Ten fine-structure intervals separating n =10, I =4, 5, 6, and 7 Rydberg states of H2, all with (v=0, R =1) H2+ cores, have been measured using fast-beam microwave-optical techniques, determining the relative positions of all these states to a precision of about +0.3 MHz. These experimental results are compared with predictions of the expected structure, which use the polarization model to relate the Rydberg fine structure to properties of the H2 ion, yielding experimental determinations of certain electric properties of the (0, 1) state of H2+. quadrupole moment, Q = 1.64295(30)eao, and dipole polarizabilities, 0. & = 3. 1770(34)ao, nT =4.015(36)ao.