Iridium and osmium concentrations were measured in dated deep-sea sediments by neutron activation analysis to attempt to set limits on the influx rate of cosmic matter. Twentyone measurements on five cores from the central Pacific gave Ir and Os contents from 0·06 to 0·4 ppb, with an observed precision of ±15 percent. The Ir and Os contents were correlated with each other: Ir = (1·2 ± 0·2) Os. Both tended to increase with decreasing sedimentation rate. The Ir content can be represented by the expression: Ir ( ppb) = (0·07 ± 0·08) + (0·094 ± 0·047)1/ rs where rs is the sedimentation rate in mm per 1000 years from Th 230/Th 232 ratios. If the first term is interpreted as an average terrestrial component and the second term, as an exclusively cosmic component which is diluted in proportion to the sedimentation rate, an upper limit to the influx rate of cosmic matter may be established on the basis of the average Ir content of some representative meteoritic material. With an assumed Ir content of 0·42 ppm, the value in Type I carbonaceous chondrites, the influx rate for the entire earth becomes (6 ± 3) × 10 4 tons/yr. This value represents an average over the last 10 5 to 10 6 years; the mass range effectively sampled by this method is ~10 -14 to ~10 12 g. A firm upper limit on the influx rate can be obtained by assuming that all the Ir and Os in deep-sea sediments is of cosmic origin. The value obtained is between 0.5 × 10 5 and 1.5 × 10 5 tons/yr. It is more than an order of magnitude lower than other estimates based on the Ni content of deep-sea sediments or particles counts by satellites.