In order to improve the reverberation-mapping based estimate of the mass of the central supermassive black hole in the Seyfert 1 galaxy NGC 4151, we have reanalyzed archival ultraviolet monitoring spectra from two campaigns undertaken with the International Ultraviolet Explorer. We measure emission-line time delays for four lines, C IV 1549, He II 1640, C III] 1909, and Mg II 2798, from both campaigns. We combine these measurements with the dispersion of the variable part of each respective emission line to obtain the mass of the central object. Despite the problematic nature of some of the data, we are able to measure a mass of 41.1 (+/- 7.3) million solar masses, although this, like all reverberation-based masses, is probably systematically uncertain by a factor of 3-4.Comment: 25 pages, 5 figures. Accepted for publication in The Astrophysical Journa

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