New measurements have been made of the reflectances of single crystals of Ag and of Ag films in the (3.5-30)-eV range. The data were analyzed with the Kramers-Kronig method and the resultant dielectric functions were compared with those in the literature and with recent calculations. We find all structures previously seen, and a new weak peak at 11.5 eV. Our magnitudes for ε2 are in considerably better agreement with those of the calculated spectra than are those in the literature. Second-derivative spectra of the absorption coefficient have been calculated and compared with previously measured thermotransmission spectra, showing the latter to arise primarily by temperature-dependent broadening.