It is pointed out that there is a need for values of the oscillator strengths of many transitions in Fe II and Fe III in order to interpret the sun's Fraunhofer spectrum in the vacuum ultraviolet. A description is given of a beam-foil experiment to measure the atomic lifetimes for some of these transitions. Results are presented for three multiplets in Fe II and one in Fe III with estimated accuracies in the range +or-5% to +or-22%. Measurements for a wider range of transitions were not attempted because of difficulties arising from the crowded nature of the spectrum, the poor spectral resolution and general weakness of the signals.