The Voyager and Pioneer 10 spacecraft are moving upstream and downstream into the local interstellar flow, monitoring H Lyman &agr; radiation resonantly scattered from heliospheric hydrogen. Voyager Cruise Maneuver observations obtained between 15 and 35 AU reveal that H Lyman &agr; intensities in the upstream direction fall as r-0.75¿0.05. Beyond 15 AU downstream, Pioneer 10 intensities fall as r-1.07¿0.1. These trends cannot be simultaneously reproduced using a hot H distribution model that does not include termination shock structure. Radiative transfer calculations using the hot H model predict that upstream intensities should fall more rapidly as a function of heliocentric distance than downstream intensities, precisely opposite to the observed trends. The Voyager H Lyman &agr; intensities also show a distinctive trend to decrease less rapidly with increasing heliocentric distance. Between 15 and 20 AU, Voyager intensities fall as r-1, whereas between 30 and 35 AU they fall as r-0.35. This flattening trend implies that the upstream H density is increasing rapidly with heliocentric distance beyond ≈25 AU. A simple analysis suggests that the density distribution changes from nearly uniform between 15 and 20 AU, to r0.65 dependence between 30 and 35 AU. This steepening trend is significant because similar H density gradients are predicted in models which include the effects of the termination shock. Taken together, the Voyager and Pioneer 10 H Lyman &agr; observations beyond 15 AU imply the existence of a solar wind termination shock, suggesting that it lies between 70 and 105 AU in the upstream direction. ¿ American Geophysical Union 1993