$ eV, for monopoles of either polarity, of charge larger than $\frac{1}{6}$ of the Dirac value, and of mass up to 14 000 proton masses, with a confidence level of 95%. For comparison, the arrival rate of particles generating extensive air showers accounting for more than ${10}^{18}$ eV is 1 per ${\mathrm{cm}}^2$ in 1.5×${10}^{16}$ sec.

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