We have analyzed radio Doppler data and star-satellite imaging data from Voyager 2 at Uranus, along with 8 years of ground-based astrometric data, and have obtained improved masses and densities for the satellites of Uranus as well as a new ratio of the mass of the Sun to the mass of the Uranian system of 22902.94¿0.04. The mean density of Uranus is 1.285¿0.001 g cm-3. The satellite densities are 1.25¿0.33 for Miranda, 1.55¿0.22 for Ariel, 1.58¿0.23 for Umbriel, 1.685¿0.068 for Titania, and 1.635¿0.060 for Oberon, all expressed in units of grams per cubic centimeter. The mean uncompressed density of all five satellites is 1.48¿0.06 g cm-3. This is 0.10 g cm-3 higher than the value expected for a homogeneous solar mix consisting of 34% anhydrous rock, 51% water ice, 7% ammonia ice, and 8% methane, present as clathrate hydrate. In order to reconcile this difference, we suggest that the Uranian moons contain roughly 15% by mass of pure graphite, in addition to a normal solar component of rocks and ices. If so, at least 50% of the carbon within the nebular gases from which Uranus and its satellites condensed was in the form of graphite, the remaining being in CH4. The high thermal conductivity of graphite ensures that the Uranian moons have remained cold and undifferentiated since the time of their formation, despite heating caused by the decay of radioactive nuclides. Apparently, an alternative cometary origin for the satellites is ruled out. ¿ American Geophysical Union 1987