Abstract: A shaft for a turbine engine, the shaft having a cavity subdivided axially into first and second chambers. The shaft also includes a distributor member having an axial duct, a first radial orifice, and a second radial orifice. The axial duct has an open first end and a second end closed in the axial direction. The first radial orifice connects the second end of the axial duct to the first chamber in order to feed a first bearing with lubricating fluid, and the second radial orifice connects the second end of the axial duct to the second chamber to feed a second bearing with lubricating fluid. The first radial orifice and the second radial orifice of the distributor member are at substantially equal axial distances from the lubricating fluid inlet.